idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
|---|---|---|---|---|---|---|
3,901 | What is the intuition behind conditional Gaussian distributions? | Synopsis
Every statement in the question can be understood as a property of ellipses. The only property particular to the bivariate Normal distribution that is needed is the fact that in a standard bivariate Normal distribution of $X,Y$--for which $X$ and $Y$ are uncorrelated--the conditional variance of $Y$ does not ... | What is the intuition behind conditional Gaussian distributions? | Synopsis
Every statement in the question can be understood as a property of ellipses. The only property particular to the bivariate Normal distribution that is needed is the fact that in a standard b | What is the intuition behind conditional Gaussian distributions?
Synopsis
Every statement in the question can be understood as a property of ellipses. The only property particular to the bivariate Normal distribution that is needed is the fact that in a standard bivariate Normal distribution of $X,Y$--for which $X$ an... | What is the intuition behind conditional Gaussian distributions?
Synopsis
Every statement in the question can be understood as a property of ellipses. The only property particular to the bivariate Normal distribution that is needed is the fact that in a standard b |
3,902 | What is the intuition behind conditional Gaussian distributions? | This is essentially linear (OLS) regression. In that case, you are finding the conditional distribution of $Y$ given that $X=x_i$. (Strictly speaking, OLS regression does not make assumptions about the distribution of $X$, whereas your example is a multivariate normal, but we will ignore these things.) Now, if the c... | What is the intuition behind conditional Gaussian distributions? | This is essentially linear (OLS) regression. In that case, you are finding the conditional distribution of $Y$ given that $X=x_i$. (Strictly speaking, OLS regression does not make assumptions about | What is the intuition behind conditional Gaussian distributions?
This is essentially linear (OLS) regression. In that case, you are finding the conditional distribution of $Y$ given that $X=x_i$. (Strictly speaking, OLS regression does not make assumptions about the distribution of $X$, whereas your example is a mult... | What is the intuition behind conditional Gaussian distributions?
This is essentially linear (OLS) regression. In that case, you are finding the conditional distribution of $Y$ given that $X=x_i$. (Strictly speaking, OLS regression does not make assumptions about |
3,903 | What is the intuition behind conditional Gaussian distributions? | Gung's answer is good (+1). There is another way of looking at it, though. Imagine that the covariance between $X_1$ and $X_2$ were to be positive. What does it mean for $\sigma_{1,2}>0$? Well, it means that when $X_2$ is above $X_2$'s mean, $X_1$ tends to be above $X_1$'s mean, and vice versa.
Now suppose I told y... | What is the intuition behind conditional Gaussian distributions? | Gung's answer is good (+1). There is another way of looking at it, though. Imagine that the covariance between $X_1$ and $X_2$ were to be positive. What does it mean for $\sigma_{1,2}>0$? Well, it | What is the intuition behind conditional Gaussian distributions?
Gung's answer is good (+1). There is another way of looking at it, though. Imagine that the covariance between $X_1$ and $X_2$ were to be positive. What does it mean for $\sigma_{1,2}>0$? Well, it means that when $X_2$ is above $X_2$'s mean, $X_1$ ten... | What is the intuition behind conditional Gaussian distributions?
Gung's answer is good (+1). There is another way of looking at it, though. Imagine that the covariance between $X_1$ and $X_2$ were to be positive. What does it mean for $\sigma_{1,2}>0$? Well, it |
3,904 | Machine learning cookbook / reference card / cheatsheet? | Some of the best and freely available resources are:
Hastie, Friedman et al. The Elements of Statistical Learning: Data Mining, Inference, and Prediction
David Barber. Bayesian Reasoning and Machine Learning
David MacKay. Information Theory, Inference and Learning Algorithms (http://www.inference.phy.cam.ac.uk/mackay/... | Machine learning cookbook / reference card / cheatsheet? | Some of the best and freely available resources are:
Hastie, Friedman et al. The Elements of Statistical Learning: Data Mining, Inference, and Prediction
David Barber. Bayesian Reasoning and Machine | Machine learning cookbook / reference card / cheatsheet?
Some of the best and freely available resources are:
Hastie, Friedman et al. The Elements of Statistical Learning: Data Mining, Inference, and Prediction
David Barber. Bayesian Reasoning and Machine Learning
David MacKay. Information Theory, Inference and Learni... | Machine learning cookbook / reference card / cheatsheet?
Some of the best and freely available resources are:
Hastie, Friedman et al. The Elements of Statistical Learning: Data Mining, Inference, and Prediction
David Barber. Bayesian Reasoning and Machine |
3,905 | Machine learning cookbook / reference card / cheatsheet? | If you want to learn Machine Learning I strongly advise you enroll in the free online ML course in the winter taught by Prof. Andrew Ng.
I did the previous one in the autumn and all learning material is of exceptional quality and geared toward practical applications, and a lot easier to grok that struggling alone with ... | Machine learning cookbook / reference card / cheatsheet? | If you want to learn Machine Learning I strongly advise you enroll in the free online ML course in the winter taught by Prof. Andrew Ng.
I did the previous one in the autumn and all learning material | Machine learning cookbook / reference card / cheatsheet?
If you want to learn Machine Learning I strongly advise you enroll in the free online ML course in the winter taught by Prof. Andrew Ng.
I did the previous one in the autumn and all learning material is of exceptional quality and geared toward practical applicati... | Machine learning cookbook / reference card / cheatsheet?
If you want to learn Machine Learning I strongly advise you enroll in the free online ML course in the winter taught by Prof. Andrew Ng.
I did the previous one in the autumn and all learning material |
3,906 | Machine learning cookbook / reference card / cheatsheet? | Yes, you are fine; Christopher Bishop's "Pattern Recognition and Machine Learning" is an excellent book for general reference, you can't really go wrong with it.
A fairly recent book but also very well-written and equally broad is David Barber's "Bayesian Reasoning and Machine Learning"; a book I would feel is slightly... | Machine learning cookbook / reference card / cheatsheet? | Yes, you are fine; Christopher Bishop's "Pattern Recognition and Machine Learning" is an excellent book for general reference, you can't really go wrong with it.
A fairly recent book but also very wel | Machine learning cookbook / reference card / cheatsheet?
Yes, you are fine; Christopher Bishop's "Pattern Recognition and Machine Learning" is an excellent book for general reference, you can't really go wrong with it.
A fairly recent book but also very well-written and equally broad is David Barber's "Bayesian Reasoni... | Machine learning cookbook / reference card / cheatsheet?
Yes, you are fine; Christopher Bishop's "Pattern Recognition and Machine Learning" is an excellent book for general reference, you can't really go wrong with it.
A fairly recent book but also very wel |
3,907 | Machine learning cookbook / reference card / cheatsheet? | Since the consensus seems to be that this question is not a duplicate, I'd like to share my favorite for machine learner beginners:
I found Programming Collective Intelligence the easiest book for beginners, since the author Toby Segaran is is focused on allowing the median software developer to get his/her hands dirty... | Machine learning cookbook / reference card / cheatsheet? | Since the consensus seems to be that this question is not a duplicate, I'd like to share my favorite for machine learner beginners:
I found Programming Collective Intelligence the easiest book for beg | Machine learning cookbook / reference card / cheatsheet?
Since the consensus seems to be that this question is not a duplicate, I'd like to share my favorite for machine learner beginners:
I found Programming Collective Intelligence the easiest book for beginners, since the author Toby Segaran is is focused on allowing... | Machine learning cookbook / reference card / cheatsheet?
Since the consensus seems to be that this question is not a duplicate, I'd like to share my favorite for machine learner beginners:
I found Programming Collective Intelligence the easiest book for beg |
3,908 | Machine learning cookbook / reference card / cheatsheet? | Witten and Frank, "Data Mining", Elsevier 2005 is a good book for self-learning as there is a Java library of code (Weka) to go with the book and is very practically oriented. I suspect there is a more recent edition than the one I have. | Machine learning cookbook / reference card / cheatsheet? | Witten and Frank, "Data Mining", Elsevier 2005 is a good book for self-learning as there is a Java library of code (Weka) to go with the book and is very practically oriented. I suspect there is a mo | Machine learning cookbook / reference card / cheatsheet?
Witten and Frank, "Data Mining", Elsevier 2005 is a good book for self-learning as there is a Java library of code (Weka) to go with the book and is very practically oriented. I suspect there is a more recent edition than the one I have. | Machine learning cookbook / reference card / cheatsheet?
Witten and Frank, "Data Mining", Elsevier 2005 is a good book for self-learning as there is a Java library of code (Weka) to go with the book and is very practically oriented. I suspect there is a mo |
3,909 | Machine learning cookbook / reference card / cheatsheet? | I have Machine Learning: An Algorithmic Perspective by Stephen Marsland and find it very useful for self-learning. Python code is given throughout the book.
I agree with what is said in this favourable review:
http://blog.rtwilson.com/review-machine-learning-an-algorithmic-perspective-by-stephen-marsland/ | Machine learning cookbook / reference card / cheatsheet? | I have Machine Learning: An Algorithmic Perspective by Stephen Marsland and find it very useful for self-learning. Python code is given throughout the book.
I agree with what is said in this favourab | Machine learning cookbook / reference card / cheatsheet?
I have Machine Learning: An Algorithmic Perspective by Stephen Marsland and find it very useful for self-learning. Python code is given throughout the book.
I agree with what is said in this favourable review:
http://blog.rtwilson.com/review-machine-learning-an-... | Machine learning cookbook / reference card / cheatsheet?
I have Machine Learning: An Algorithmic Perspective by Stephen Marsland and find it very useful for self-learning. Python code is given throughout the book.
I agree with what is said in this favourab |
3,910 | Machine learning cookbook / reference card / cheatsheet? | http://scikit-learn.org/stable/tutorial/machine_learning_map/
Often the hardest part of solving a machine learning problem can be finding the right estimator for the job.
Different estimators are better suited for different types of data and different problems.
The flowchart below is designed to give users a bit ... | Machine learning cookbook / reference card / cheatsheet? | http://scikit-learn.org/stable/tutorial/machine_learning_map/
Often the hardest part of solving a machine learning problem can be finding the right estimator for the job.
Different estimators are | Machine learning cookbook / reference card / cheatsheet?
http://scikit-learn.org/stable/tutorial/machine_learning_map/
Often the hardest part of solving a machine learning problem can be finding the right estimator for the job.
Different estimators are better suited for different types of data and different problem... | Machine learning cookbook / reference card / cheatsheet?
http://scikit-learn.org/stable/tutorial/machine_learning_map/
Often the hardest part of solving a machine learning problem can be finding the right estimator for the job.
Different estimators are |
3,911 | Machine learning cookbook / reference card / cheatsheet? | "Elements of Statistical Learning" would be a great book for your purposes. The and 5th printing (2011) of the 2nd edition (2009) of the book is freely available at http://www.stanford.edu/~hastie/local.ftp/Springer/ESLII_print5.pdf | Machine learning cookbook / reference card / cheatsheet? | "Elements of Statistical Learning" would be a great book for your purposes. The and 5th printing (2011) of the 2nd edition (2009) of the book is freely available at http://www.stanford.edu/~hastie/lo | Machine learning cookbook / reference card / cheatsheet?
"Elements of Statistical Learning" would be a great book for your purposes. The and 5th printing (2011) of the 2nd edition (2009) of the book is freely available at http://www.stanford.edu/~hastie/local.ftp/Springer/ESLII_print5.pdf | Machine learning cookbook / reference card / cheatsheet?
"Elements of Statistical Learning" would be a great book for your purposes. The and 5th printing (2011) of the 2nd edition (2009) of the book is freely available at http://www.stanford.edu/~hastie/lo |
3,912 | Machine learning cookbook / reference card / cheatsheet? | The awesome-machine-learning repository seems to be a master list of resources, including code, tutorials and books. | Machine learning cookbook / reference card / cheatsheet? | The awesome-machine-learning repository seems to be a master list of resources, including code, tutorials and books. | Machine learning cookbook / reference card / cheatsheet?
The awesome-machine-learning repository seems to be a master list of resources, including code, tutorials and books. | Machine learning cookbook / reference card / cheatsheet?
The awesome-machine-learning repository seems to be a master list of resources, including code, tutorials and books. |
3,913 | Machine learning cookbook / reference card / cheatsheet? | Most books mentioned in other answers are very good and you can't really go wrong with any of them. Additionally, I find the following cheat sheet for Python's scikit-learn quite useful. | Machine learning cookbook / reference card / cheatsheet? | Most books mentioned in other answers are very good and you can't really go wrong with any of them. Additionally, I find the following cheat sheet for Python's scikit-learn quite useful. | Machine learning cookbook / reference card / cheatsheet?
Most books mentioned in other answers are very good and you can't really go wrong with any of them. Additionally, I find the following cheat sheet for Python's scikit-learn quite useful. | Machine learning cookbook / reference card / cheatsheet?
Most books mentioned in other answers are very good and you can't really go wrong with any of them. Additionally, I find the following cheat sheet for Python's scikit-learn quite useful. |
3,914 | Machine learning cookbook / reference card / cheatsheet? | Microsoft Azure also provides a similar cheat-sheet to the scikit-learn one posted by Anton Tarasenko.
(source: https://docs.microsoft.com/en-us/azure/machine-learning/machine-learning-algorithm-cheat-sheet)
They accompany it with a notice:
The suggestions offered in this algorithm cheat sheet are approximate
rules... | Machine learning cookbook / reference card / cheatsheet? | Microsoft Azure also provides a similar cheat-sheet to the scikit-learn one posted by Anton Tarasenko.
(source: https://docs.microsoft.com/en-us/azure/machine-learning/machine-learning-algorithm-chea | Machine learning cookbook / reference card / cheatsheet?
Microsoft Azure also provides a similar cheat-sheet to the scikit-learn one posted by Anton Tarasenko.
(source: https://docs.microsoft.com/en-us/azure/machine-learning/machine-learning-algorithm-cheat-sheet)
They accompany it with a notice:
The suggestions offe... | Machine learning cookbook / reference card / cheatsheet?
Microsoft Azure also provides a similar cheat-sheet to the scikit-learn one posted by Anton Tarasenko.
(source: https://docs.microsoft.com/en-us/azure/machine-learning/machine-learning-algorithm-chea |
3,915 | Machine learning cookbook / reference card / cheatsheet? | I like Duda, Hart and Stork "Pattern Classification". This is a recent revision of a classic text that explains everything very well. Not sure that it is updated to have much coverage of neural networks and SVMs. The book by Hastie, Tibshirani and Friedman is about the best there is but may be a bit more technical t... | Machine learning cookbook / reference card / cheatsheet? | I like Duda, Hart and Stork "Pattern Classification". This is a recent revision of a classic text that explains everything very well. Not sure that it is updated to have much coverage of neural netw | Machine learning cookbook / reference card / cheatsheet?
I like Duda, Hart and Stork "Pattern Classification". This is a recent revision of a classic text that explains everything very well. Not sure that it is updated to have much coverage of neural networks and SVMs. The book by Hastie, Tibshirani and Friedman is ... | Machine learning cookbook / reference card / cheatsheet?
I like Duda, Hart and Stork "Pattern Classification". This is a recent revision of a classic text that explains everything very well. Not sure that it is updated to have much coverage of neural netw |
3,916 | Machine learning cookbook / reference card / cheatsheet? | Don't start with Elements of Statistical Learning. It is great, but it is a reference book, which doesn't sound like what you are looking for. I would start with Programming Collective Intelligence as it's an easy read. | Machine learning cookbook / reference card / cheatsheet? | Don't start with Elements of Statistical Learning. It is great, but it is a reference book, which doesn't sound like what you are looking for. I would start with Programming Collective Intelligence as | Machine learning cookbook / reference card / cheatsheet?
Don't start with Elements of Statistical Learning. It is great, but it is a reference book, which doesn't sound like what you are looking for. I would start with Programming Collective Intelligence as it's an easy read. | Machine learning cookbook / reference card / cheatsheet?
Don't start with Elements of Statistical Learning. It is great, but it is a reference book, which doesn't sound like what you are looking for. I would start with Programming Collective Intelligence as |
3,917 | Machine learning cookbook / reference card / cheatsheet? | For a first book on machine learning, which does a good job of explaining the principles, I would strongly recommend
Rogers and Girolami, A First Course in Machine Learning,
(Chapman & Hall/CRC Machine Learning & Pattern Recognition), 2011.
Chris Bishop's book, or David Barber's both make good choices for a book wi... | Machine learning cookbook / reference card / cheatsheet? | For a first book on machine learning, which does a good job of explaining the principles, I would strongly recommend
Rogers and Girolami, A First Course in Machine Learning,
(Chapman & Hall/CRC Mac | Machine learning cookbook / reference card / cheatsheet?
For a first book on machine learning, which does a good job of explaining the principles, I would strongly recommend
Rogers and Girolami, A First Course in Machine Learning,
(Chapman & Hall/CRC Machine Learning & Pattern Recognition), 2011.
Chris Bishop's boo... | Machine learning cookbook / reference card / cheatsheet?
For a first book on machine learning, which does a good job of explaining the principles, I would strongly recommend
Rogers and Girolami, A First Course in Machine Learning,
(Chapman & Hall/CRC Mac |
3,918 | Machine learning cookbook / reference card / cheatsheet? | I wrote a summary like that, but only on one machine learning task (Netflix Prize), and it has 195 pages:
http://arek-paterek.com/book | Machine learning cookbook / reference card / cheatsheet? | I wrote a summary like that, but only on one machine learning task (Netflix Prize), and it has 195 pages:
http://arek-paterek.com/book | Machine learning cookbook / reference card / cheatsheet?
I wrote a summary like that, but only on one machine learning task (Netflix Prize), and it has 195 pages:
http://arek-paterek.com/book | Machine learning cookbook / reference card / cheatsheet?
I wrote a summary like that, but only on one machine learning task (Netflix Prize), and it has 195 pages:
http://arek-paterek.com/book |
3,919 | Machine learning cookbook / reference card / cheatsheet? | Check this link featuring some free ebooks on machine learning : http://designimag.com/best-free-machine-learning-ebooks/. it might be useful for you. | Machine learning cookbook / reference card / cheatsheet? | Check this link featuring some free ebooks on machine learning : http://designimag.com/best-free-machine-learning-ebooks/. it might be useful for you. | Machine learning cookbook / reference card / cheatsheet?
Check this link featuring some free ebooks on machine learning : http://designimag.com/best-free-machine-learning-ebooks/. it might be useful for you. | Machine learning cookbook / reference card / cheatsheet?
Check this link featuring some free ebooks on machine learning : http://designimag.com/best-free-machine-learning-ebooks/. it might be useful for you. |
3,920 | Machine learning cookbook / reference card / cheatsheet? | A good cheatsheet is the one in Max Kuhn book Applied Predictive Modeling. In the book there is a good summary table of several ML learning models. The table is in appendix A page 549: | Machine learning cookbook / reference card / cheatsheet? | A good cheatsheet is the one in Max Kuhn book Applied Predictive Modeling. In the book there is a good summary table of several ML learning models. The table is in appendix A page 549: | Machine learning cookbook / reference card / cheatsheet?
A good cheatsheet is the one in Max Kuhn book Applied Predictive Modeling. In the book there is a good summary table of several ML learning models. The table is in appendix A page 549: | Machine learning cookbook / reference card / cheatsheet?
A good cheatsheet is the one in Max Kuhn book Applied Predictive Modeling. In the book there is a good summary table of several ML learning models. The table is in appendix A page 549: |
3,921 | Is it a good practice to always scale/normalize data for machine learning? [duplicate] | First things first, I don't think there are many questions of the form "Is it a good practice to always X in machine learning" where the answer is going to be definitive. Always? Always always? Across parametric, non-parametric, Bayesian, Monte Carlo, social science, purely mathematic, and million feature models? That'... | Is it a good practice to always scale/normalize data for machine learning? [duplicate] | First things first, I don't think there are many questions of the form "Is it a good practice to always X in machine learning" where the answer is going to be definitive. Always? Always always? Across | Is it a good practice to always scale/normalize data for machine learning? [duplicate]
First things first, I don't think there are many questions of the form "Is it a good practice to always X in machine learning" where the answer is going to be definitive. Always? Always always? Across parametric, non-parametric, Baye... | Is it a good practice to always scale/normalize data for machine learning? [duplicate]
First things first, I don't think there are many questions of the form "Is it a good practice to always X in machine learning" where the answer is going to be definitive. Always? Always always? Across |
3,922 | Is it a good practice to always scale/normalize data for machine learning? [duplicate] | Well, I believe a more geometric point of view will help better decide whether normalization helps or not. Imagine your problem of interest has only two features and they range differently. Then geometrically, the data points are spread around and form an ellipsoid. However, if the features are normalized they will be ... | Is it a good practice to always scale/normalize data for machine learning? [duplicate] | Well, I believe a more geometric point of view will help better decide whether normalization helps or not. Imagine your problem of interest has only two features and they range differently. Then geome | Is it a good practice to always scale/normalize data for machine learning? [duplicate]
Well, I believe a more geometric point of view will help better decide whether normalization helps or not. Imagine your problem of interest has only two features and they range differently. Then geometrically, the data points are spr... | Is it a good practice to always scale/normalize data for machine learning? [duplicate]
Well, I believe a more geometric point of view will help better decide whether normalization helps or not. Imagine your problem of interest has only two features and they range differently. Then geome |
3,923 | Is it a good practice to always scale/normalize data for machine learning? [duplicate] | Let me tell you the story of how I learned the importance of normalization.
I was trying to classify a handwritten digits data (it is a simple task of classifying features extracted from images of hand-written digits) with Neural Networks as an assignment for a Machine Learning course.
Just like anyone else, I started ... | Is it a good practice to always scale/normalize data for machine learning? [duplicate] | Let me tell you the story of how I learned the importance of normalization.
I was trying to classify a handwritten digits data (it is a simple task of classifying features extracted from images of han | Is it a good practice to always scale/normalize data for machine learning? [duplicate]
Let me tell you the story of how I learned the importance of normalization.
I was trying to classify a handwritten digits data (it is a simple task of classifying features extracted from images of hand-written digits) with Neural Net... | Is it a good practice to always scale/normalize data for machine learning? [duplicate]
Let me tell you the story of how I learned the importance of normalization.
I was trying to classify a handwritten digits data (it is a simple task of classifying features extracted from images of han |
3,924 | Is it a good practice to always scale/normalize data for machine learning? [duplicate] | As others said, normalization is not always applicable; e.g. from a practical point of view.
In order to be able to scale or normalize features to a common range like [0,1], you need to know the min/max (or mean/stdev depending on which scaling method you apply) of each feature. IOW: you need to have all the data for a... | Is it a good practice to always scale/normalize data for machine learning? [duplicate] | As others said, normalization is not always applicable; e.g. from a practical point of view.
In order to be able to scale or normalize features to a common range like [0,1], you need to know the min/m | Is it a good practice to always scale/normalize data for machine learning? [duplicate]
As others said, normalization is not always applicable; e.g. from a practical point of view.
In order to be able to scale or normalize features to a common range like [0,1], you need to know the min/max (or mean/stdev depending on wh... | Is it a good practice to always scale/normalize data for machine learning? [duplicate]
As others said, normalization is not always applicable; e.g. from a practical point of view.
In order to be able to scale or normalize features to a common range like [0,1], you need to know the min/m |
3,925 | Is it a good practice to always scale/normalize data for machine learning? [duplicate] | Scaling/normalizing does change your model slightly. Most of the time this corresponds to applying an affine function. So you have $Z=A_X+B_XXC_X$ where $X$ is your "input/original data" (one row for each training example, one column for each feature). Then $A_X,B_X,C_X$ are matrices that are typically functions of $X$... | Is it a good practice to always scale/normalize data for machine learning? [duplicate] | Scaling/normalizing does change your model slightly. Most of the time this corresponds to applying an affine function. So you have $Z=A_X+B_XXC_X$ where $X$ is your "input/original data" (one row for | Is it a good practice to always scale/normalize data for machine learning? [duplicate]
Scaling/normalizing does change your model slightly. Most of the time this corresponds to applying an affine function. So you have $Z=A_X+B_XXC_X$ where $X$ is your "input/original data" (one row for each training example, one column... | Is it a good practice to always scale/normalize data for machine learning? [duplicate]
Scaling/normalizing does change your model slightly. Most of the time this corresponds to applying an affine function. So you have $Z=A_X+B_XXC_X$ where $X$ is your "input/original data" (one row for |
3,926 | Is it a good practice to always scale/normalize data for machine learning? [duplicate] | For machine learning models that include coefficients (e.g. regression, logistic regression, etc) the main reason to normalize is numerical stability. Mathematically, if one of your predictor columns is multiplied by 10^6, then the corresponding regression coefficient will get multiplied by 10^{-6} and the results wil... | Is it a good practice to always scale/normalize data for machine learning? [duplicate] | For machine learning models that include coefficients (e.g. regression, logistic regression, etc) the main reason to normalize is numerical stability. Mathematically, if one of your predictor columns | Is it a good practice to always scale/normalize data for machine learning? [duplicate]
For machine learning models that include coefficients (e.g. regression, logistic regression, etc) the main reason to normalize is numerical stability. Mathematically, if one of your predictor columns is multiplied by 10^6, then the ... | Is it a good practice to always scale/normalize data for machine learning? [duplicate]
For machine learning models that include coefficients (e.g. regression, logistic regression, etc) the main reason to normalize is numerical stability. Mathematically, if one of your predictor columns |
3,927 | Is it a good practice to always scale/normalize data for machine learning? [duplicate] | I was trying to solve ridge regression problem using gradient descent. Now without normalization I set some appropriate step size and ran the code. In order to make sure my coding was error-free, I coded the same objective in CVX too. Now CVX took only few iterations to converge to a certain optimal value but I ran my ... | Is it a good practice to always scale/normalize data for machine learning? [duplicate] | I was trying to solve ridge regression problem using gradient descent. Now without normalization I set some appropriate step size and ran the code. In order to make sure my coding was error-free, I co | Is it a good practice to always scale/normalize data for machine learning? [duplicate]
I was trying to solve ridge regression problem using gradient descent. Now without normalization I set some appropriate step size and ran the code. In order to make sure my coding was error-free, I coded the same objective in CVX too... | Is it a good practice to always scale/normalize data for machine learning? [duplicate]
I was trying to solve ridge regression problem using gradient descent. Now without normalization I set some appropriate step size and ran the code. In order to make sure my coding was error-free, I co |
3,928 | What is the objective function of PCA? | Without trying to give a full primer on PCA, from an optimization standpoint, the primary objective function is the Rayleigh quotient. The matrix that figures in the quotient is (some multiple of) the sample covariance matrix
$$\newcommand{\m}[1]{\mathbf{#1}}\newcommand{\x}{\m{x}}\newcommand{\S}{\m{S}}\newcommand{\u}{\... | What is the objective function of PCA? | Without trying to give a full primer on PCA, from an optimization standpoint, the primary objective function is the Rayleigh quotient. The matrix that figures in the quotient is (some multiple of) the | What is the objective function of PCA?
Without trying to give a full primer on PCA, from an optimization standpoint, the primary objective function is the Rayleigh quotient. The matrix that figures in the quotient is (some multiple of) the sample covariance matrix
$$\newcommand{\m}[1]{\mathbf{#1}}\newcommand{\x}{\m{x}}... | What is the objective function of PCA?
Without trying to give a full primer on PCA, from an optimization standpoint, the primary objective function is the Rayleigh quotient. The matrix that figures in the quotient is (some multiple of) the |
3,929 | What is the objective function of PCA? | The solution presented by cardinal focuses on the sample covariance matrix. Another starting point is the reconstruction error of the data by a q-dimensional hyperplane. If the p-dimensional data points are $x_1, \ldots, x_n$ the objective is to solve
$$\min_{\mu, \lambda_1,\ldots, \lambda_n, \mathbf{V}_q} \sum_{i=1}^n... | What is the objective function of PCA? | The solution presented by cardinal focuses on the sample covariance matrix. Another starting point is the reconstruction error of the data by a q-dimensional hyperplane. If the p-dimensional data poin | What is the objective function of PCA?
The solution presented by cardinal focuses on the sample covariance matrix. Another starting point is the reconstruction error of the data by a q-dimensional hyperplane. If the p-dimensional data points are $x_1, \ldots, x_n$ the objective is to solve
$$\min_{\mu, \lambda_1,\ldots... | What is the objective function of PCA?
The solution presented by cardinal focuses on the sample covariance matrix. Another starting point is the reconstruction error of the data by a q-dimensional hyperplane. If the p-dimensional data poin |
3,930 | What is the objective function of PCA? | See NIPALS (wiki) for one algorithm which doesn't explicitly use a matrix decomposition. I suppose that's what you mean when you say that you want to avoid matrix algebra since you really can't avoid matrix algebra here :) | What is the objective function of PCA? | See NIPALS (wiki) for one algorithm which doesn't explicitly use a matrix decomposition. I suppose that's what you mean when you say that you want to avoid matrix algebra since you really can't avoid | What is the objective function of PCA?
See NIPALS (wiki) for one algorithm which doesn't explicitly use a matrix decomposition. I suppose that's what you mean when you say that you want to avoid matrix algebra since you really can't avoid matrix algebra here :) | What is the objective function of PCA?
See NIPALS (wiki) for one algorithm which doesn't explicitly use a matrix decomposition. I suppose that's what you mean when you say that you want to avoid matrix algebra since you really can't avoid |
3,931 | Does the optimal number of trees in a random forest depend on the number of predictors? | Random forest uses bagging (picking a sample of observations rather than all of them) and random subspace method (picking a sample of features rather than all of them, in other words - attribute bagging) to grow a tree. If the number of observations is large, but the number of trees is too small, then some observations... | Does the optimal number of trees in a random forest depend on the number of predictors? | Random forest uses bagging (picking a sample of observations rather than all of them) and random subspace method (picking a sample of features rather than all of them, in other words - attribute baggi | Does the optimal number of trees in a random forest depend on the number of predictors?
Random forest uses bagging (picking a sample of observations rather than all of them) and random subspace method (picking a sample of features rather than all of them, in other words - attribute bagging) to grow a tree. If the numbe... | Does the optimal number of trees in a random forest depend on the number of predictors?
Random forest uses bagging (picking a sample of observations rather than all of them) and random subspace method (picking a sample of features rather than all of them, in other words - attribute baggi |
3,932 | Does the optimal number of trees in a random forest depend on the number of predictors? | The number of trees in the Random Forest depends on the number of rows in the data set. I was doing an experiment when tuning the number of trees on 72 classification tasks from OpenML-CC18 benchmark. I got such dependency between optimal number of trees and number of rows in the data: | Does the optimal number of trees in a random forest depend on the number of predictors? | The number of trees in the Random Forest depends on the number of rows in the data set. I was doing an experiment when tuning the number of trees on 72 classification tasks from OpenML-CC18 benchmark. | Does the optimal number of trees in a random forest depend on the number of predictors?
The number of trees in the Random Forest depends on the number of rows in the data set. I was doing an experiment when tuning the number of trees on 72 classification tasks from OpenML-CC18 benchmark. I got such dependency between o... | Does the optimal number of trees in a random forest depend on the number of predictors?
The number of trees in the Random Forest depends on the number of rows in the data set. I was doing an experiment when tuning the number of trees on 72 classification tasks from OpenML-CC18 benchmark. |
3,933 | Does the optimal number of trees in a random forest depend on the number of predictors? | Accordingly to this article
They suggest that a random forest should have a number of trees between 64 - 128 trees.
With that, you should have a good balance between ROC AUC and processing time. | Does the optimal number of trees in a random forest depend on the number of predictors? | Accordingly to this article
They suggest that a random forest should have a number of trees between 64 - 128 trees.
With that, you should have a good balance between ROC AUC and processing time. | Does the optimal number of trees in a random forest depend on the number of predictors?
Accordingly to this article
They suggest that a random forest should have a number of trees between 64 - 128 trees.
With that, you should have a good balance between ROC AUC and processing time. | Does the optimal number of trees in a random forest depend on the number of predictors?
Accordingly to this article
They suggest that a random forest should have a number of trees between 64 - 128 trees.
With that, you should have a good balance between ROC AUC and processing time. |
3,934 | Does the optimal number of trees in a random forest depend on the number of predictors? | i want add somthings if you have more than 1000 features you and 1000 rows you can't just take rondom number of tree .
my suggest you should first detect the number of cpu and ram before trying to launch cross validation in find the ratio between them and number of tree
if you use sikit learn in python you have opt... | Does the optimal number of trees in a random forest depend on the number of predictors? | i want add somthings if you have more than 1000 features you and 1000 rows you can't just take rondom number of tree .
my suggest you should first detect the number of cpu and ram before trying to l | Does the optimal number of trees in a random forest depend on the number of predictors?
i want add somthings if you have more than 1000 features you and 1000 rows you can't just take rondom number of tree .
my suggest you should first detect the number of cpu and ram before trying to launch cross validation in find ... | Does the optimal number of trees in a random forest depend on the number of predictors?
i want add somthings if you have more than 1000 features you and 1000 rows you can't just take rondom number of tree .
my suggest you should first detect the number of cpu and ram before trying to l |
3,935 | Why do Convolutional Neural Networks not use a Support Vector Machine to classify? | What is an SVM, anyway?
I think the answer for most purposes is “the solution to the following optimization problem”:
$$
\begin{split}
\operatorname*{arg\,min}_{f \in \mathcal H} \frac{1}{n} \sum_{i=1}^n \ell_\mathit{hinge}(f(x_i), y_i) \, + \lambda \lVert f \rVert_{\mathcal H}^2
\\ \ell_\mathit{hinge}(t, y) = \max(0, ... | Why do Convolutional Neural Networks not use a Support Vector Machine to classify? | What is an SVM, anyway?
I think the answer for most purposes is “the solution to the following optimization problem”:
$$
\begin{split}
\operatorname*{arg\,min}_{f \in \mathcal H} \frac{1}{n} \sum_{i=1 | Why do Convolutional Neural Networks not use a Support Vector Machine to classify?
What is an SVM, anyway?
I think the answer for most purposes is “the solution to the following optimization problem”:
$$
\begin{split}
\operatorname*{arg\,min}_{f \in \mathcal H} \frac{1}{n} \sum_{i=1}^n \ell_\mathit{hinge}(f(x_i), y_i) ... | Why do Convolutional Neural Networks not use a Support Vector Machine to classify?
What is an SVM, anyway?
I think the answer for most purposes is “the solution to the following optimization problem”:
$$
\begin{split}
\operatorname*{arg\,min}_{f \in \mathcal H} \frac{1}{n} \sum_{i=1 |
3,936 | Why do Convolutional Neural Networks not use a Support Vector Machine to classify? | Most of the theory behind the support vector machine assumes you are constructing a maximal margin classifier following a fixed transformation of the input space (via a kernel). The theory is less applicable if the fixed transformation has been learned from the data (as would be the case for the lower levels of the de... | Why do Convolutional Neural Networks not use a Support Vector Machine to classify? | Most of the theory behind the support vector machine assumes you are constructing a maximal margin classifier following a fixed transformation of the input space (via a kernel). The theory is less ap | Why do Convolutional Neural Networks not use a Support Vector Machine to classify?
Most of the theory behind the support vector machine assumes you are constructing a maximal margin classifier following a fixed transformation of the input space (via a kernel). The theory is less applicable if the fixed transformation ... | Why do Convolutional Neural Networks not use a Support Vector Machine to classify?
Most of the theory behind the support vector machine assumes you are constructing a maximal margin classifier following a fixed transformation of the input space (via a kernel). The theory is less ap |
3,937 | Why do Convolutional Neural Networks not use a Support Vector Machine to classify? | As far I can see, there are at least couple differences:
CNNs are designed to work with image data, while SVM is a more generic classifier;
CNNs extract features while SVM simply maps its input to some high dimensional space where (hopefully) the differences between the classes can be revealed;
Similar to 2., CNNs are... | Why do Convolutional Neural Networks not use a Support Vector Machine to classify? | As far I can see, there are at least couple differences:
CNNs are designed to work with image data, while SVM is a more generic classifier;
CNNs extract features while SVM simply maps its input to so | Why do Convolutional Neural Networks not use a Support Vector Machine to classify?
As far I can see, there are at least couple differences:
CNNs are designed to work with image data, while SVM is a more generic classifier;
CNNs extract features while SVM simply maps its input to some high dimensional space where (hope... | Why do Convolutional Neural Networks not use a Support Vector Machine to classify?
As far I can see, there are at least couple differences:
CNNs are designed to work with image data, while SVM is a more generic classifier;
CNNs extract features while SVM simply maps its input to so |
3,938 | How are regression, the t-test, and the ANOVA all versions of the general linear model? | Consider that they can all be written as a regression equation (perhaps with slightly differing interpretations than their traditional forms).
Regression:
$$
Y=\beta_0 + \beta_1X_{\text{(continuous)}} + \varepsilon \\
\text{where }\varepsilon\sim\mathcal N(0, \sigma^2)
$$
t-test:
$$
Y=\beta_0 + \beta_1X_{\text{(dumm... | How are regression, the t-test, and the ANOVA all versions of the general linear model? | Consider that they can all be written as a regression equation (perhaps with slightly differing interpretations than their traditional forms).
Regression:
$$
Y=\beta_0 + \beta_1X_{\text{(continuous) | How are regression, the t-test, and the ANOVA all versions of the general linear model?
Consider that they can all be written as a regression equation (perhaps with slightly differing interpretations than their traditional forms).
Regression:
$$
Y=\beta_0 + \beta_1X_{\text{(continuous)}} + \varepsilon \\
\text{where... | How are regression, the t-test, and the ANOVA all versions of the general linear model?
Consider that they can all be written as a regression equation (perhaps with slightly differing interpretations than their traditional forms).
Regression:
$$
Y=\beta_0 + \beta_1X_{\text{(continuous) |
3,939 | How are regression, the t-test, and the ANOVA all versions of the general linear model? | They can all be written as particular cases of the general linear model.
The t-test is a two-sample case of ANOVA. If you square the t-test statistic you get the corresponding $F$ in the ANOVA.
An ANOVA model is basically just a regression model where the factor levels are represented by dummy (or indicator) variables... | How are regression, the t-test, and the ANOVA all versions of the general linear model? | They can all be written as particular cases of the general linear model.
The t-test is a two-sample case of ANOVA. If you square the t-test statistic you get the corresponding $F$ in the ANOVA.
An AN | How are regression, the t-test, and the ANOVA all versions of the general linear model?
They can all be written as particular cases of the general linear model.
The t-test is a two-sample case of ANOVA. If you square the t-test statistic you get the corresponding $F$ in the ANOVA.
An ANOVA model is basically just a re... | How are regression, the t-test, and the ANOVA all versions of the general linear model?
They can all be written as particular cases of the general linear model.
The t-test is a two-sample case of ANOVA. If you square the t-test statistic you get the corresponding $F$ in the ANOVA.
An AN |
3,940 | How are regression, the t-test, and the ANOVA all versions of the general linear model? | This answer that I posted earlier is somewhat relevant, but this question is somewhat different.
You might want to think about the differences and similarities between the following linear models:
$$
\begin{bmatrix} Y_1 \\ \vdots \\ Y_n \end{bmatrix} = \begin{bmatrix} 1 & x_1 \\ 1 & x_2 \\ 1 & x_3 \\ \vdots & \vdots \\... | How are regression, the t-test, and the ANOVA all versions of the general linear model? | This answer that I posted earlier is somewhat relevant, but this question is somewhat different.
You might want to think about the differences and similarities between the following linear models:
$$
| How are regression, the t-test, and the ANOVA all versions of the general linear model?
This answer that I posted earlier is somewhat relevant, but this question is somewhat different.
You might want to think about the differences and similarities between the following linear models:
$$
\begin{bmatrix} Y_1 \\ \vdots \\... | How are regression, the t-test, and the ANOVA all versions of the general linear model?
This answer that I posted earlier is somewhat relevant, but this question is somewhat different.
You might want to think about the differences and similarities between the following linear models:
$$
|
3,941 | How are regression, the t-test, and the ANOVA all versions of the general linear model? | Anova is similar to a t-test for equality of means under the assumption of unknown but equal variances among treatments. This is because in ANOVA MSE is identical to pooled-variance used in t-test. There are other versions of t-test such as one for un-equal variances and pair-wise t-test. From this view, t-test can be ... | How are regression, the t-test, and the ANOVA all versions of the general linear model? | Anova is similar to a t-test for equality of means under the assumption of unknown but equal variances among treatments. This is because in ANOVA MSE is identical to pooled-variance used in t-test. Th | How are regression, the t-test, and the ANOVA all versions of the general linear model?
Anova is similar to a t-test for equality of means under the assumption of unknown but equal variances among treatments. This is because in ANOVA MSE is identical to pooled-variance used in t-test. There are other versions of t-test... | How are regression, the t-test, and the ANOVA all versions of the general linear model?
Anova is similar to a t-test for equality of means under the assumption of unknown but equal variances among treatments. This is because in ANOVA MSE is identical to pooled-variance used in t-test. Th |
3,942 | Measuring entropy/ information/ patterns of a 2d binary matrix | There is a simple procedure that captures all the intuition, including the psychological and geometrical elements. It relies on using spatial proximity, which is the basis of our perception and provides an intrinsic way to capture what is only imperfectly measured by symmetries.
To do this, we need to measure the "com... | Measuring entropy/ information/ patterns of a 2d binary matrix | There is a simple procedure that captures all the intuition, including the psychological and geometrical elements. It relies on using spatial proximity, which is the basis of our perception and provi | Measuring entropy/ information/ patterns of a 2d binary matrix
There is a simple procedure that captures all the intuition, including the psychological and geometrical elements. It relies on using spatial proximity, which is the basis of our perception and provides an intrinsic way to capture what is only imperfectly ... | Measuring entropy/ information/ patterns of a 2d binary matrix
There is a simple procedure that captures all the intuition, including the psychological and geometrical elements. It relies on using spatial proximity, which is the basis of our perception and provi |
3,943 | Measuring entropy/ information/ patterns of a 2d binary matrix | First, my suggestion is purely intuitive: I know nothing in pattern recognition field. Second, alternative dozens suggestions like mine could be made.
I start with idea that a regular configuration (that is, with low entropy) should be somehow symmetric, isomorphic to this or that its tranformants. For example, in rota... | Measuring entropy/ information/ patterns of a 2d binary matrix | First, my suggestion is purely intuitive: I know nothing in pattern recognition field. Second, alternative dozens suggestions like mine could be made.
I start with idea that a regular configuration (t | Measuring entropy/ information/ patterns of a 2d binary matrix
First, my suggestion is purely intuitive: I know nothing in pattern recognition field. Second, alternative dozens suggestions like mine could be made.
I start with idea that a regular configuration (that is, with low entropy) should be somehow symmetric, is... | Measuring entropy/ information/ patterns of a 2d binary matrix
First, my suggestion is purely intuitive: I know nothing in pattern recognition field. Second, alternative dozens suggestions like mine could be made.
I start with idea that a regular configuration (t |
3,944 | Measuring entropy/ information/ patterns of a 2d binary matrix | The information is commonly defined as $h(x) = \log p(x)$. There is some nice theory explaining that $\log_2 p(x)$ is the amount of bits you need to code $x$ using $p$. If you want to know more about this read up on arithmetic coding.
So how can that solve your problem? Easy. Find some $p$ that represents your data and... | Measuring entropy/ information/ patterns of a 2d binary matrix | The information is commonly defined as $h(x) = \log p(x)$. There is some nice theory explaining that $\log_2 p(x)$ is the amount of bits you need to code $x$ using $p$. If you want to know more about | Measuring entropy/ information/ patterns of a 2d binary matrix
The information is commonly defined as $h(x) = \log p(x)$. There is some nice theory explaining that $\log_2 p(x)$ is the amount of bits you need to code $x$ using $p$. If you want to know more about this read up on arithmetic coding.
So how can that solve ... | Measuring entropy/ information/ patterns of a 2d binary matrix
The information is commonly defined as $h(x) = \log p(x)$. There is some nice theory explaining that $\log_2 p(x)$ is the amount of bits you need to code $x$ using $p$. If you want to know more about |
3,945 | Measuring entropy/ information/ patterns of a 2d binary matrix | My following proposal is rather insighted than deduced, so I cannot prove it, but can at least offer some rationale. The procedure of assessing of "entropy" of the configuration of spots includes:
Digitize spots.
Perform comparison of the configuration with itself permuted, many
times, by orthogonal Procrustes analysi... | Measuring entropy/ information/ patterns of a 2d binary matrix | My following proposal is rather insighted than deduced, so I cannot prove it, but can at least offer some rationale. The procedure of assessing of "entropy" of the configuration of spots includes:
Di | Measuring entropy/ information/ patterns of a 2d binary matrix
My following proposal is rather insighted than deduced, so I cannot prove it, but can at least offer some rationale. The procedure of assessing of "entropy" of the configuration of spots includes:
Digitize spots.
Perform comparison of the configuration wit... | Measuring entropy/ information/ patterns of a 2d binary matrix
My following proposal is rather insighted than deduced, so I cannot prove it, but can at least offer some rationale. The procedure of assessing of "entropy" of the configuration of spots includes:
Di |
3,946 | Measuring entropy/ information/ patterns of a 2d binary matrix | Mutual information, considering each dimension as a random variable, thus each matrix as a set of pairs of numbers, should help in all cases, except for C, where I am not sure of the result.
See the discussion around Fig 8 (starting in p24) on regression performance analysis in the TMVA manual or the corresponding arxi... | Measuring entropy/ information/ patterns of a 2d binary matrix | Mutual information, considering each dimension as a random variable, thus each matrix as a set of pairs of numbers, should help in all cases, except for C, where I am not sure of the result.
See the d | Measuring entropy/ information/ patterns of a 2d binary matrix
Mutual information, considering each dimension as a random variable, thus each matrix as a set of pairs of numbers, should help in all cases, except for C, where I am not sure of the result.
See the discussion around Fig 8 (starting in p24) on regression pe... | Measuring entropy/ information/ patterns of a 2d binary matrix
Mutual information, considering each dimension as a random variable, thus each matrix as a set of pairs of numbers, should help in all cases, except for C, where I am not sure of the result.
See the d |
3,947 | Measuring entropy/ information/ patterns of a 2d binary matrix | Instead of looking at global properties of the pattern (like symmetries), one can take a look at the local ones, e.g. the number of neighbors each stone (=black circle) has. Let's denote the total number of stones by $s$.
If the stones where thrown at random, the distribution of neighbors is
$$P_{rand,p}(k\ \text{neigh... | Measuring entropy/ information/ patterns of a 2d binary matrix | Instead of looking at global properties of the pattern (like symmetries), one can take a look at the local ones, e.g. the number of neighbors each stone (=black circle) has. Let's denote the total num | Measuring entropy/ information/ patterns of a 2d binary matrix
Instead of looking at global properties of the pattern (like symmetries), one can take a look at the local ones, e.g. the number of neighbors each stone (=black circle) has. Let's denote the total number of stones by $s$.
If the stones where thrown at rando... | Measuring entropy/ information/ patterns of a 2d binary matrix
Instead of looking at global properties of the pattern (like symmetries), one can take a look at the local ones, e.g. the number of neighbors each stone (=black circle) has. Let's denote the total num |
3,948 | Measuring entropy/ information/ patterns of a 2d binary matrix | There is a really simple way to conceptualize the information content that harks back to Shannon's (admittedly one dimensional) idea using probabilities and transition probabilities to find a least redundant representation of a text string. For an image (in this particular case a binary image defined on a square matri... | Measuring entropy/ information/ patterns of a 2d binary matrix | There is a really simple way to conceptualize the information content that harks back to Shannon's (admittedly one dimensional) idea using probabilities and transition probabilities to find a least re | Measuring entropy/ information/ patterns of a 2d binary matrix
There is a really simple way to conceptualize the information content that harks back to Shannon's (admittedly one dimensional) idea using probabilities and transition probabilities to find a least redundant representation of a text string. For an image (i... | Measuring entropy/ information/ patterns of a 2d binary matrix
There is a really simple way to conceptualize the information content that harks back to Shannon's (admittedly one dimensional) idea using probabilities and transition probabilities to find a least re |
3,949 | Measuring entropy/ information/ patterns of a 2d binary matrix | In reading this, two things come to mind. The first is that a lot of the gestalt properties are quite challenging to predict, and a lot of PhD level work goes into trying to figure out models for how groupings take place. My instinct is that most easy rules that you could think of will end up with counter examples.
I... | Measuring entropy/ information/ patterns of a 2d binary matrix | In reading this, two things come to mind. The first is that a lot of the gestalt properties are quite challenging to predict, and a lot of PhD level work goes into trying to figure out models for how | Measuring entropy/ information/ patterns of a 2d binary matrix
In reading this, two things come to mind. The first is that a lot of the gestalt properties are quite challenging to predict, and a lot of PhD level work goes into trying to figure out models for how groupings take place. My instinct is that most easy rul... | Measuring entropy/ information/ patterns of a 2d binary matrix
In reading this, two things come to mind. The first is that a lot of the gestalt properties are quite challenging to predict, and a lot of PhD level work goes into trying to figure out models for how |
3,950 | Measuring entropy/ information/ patterns of a 2d binary matrix | Your examples remind me of truth tables from boolean algebra and digital circuits. In this realm, Karnaugh maps (http://en.wikipedia.org/wiki/Karnaugh_map) can be used as a tool to provide the minimal boolean function to express the entire grid. Alternatively, using boolean algebra identities can help to reduce the fun... | Measuring entropy/ information/ patterns of a 2d binary matrix | Your examples remind me of truth tables from boolean algebra and digital circuits. In this realm, Karnaugh maps (http://en.wikipedia.org/wiki/Karnaugh_map) can be used as a tool to provide the minimal | Measuring entropy/ information/ patterns of a 2d binary matrix
Your examples remind me of truth tables from boolean algebra and digital circuits. In this realm, Karnaugh maps (http://en.wikipedia.org/wiki/Karnaugh_map) can be used as a tool to provide the minimal boolean function to express the entire grid. Alternative... | Measuring entropy/ information/ patterns of a 2d binary matrix
Your examples remind me of truth tables from boolean algebra and digital circuits. In this realm, Karnaugh maps (http://en.wikipedia.org/wiki/Karnaugh_map) can be used as a tool to provide the minimal |
3,951 | Measuring entropy/ information/ patterns of a 2d binary matrix | I would point out the rank of the matrix used in binary matrix factorization as an indicator of the entropy. Although exact computation is NP-hard, the rank can be estimated in O(log2n) time.
I would also merely point out that comparison with 3 rotations and 4 reflections method has a real flaw.
For a matrix with an o... | Measuring entropy/ information/ patterns of a 2d binary matrix | I would point out the rank of the matrix used in binary matrix factorization as an indicator of the entropy. Although exact computation is NP-hard, the rank can be estimated in O(log2n) time.
I would | Measuring entropy/ information/ patterns of a 2d binary matrix
I would point out the rank of the matrix used in binary matrix factorization as an indicator of the entropy. Although exact computation is NP-hard, the rank can be estimated in O(log2n) time.
I would also merely point out that comparison with 3 rotations a... | Measuring entropy/ information/ patterns of a 2d binary matrix
I would point out the rank of the matrix used in binary matrix factorization as an indicator of the entropy. Although exact computation is NP-hard, the rank can be estimated in O(log2n) time.
I would |
3,952 | Are all values within a 95% confidence interval equally likely? | One question that needs to be answered is what does "likely" mean in this context?
If it means probability (as it is sometimes used as a synonym of) and we are using strict frequentist definitions then the true parameter value is a single value that does not change, so the probability (likelihood) of that point is 100%... | Are all values within a 95% confidence interval equally likely? | One question that needs to be answered is what does "likely" mean in this context?
If it means probability (as it is sometimes used as a synonym of) and we are using strict frequentist definitions the | Are all values within a 95% confidence interval equally likely?
One question that needs to be answered is what does "likely" mean in this context?
If it means probability (as it is sometimes used as a synonym of) and we are using strict frequentist definitions then the true parameter value is a single value that does n... | Are all values within a 95% confidence interval equally likely?
One question that needs to be answered is what does "likely" mean in this context?
If it means probability (as it is sometimes used as a synonym of) and we are using strict frequentist definitions the |
3,953 | Are all values within a 95% confidence interval equally likely? | Suppose someone told me that I should place equal trust in all values within a CI95 as potential indicators of the population value. (I'm deliberately avoiding the terms "likely" and "probable.") What's special about 95? Nothing: to be consistent I would also have to place equal trust in all values within a CI96, a... | Are all values within a 95% confidence interval equally likely? | Suppose someone told me that I should place equal trust in all values within a CI95 as potential indicators of the population value. (I'm deliberately avoiding the terms "likely" and "probable.") Wh | Are all values within a 95% confidence interval equally likely?
Suppose someone told me that I should place equal trust in all values within a CI95 as potential indicators of the population value. (I'm deliberately avoiding the terms "likely" and "probable.") What's special about 95? Nothing: to be consistent I wou... | Are all values within a 95% confidence interval equally likely?
Suppose someone told me that I should place equal trust in all values within a CI95 as potential indicators of the population value. (I'm deliberately avoiding the terms "likely" and "probable.") Wh |
3,954 | Are all values within a 95% confidence interval equally likely? | This is a great question! There is a mathematical concept called likelihood that will help you understand the issues. Fisher invented likelihood but considered it to be somewhat less desirable than probability, but likelihood turns out to be more 'primitive' than probability and Ian Hacking (1965) considered it to be a... | Are all values within a 95% confidence interval equally likely? | This is a great question! There is a mathematical concept called likelihood that will help you understand the issues. Fisher invented likelihood but considered it to be somewhat less desirable than pr | Are all values within a 95% confidence interval equally likely?
This is a great question! There is a mathematical concept called likelihood that will help you understand the issues. Fisher invented likelihood but considered it to be somewhat less desirable than probability, but likelihood turns out to be more 'primitiv... | Are all values within a 95% confidence interval equally likely?
This is a great question! There is a mathematical concept called likelihood that will help you understand the issues. Fisher invented likelihood but considered it to be somewhat less desirable than pr |
3,955 | Are all values within a 95% confidence interval equally likely? | Let's start with the definition of a confidence interval. If I say that a 95% confidence interval goes from this to that I mean that statements of that nature will be true about 95% of the time and false about 5% of the time. I do not necessarily mean that I am 95% confident about this particular statement. A 90% con... | Are all values within a 95% confidence interval equally likely? | Let's start with the definition of a confidence interval. If I say that a 95% confidence interval goes from this to that I mean that statements of that nature will be true about 95% of the time and fa | Are all values within a 95% confidence interval equally likely?
Let's start with the definition of a confidence interval. If I say that a 95% confidence interval goes from this to that I mean that statements of that nature will be true about 95% of the time and false about 5% of the time. I do not necessarily mean tha... | Are all values within a 95% confidence interval equally likely?
Let's start with the definition of a confidence interval. If I say that a 95% confidence interval goes from this to that I mean that statements of that nature will be true about 95% of the time and fa |
3,956 | What is quasi-binomial distribution (in the context of GLM)? | The difference between the binomial distribution and quasi-binomial can be seen in their probability density functions (pdf), which characterize these distributions.
Binomial pdf:
$$P(X=k)={n \choose k}p^{k}(1-p)^{n-k}$$
Quasi-binomial pdf:
$$P(X=k)={n \choose k}p(p+k\phi)^{k-1}(1-p-k\phi)^{n-k}$$
The quasi-binomial di... | What is quasi-binomial distribution (in the context of GLM)? | The difference between the binomial distribution and quasi-binomial can be seen in their probability density functions (pdf), which characterize these distributions.
Binomial pdf:
$$P(X=k)={n \choose | What is quasi-binomial distribution (in the context of GLM)?
The difference between the binomial distribution and quasi-binomial can be seen in their probability density functions (pdf), which characterize these distributions.
Binomial pdf:
$$P(X=k)={n \choose k}p^{k}(1-p)^{n-k}$$
Quasi-binomial pdf:
$$P(X=k)={n \choos... | What is quasi-binomial distribution (in the context of GLM)?
The difference between the binomial distribution and quasi-binomial can be seen in their probability density functions (pdf), which characterize these distributions.
Binomial pdf:
$$P(X=k)={n \choose |
3,957 | What is quasi-binomial distribution (in the context of GLM)? | The quasi-binomial isn't necessarily a particular distribution; it describes a model for the relationship between variance and mean in generalized linear models which is $\phi$ times the variance for a binomial in terms of the mean for a binomial.
There is a distribution that fits such a specification (the obvious one ... | What is quasi-binomial distribution (in the context of GLM)? | The quasi-binomial isn't necessarily a particular distribution; it describes a model for the relationship between variance and mean in generalized linear models which is $\phi$ times the variance for | What is quasi-binomial distribution (in the context of GLM)?
The quasi-binomial isn't necessarily a particular distribution; it describes a model for the relationship between variance and mean in generalized linear models which is $\phi$ times the variance for a binomial in terms of the mean for a binomial.
There is a ... | What is quasi-binomial distribution (in the context of GLM)?
The quasi-binomial isn't necessarily a particular distribution; it describes a model for the relationship between variance and mean in generalized linear models which is $\phi$ times the variance for |
3,958 | Optimal number of folds in $K$-fold cross-validation: is leave-one-out CV always the best choice? | Leave-one-out cross-validation does not generally lead to better performance than K-fold, and is more likely to be worse, as it has a relatively high variance (i.e. its value changes more for different samples of data than the value for k-fold cross-validation). This is bad in a model selection criterion as it means t... | Optimal number of folds in $K$-fold cross-validation: is leave-one-out CV always the best choice? | Leave-one-out cross-validation does not generally lead to better performance than K-fold, and is more likely to be worse, as it has a relatively high variance (i.e. its value changes more for differen | Optimal number of folds in $K$-fold cross-validation: is leave-one-out CV always the best choice?
Leave-one-out cross-validation does not generally lead to better performance than K-fold, and is more likely to be worse, as it has a relatively high variance (i.e. its value changes more for different samples of data than... | Optimal number of folds in $K$-fold cross-validation: is leave-one-out CV always the best choice?
Leave-one-out cross-validation does not generally lead to better performance than K-fold, and is more likely to be worse, as it has a relatively high variance (i.e. its value changes more for differen |
3,959 | Optimal number of folds in $K$-fold cross-validation: is leave-one-out CV always the best choice? | Choosing the number K folds by considering the learning curve
I would like to argue that choosing the appropriate number of $K$ folds depends a lot on the shape and position of the learning curve, mostly due to its impact on the bias. This argument, which extends to leave-one-out CV, is largely taken from the book "Ele... | Optimal number of folds in $K$-fold cross-validation: is leave-one-out CV always the best choice? | Choosing the number K folds by considering the learning curve
I would like to argue that choosing the appropriate number of $K$ folds depends a lot on the shape and position of the learning curve, mos | Optimal number of folds in $K$-fold cross-validation: is leave-one-out CV always the best choice?
Choosing the number K folds by considering the learning curve
I would like to argue that choosing the appropriate number of $K$ folds depends a lot on the shape and position of the learning curve, mostly due to its impact ... | Optimal number of folds in $K$-fold cross-validation: is leave-one-out CV always the best choice?
Choosing the number K folds by considering the learning curve
I would like to argue that choosing the appropriate number of $K$ folds depends a lot on the shape and position of the learning curve, mos |
3,960 | Statistics and causal inference? | This is a broad question, but given the Box, Hunter and Hunter quote is true I think what it comes down to is
The quality of the experimental design:
randomization, sample sizes, control of confounders,...
The quality of the implementation of the design:
adherance to protocol, measurement error, data handling, ...
... | Statistics and causal inference? | This is a broad question, but given the Box, Hunter and Hunter quote is true I think what it comes down to is
The quality of the experimental design:
randomization, sample sizes, control of confound | Statistics and causal inference?
This is a broad question, but given the Box, Hunter and Hunter quote is true I think what it comes down to is
The quality of the experimental design:
randomization, sample sizes, control of confounders,...
The quality of the implementation of the design:
adherance to protocol, measu... | Statistics and causal inference?
This is a broad question, but given the Box, Hunter and Hunter quote is true I think what it comes down to is
The quality of the experimental design:
randomization, sample sizes, control of confound |
3,961 | Statistics and causal inference? | What can a statistical model say about causation? What considerations should be made when making a causal inference from
a statistical model?
The first thing to make clear is that you can't make causal inference from a purely statistical model. No statistical model can say anything about causation without causal ass... | Statistics and causal inference? | What can a statistical model say about causation? What considerations should be made when making a causal inference from
a statistical model?
The first thing to make clear is that you can't make ca | Statistics and causal inference?
What can a statistical model say about causation? What considerations should be made when making a causal inference from
a statistical model?
The first thing to make clear is that you can't make causal inference from a purely statistical model. No statistical model can say anything a... | Statistics and causal inference?
What can a statistical model say about causation? What considerations should be made when making a causal inference from
a statistical model?
The first thing to make clear is that you can't make ca |
3,962 | Statistics and causal inference? | In addition to the excellent answer above, there is a statistical method that can get you closer to demonstrating causality. It is Granger Causality that demonstrates that one independent variable occurring before a dependent variable has a causal effect or not. I introduce this method in an easy to follow presentati... | Statistics and causal inference? | In addition to the excellent answer above, there is a statistical method that can get you closer to demonstrating causality. It is Granger Causality that demonstrates that one independent variable oc | Statistics and causal inference?
In addition to the excellent answer above, there is a statistical method that can get you closer to demonstrating causality. It is Granger Causality that demonstrates that one independent variable occurring before a dependent variable has a causal effect or not. I introduce this metho... | Statistics and causal inference?
In addition to the excellent answer above, there is a statistical method that can get you closer to demonstrating causality. It is Granger Causality that demonstrates that one independent variable oc |
3,963 | Choosing between LM and GLM for a log-transformed response variable | Good effort for thinking through this issue. Here's an incomplete answer, but some starters for the next steps.
First, the AIC scores - based on likelihoods - are on different scales because of the different distributions and link functions, so aren't comparable. Your sum of squares and mean sum of squares have been ... | Choosing between LM and GLM for a log-transformed response variable | Good effort for thinking through this issue. Here's an incomplete answer, but some starters for the next steps.
First, the AIC scores - based on likelihoods - are on different scales because of the d | Choosing between LM and GLM for a log-transformed response variable
Good effort for thinking through this issue. Here's an incomplete answer, but some starters for the next steps.
First, the AIC scores - based on likelihoods - are on different scales because of the different distributions and link functions, so aren't... | Choosing between LM and GLM for a log-transformed response variable
Good effort for thinking through this issue. Here's an incomplete answer, but some starters for the next steps.
First, the AIC scores - based on likelihoods - are on different scales because of the d |
3,964 | Choosing between LM and GLM for a log-transformed response variable | In a more general way, $E[\ln(Y|x)]$ and $\ln([E(Y|X])$ are not the same. Also the variance assumptions made by GLM are more flexible than in OLS, and for certain modeling situation as counts variance can be different taking distinct distribution families.
About the distribution family in my opinion is a question about... | Choosing between LM and GLM for a log-transformed response variable | In a more general way, $E[\ln(Y|x)]$ and $\ln([E(Y|X])$ are not the same. Also the variance assumptions made by GLM are more flexible than in OLS, and for certain modeling situation as counts variance | Choosing between LM and GLM for a log-transformed response variable
In a more general way, $E[\ln(Y|x)]$ and $\ln([E(Y|X])$ are not the same. Also the variance assumptions made by GLM are more flexible than in OLS, and for certain modeling situation as counts variance can be different taking distinct distribution famil... | Choosing between LM and GLM for a log-transformed response variable
In a more general way, $E[\ln(Y|x)]$ and $\ln([E(Y|X])$ are not the same. Also the variance assumptions made by GLM are more flexible than in OLS, and for certain modeling situation as counts variance |
3,965 | Choosing between LM and GLM for a log-transformed response variable | Unfortunately, your R code does not lead to an example where $\log(y) = x + \varepsilon$. Instead, your example is $x = \log(y) + \varepsilon$. The errors here are horizontal, not vertical; they are errors in $x$, not errors in $y$. Intuitively, it seems like this shouldn't make a difference, but it does. You may w... | Choosing between LM and GLM for a log-transformed response variable | Unfortunately, your R code does not lead to an example where $\log(y) = x + \varepsilon$. Instead, your example is $x = \log(y) + \varepsilon$. The errors here are horizontal, not vertical; they are | Choosing between LM and GLM for a log-transformed response variable
Unfortunately, your R code does not lead to an example where $\log(y) = x + \varepsilon$. Instead, your example is $x = \log(y) + \varepsilon$. The errors here are horizontal, not vertical; they are errors in $x$, not errors in $y$. Intuitively, it ... | Choosing between LM and GLM for a log-transformed response variable
Unfortunately, your R code does not lead to an example where $\log(y) = x + \varepsilon$. Instead, your example is $x = \log(y) + \varepsilon$. The errors here are horizontal, not vertical; they are |
3,966 | Choosing between LM and GLM for a log-transformed response variable | The choice is based on your hypothesis on your variable.
the log transformation is based on
$$\frac{\sqrt{\mathrm{Var}(X_t} }{\mathrm{E}(X_t)} = \mathrm{constant}$$
the gamma distribution is based on
$$\frac{\mathrm{Var}(X_t) }{\mathrm{E}(X_t)} = \mathrm{constant}$$
The log transformation rests on the hypothesis tha... | Choosing between LM and GLM for a log-transformed response variable | The choice is based on your hypothesis on your variable.
the log transformation is based on
$$\frac{\sqrt{\mathrm{Var}(X_t} }{\mathrm{E}(X_t)} = \mathrm{constant}$$
the gamma distribution is based on | Choosing between LM and GLM for a log-transformed response variable
The choice is based on your hypothesis on your variable.
the log transformation is based on
$$\frac{\sqrt{\mathrm{Var}(X_t} }{\mathrm{E}(X_t)} = \mathrm{constant}$$
the gamma distribution is based on
$$\frac{\mathrm{Var}(X_t) }{\mathrm{E}(X_t)} = \ma... | Choosing between LM and GLM for a log-transformed response variable
The choice is based on your hypothesis on your variable.
the log transformation is based on
$$\frac{\sqrt{\mathrm{Var}(X_t} }{\mathrm{E}(X_t)} = \mathrm{constant}$$
the gamma distribution is based on |
3,967 | What are disadvantages of state-space models and Kalman Filter for time-series modelling? | Here is some preliminary list of disadvantages I was able to extract from your comments. Criticism and additions are very welcome!
Overall - compared to ARIMA, state-space models allow you to model more complex processes, have interpretable structure and easily handle data irregularities; but for this you pay with incr... | What are disadvantages of state-space models and Kalman Filter for time-series modelling? | Here is some preliminary list of disadvantages I was able to extract from your comments. Criticism and additions are very welcome!
Overall - compared to ARIMA, state-space models allow you to model mo | What are disadvantages of state-space models and Kalman Filter for time-series modelling?
Here is some preliminary list of disadvantages I was able to extract from your comments. Criticism and additions are very welcome!
Overall - compared to ARIMA, state-space models allow you to model more complex processes, have int... | What are disadvantages of state-space models and Kalman Filter for time-series modelling?
Here is some preliminary list of disadvantages I was able to extract from your comments. Criticism and additions are very welcome!
Overall - compared to ARIMA, state-space models allow you to model mo |
3,968 | What are disadvantages of state-space models and Kalman Filter for time-series modelling? | Thanks @IrishStat for several very good questions in comments, the answer for your questions is too long to post as comment, so I post it as an answer (unfortunately, not to original question of the topic).
Questions were: "Does it clearly identify time trend changes and report the points in time where the trend change... | What are disadvantages of state-space models and Kalman Filter for time-series modelling? | Thanks @IrishStat for several very good questions in comments, the answer for your questions is too long to post as comment, so I post it as an answer (unfortunately, not to original question of the t | What are disadvantages of state-space models and Kalman Filter for time-series modelling?
Thanks @IrishStat for several very good questions in comments, the answer for your questions is too long to post as comment, so I post it as an answer (unfortunately, not to original question of the topic).
Questions were: "Does i... | What are disadvantages of state-space models and Kalman Filter for time-series modelling?
Thanks @IrishStat for several very good questions in comments, the answer for your questions is too long to post as comment, so I post it as an answer (unfortunately, not to original question of the t |
3,969 | What are disadvantages of state-space models and Kalman Filter for time-series modelling? | The Kalman Filter is the optimal linear quadratic estimator when the state dynamics and measurement errors follow the so-called linear Gaussian assumptions (http://wp.me/p491t5-PS). So, as long as you know your dynamics and measurement models and they follow the linear Gaussian assumptions, there is no better estimator... | What are disadvantages of state-space models and Kalman Filter for time-series modelling? | The Kalman Filter is the optimal linear quadratic estimator when the state dynamics and measurement errors follow the so-called linear Gaussian assumptions (http://wp.me/p491t5-PS). So, as long as you | What are disadvantages of state-space models and Kalman Filter for time-series modelling?
The Kalman Filter is the optimal linear quadratic estimator when the state dynamics and measurement errors follow the so-called linear Gaussian assumptions (http://wp.me/p491t5-PS). So, as long as you know your dynamics and measur... | What are disadvantages of state-space models and Kalman Filter for time-series modelling?
The Kalman Filter is the optimal linear quadratic estimator when the state dynamics and measurement errors follow the so-called linear Gaussian assumptions (http://wp.me/p491t5-PS). So, as long as you |
3,970 | What are disadvantages of state-space models and Kalman Filter for time-series modelling? | I'd add that if you directly use a State Space function, you're probably going to have to understand the several matrices that make up a model, and how they interact and work. It's much more like defining a program than defining an ARIMA model. If you're working with a dynamic State Space model, it gets even more compl... | What are disadvantages of state-space models and Kalman Filter for time-series modelling? | I'd add that if you directly use a State Space function, you're probably going to have to understand the several matrices that make up a model, and how they interact and work. It's much more like defi | What are disadvantages of state-space models and Kalman Filter for time-series modelling?
I'd add that if you directly use a State Space function, you're probably going to have to understand the several matrices that make up a model, and how they interact and work. It's much more like defining a program than defining a... | What are disadvantages of state-space models and Kalman Filter for time-series modelling?
I'd add that if you directly use a State Space function, you're probably going to have to understand the several matrices that make up a model, and how they interact and work. It's much more like defi |
3,971 | What are disadvantages of state-space models and Kalman Filter for time-series modelling? | You can refer to the excellent book Bayesian forecasting and dynamic models (Harrison and West, 1997). The authors show that almost all traditional time series models are particular cases of the general dynamic model. They also emphasize the advantages. Perhaps one of the major advantages is the easiness with which you... | What are disadvantages of state-space models and Kalman Filter for time-series modelling? | You can refer to the excellent book Bayesian forecasting and dynamic models (Harrison and West, 1997). The authors show that almost all traditional time series models are particular cases of the gener | What are disadvantages of state-space models and Kalman Filter for time-series modelling?
You can refer to the excellent book Bayesian forecasting and dynamic models (Harrison and West, 1997). The authors show that almost all traditional time series models are particular cases of the general dynamic model. They also em... | What are disadvantages of state-space models and Kalman Filter for time-series modelling?
You can refer to the excellent book Bayesian forecasting and dynamic models (Harrison and West, 1997). The authors show that almost all traditional time series models are particular cases of the gener |
3,972 | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(head) = p? | Flip the coin twice. If it lands HH or TT, ignore it and flip it twice again.
Now, the coin has equal probability of coming up HT or TH. If it comes up HT, call this H1. If it comes up TH, call this T1.
Keep obtaining H1 or T1 until you have three in a row. These three results give you a number based on the table belo... | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(he | Flip the coin twice. If it lands HH or TT, ignore it and flip it twice again.
Now, the coin has equal probability of coming up HT or TH. If it comes up HT, call this H1. If it comes up TH, call this | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(head) = p?
Flip the coin twice. If it lands HH or TT, ignore it and flip it twice again.
Now, the coin has equal probability of coming up HT or TH. If it comes up HT, call this H1. If it comes up TH, call this T1.
Keep ob... | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(he
Flip the coin twice. If it lands HH or TT, ignore it and flip it twice again.
Now, the coin has equal probability of coming up HT or TH. If it comes up HT, call this H1. If it comes up TH, call this |
3,973 | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(head) = p? | Assume that $p \in (0,1)$.
Step 1:. Toss the coin 5 times.
If the outcome is
$(H, H, H, T, T)$, return $1$ and stop.
$(H, H, T, T, H)$, return $2$ and stop.
$(H, T, T, H, H)$, return $3$ and stop.
$(T, T, H, H, H)$, return $4$ and stop.
$(T, H, H, H, T)$, return $5$ and stop.
$(H, H, T, H, T)$, return $6$ and stop.
$... | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(he | Assume that $p \in (0,1)$.
Step 1:. Toss the coin 5 times.
If the outcome is
$(H, H, H, T, T)$, return $1$ and stop.
$(H, H, T, T, H)$, return $2$ and stop.
$(H, T, T, H, H)$, return $3$ and stop.
$ | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(head) = p?
Assume that $p \in (0,1)$.
Step 1:. Toss the coin 5 times.
If the outcome is
$(H, H, H, T, T)$, return $1$ and stop.
$(H, H, T, T, H)$, return $2$ and stop.
$(H, T, T, H, H)$, return $3$ and stop.
$(T, T, H, H... | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(he
Assume that $p \in (0,1)$.
Step 1:. Toss the coin 5 times.
If the outcome is
$(H, H, H, T, T)$, return $1$ and stop.
$(H, H, T, T, H)$, return $2$ and stop.
$(H, T, T, H, H)$, return $3$ and stop.
$ |
3,974 | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(head) = p? | Generalizing the case described by Dilip Sarwate
Some of the methods described in the other answers use a scheme in which you throw a sequence of $n$ coins in a 'turn' and depending on the result you choose a number between 1 or 7 or discard the turn and throw again.
The trick is to find in the expansion of possibiliti... | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(he | Generalizing the case described by Dilip Sarwate
Some of the methods described in the other answers use a scheme in which you throw a sequence of $n$ coins in a 'turn' and depending on the result you | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(head) = p?
Generalizing the case described by Dilip Sarwate
Some of the methods described in the other answers use a scheme in which you throw a sequence of $n$ coins in a 'turn' and depending on the result you choose a nu... | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(he
Generalizing the case described by Dilip Sarwate
Some of the methods described in the other answers use a scheme in which you throw a sequence of $n$ coins in a 'turn' and depending on the result you |
3,975 | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(head) = p? | Divide a box into seven equal-area regions, each labeled with an integer. Throw the coin into the box in such a way that it has equal probability of landing in each region.
This is only half in jest -- it's essentially the same procedure as estimating $\pi$ using a physical Monte Carlo procedure, like dropping rice gra... | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(he | Divide a box into seven equal-area regions, each labeled with an integer. Throw the coin into the box in such a way that it has equal probability of landing in each region.
This is only half in jest - | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(head) = p?
Divide a box into seven equal-area regions, each labeled with an integer. Throw the coin into the box in such a way that it has equal probability of landing in each region.
This is only half in jest -- it's esse... | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(he
Divide a box into seven equal-area regions, each labeled with an integer. Throw the coin into the box in such a way that it has equal probability of landing in each region.
This is only half in jest - |
3,976 | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(head) = p? | EDIT: based on others' feedback.
Here's an interesting thought:
set the list of {1,2,3,4,5,6,7}. Throw the coin for each element in the list sequentially. If it lands head side up for a particular element, remove the number from the list. If all the numbers from a particular iteration of the list are removed, repeat th... | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(he | EDIT: based on others' feedback.
Here's an interesting thought:
set the list of {1,2,3,4,5,6,7}. Throw the coin for each element in the list sequentially. If it lands head side up for a particular ele | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(head) = p?
EDIT: based on others' feedback.
Here's an interesting thought:
set the list of {1,2,3,4,5,6,7}. Throw the coin for each element in the list sequentially. If it lands head side up for a particular element, remov... | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(he
EDIT: based on others' feedback.
Here's an interesting thought:
set the list of {1,2,3,4,5,6,7}. Throw the coin for each element in the list sequentially. If it lands head side up for a particular ele |
3,977 | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(head) = p? | The question is a bit ambiguous, is it asking "generate a random integer equal or less than 7 with equal probability", or is it asking "generate 7 random integers with equal probability?" - but what is the space of integers?!?
I'll assume it's the former, but the same logic I'm applying can be extended to the latter ca... | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(he | The question is a bit ambiguous, is it asking "generate a random integer equal or less than 7 with equal probability", or is it asking "generate 7 random integers with equal probability?" - but what i | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(head) = p?
The question is a bit ambiguous, is it asking "generate a random integer equal or less than 7 with equal probability", or is it asking "generate 7 random integers with equal probability?" - but what is the space... | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(he
The question is a bit ambiguous, is it asking "generate a random integer equal or less than 7 with equal probability", or is it asking "generate 7 random integers with equal probability?" - but what i |
3,978 | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(head) = p? | As mentioned in earlier comments, this puzzle relates to John von Neumann's 1951 paper "Various Techniques Used in Connection With Random Digits" published in the research journal of the National Bureau of Standards:
There is a wider literature about such problems that goes under the name of Bernoulli factory problems... | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(he | As mentioned in earlier comments, this puzzle relates to John von Neumann's 1951 paper "Various Techniques Used in Connection With Random Digits" published in the research journal of the National Bure | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(head) = p?
As mentioned in earlier comments, this puzzle relates to John von Neumann's 1951 paper "Various Techniques Used in Connection With Random Digits" published in the research journal of the National Bureau of Stand... | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(he
As mentioned in earlier comments, this puzzle relates to John von Neumann's 1951 paper "Various Techniques Used in Connection With Random Digits" published in the research journal of the National Bure |
3,979 | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(head) = p? | A solution that never wastes flips, which helps a lot for very-biased coins.
The disadvantage of this algorithm (as written, at least) is that it's using arbitrary-precision arithmetic. Practically, you probably want to use this until integer overflow, and only then throw it away and start over.
Also, you need to know ... | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(he | A solution that never wastes flips, which helps a lot for very-biased coins.
The disadvantage of this algorithm (as written, at least) is that it's using arbitrary-precision arithmetic. Practically, y | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(head) = p?
A solution that never wastes flips, which helps a lot for very-biased coins.
The disadvantage of this algorithm (as written, at least) is that it's using arbitrary-precision arithmetic. Practically, you probably... | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(he
A solution that never wastes flips, which helps a lot for very-biased coins.
The disadvantage of this algorithm (as written, at least) is that it's using arbitrary-precision arithmetic. Practically, y |
3,980 | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(head) = p? | This also only works for $p \neq 1$ and $p \neq 0$.
We first turn the (possibly) unfair coin into a fair coin using the process from NcAdams answer:
Flip the coin twice. If it lands HH or TT, ignore it and flip it twice again.
Now, the coin has equal probability of coming up HT or TH. If it comes up HT, call this H1.... | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(he | This also only works for $p \neq 1$ and $p \neq 0$.
We first turn the (possibly) unfair coin into a fair coin using the process from NcAdams answer:
Flip the coin twice. If it lands HH or TT, ignore | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(head) = p?
This also only works for $p \neq 1$ and $p \neq 0$.
We first turn the (possibly) unfair coin into a fair coin using the process from NcAdams answer:
Flip the coin twice. If it lands HH or TT, ignore it and flip... | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(he
This also only works for $p \neq 1$ and $p \neq 0$.
We first turn the (possibly) unfair coin into a fair coin using the process from NcAdams answer:
Flip the coin twice. If it lands HH or TT, ignore |
3,981 | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(head) = p? | Inspired by AdamO's answer, here is a Python solution that avoids bias:
def roll(p, n):
remaining = range(1,n+1)
flips = 0
while len(remaining) > 1:
round_winners = [c for c in remaining if random.choices(['H','T'], [p, 1.0-p]) == ['H']]
flips += len(remaining)
if len(round_winners) ... | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(he | Inspired by AdamO's answer, here is a Python solution that avoids bias:
def roll(p, n):
remaining = range(1,n+1)
flips = 0
while len(remaining) > 1:
round_winners = [c for c in rem | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(head) = p?
Inspired by AdamO's answer, here is a Python solution that avoids bias:
def roll(p, n):
remaining = range(1,n+1)
flips = 0
while len(remaining) > 1:
round_winners = [c for c in remaining if r... | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(he
Inspired by AdamO's answer, here is a Python solution that avoids bias:
def roll(p, n):
remaining = range(1,n+1)
flips = 0
while len(remaining) > 1:
round_winners = [c for c in rem |
3,982 | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(head) = p? | It appears we are allowed to change the mapping of the outcome of each flip, every time we flip. So, using for convenience the first seven positive integers, we give the following orders:
1st Flip, map $H \to 1$
2nd Flip, map $H \to 2$
...
7th flip, map $H \to 7$
8th flip, map $H \to 1$
etc
Repeat, always in batches ... | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(he | It appears we are allowed to change the mapping of the outcome of each flip, every time we flip. So, using for convenience the first seven positive integers, we give the following orders:
1st Flip, m | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(head) = p?
It appears we are allowed to change the mapping of the outcome of each flip, every time we flip. So, using for convenience the first seven positive integers, we give the following orders:
1st Flip, map $H \to 1... | Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(he
It appears we are allowed to change the mapping of the outcome of each flip, every time we flip. So, using for convenience the first seven positive integers, we give the following orders:
1st Flip, m |
3,983 | Does 10 heads in a row increase the chance of the next toss being a tail? | they are trying to assert that [...] if there have been 10 heads, then the next in the sequence will more likely be a tail because statistics says it will balance out in the end
There's only a "balancing out" in a very particular sense.
If it's a fair coin, then it's still 50-50 at every toss. The coin cannot know its... | Does 10 heads in a row increase the chance of the next toss being a tail? | they are trying to assert that [...] if there have been 10 heads, then the next in the sequence will more likely be a tail because statistics says it will balance out in the end
There's only a "balan | Does 10 heads in a row increase the chance of the next toss being a tail?
they are trying to assert that [...] if there have been 10 heads, then the next in the sequence will more likely be a tail because statistics says it will balance out in the end
There's only a "balancing out" in a very particular sense.
If it's ... | Does 10 heads in a row increase the chance of the next toss being a tail?
they are trying to assert that [...] if there have been 10 heads, then the next in the sequence will more likely be a tail because statistics says it will balance out in the end
There's only a "balan |
3,984 | Does 10 heads in a row increase the chance of the next toss being a tail? | The confusion is because he is looking at the probability from the start without looking at what else has already happened.
Lets simplify things:
First flip:
T
Now the chance of a T was 50%, so 0.5.
The chance that the next flip will be T again is 0.5
TT 0.5
TF 0.5
However, what about the first flip? If we include th... | Does 10 heads in a row increase the chance of the next toss being a tail? | The confusion is because he is looking at the probability from the start without looking at what else has already happened.
Lets simplify things:
First flip:
T
Now the chance of a T was 50%, so 0.5.
| Does 10 heads in a row increase the chance of the next toss being a tail?
The confusion is because he is looking at the probability from the start without looking at what else has already happened.
Lets simplify things:
First flip:
T
Now the chance of a T was 50%, so 0.5.
The chance that the next flip will be T again ... | Does 10 heads in a row increase the chance of the next toss being a tail?
The confusion is because he is looking at the probability from the start without looking at what else has already happened.
Lets simplify things:
First flip:
T
Now the chance of a T was 50%, so 0.5.
|
3,985 | Does 10 heads in a row increase the chance of the next toss being a tail? | The odds are still 50-50 that the next flip will be tails.
Very simple explanation: The odds of flipping 10 heads + 1 tail in that order are very low. But by the time you've flipped 10 heads, you've already beaten most of the odds... you have a 50-50 chance of finishing the sequence with the next coin flip. | Does 10 heads in a row increase the chance of the next toss being a tail? | The odds are still 50-50 that the next flip will be tails.
Very simple explanation: The odds of flipping 10 heads + 1 tail in that order are very low. But by the time you've flipped 10 heads, you've | Does 10 heads in a row increase the chance of the next toss being a tail?
The odds are still 50-50 that the next flip will be tails.
Very simple explanation: The odds of flipping 10 heads + 1 tail in that order are very low. But by the time you've flipped 10 heads, you've already beaten most of the odds... you have a... | Does 10 heads in a row increase the chance of the next toss being a tail?
The odds are still 50-50 that the next flip will be tails.
Very simple explanation: The odds of flipping 10 heads + 1 tail in that order are very low. But by the time you've flipped 10 heads, you've |
3,986 | Does 10 heads in a row increase the chance of the next toss being a tail? | You should try convincing them that if the previous results were to impact the upcoming tosses then not only the last 10 tosses should have been taken into consideration, but also every previous toss in the coin life.
I think it's a more logical approach. | Does 10 heads in a row increase the chance of the next toss being a tail? | You should try convincing them that if the previous results were to impact the upcoming tosses then not only the last 10 tosses should have been taken into consideration, but also every previous toss | Does 10 heads in a row increase the chance of the next toss being a tail?
You should try convincing them that if the previous results were to impact the upcoming tosses then not only the last 10 tosses should have been taken into consideration, but also every previous toss in the coin life.
I think it's a more logical... | Does 10 heads in a row increase the chance of the next toss being a tail?
You should try convincing them that if the previous results were to impact the upcoming tosses then not only the last 10 tosses should have been taken into consideration, but also every previous toss |
3,987 | Does 10 heads in a row increase the chance of the next toss being a tail? | To add to earlier answers, there are two issues here, first, what happens when the count is actually fair and each toss is independent of all other tosses. Then, we have the "law of large numbers", saying that in the limit of an ever increasing sequence of tosses, the frequency of tails will approach probability of ta... | Does 10 heads in a row increase the chance of the next toss being a tail? | To add to earlier answers, there are two issues here, first, what happens when the count is actually fair and each toss is independent of all other tosses. Then, we have the "law of large numbers", s | Does 10 heads in a row increase the chance of the next toss being a tail?
To add to earlier answers, there are two issues here, first, what happens when the count is actually fair and each toss is independent of all other tosses. Then, we have the "law of large numbers", saying that in the limit of an ever increasing ... | Does 10 heads in a row increase the chance of the next toss being a tail?
To add to earlier answers, there are two issues here, first, what happens when the count is actually fair and each toss is independent of all other tosses. Then, we have the "law of large numbers", s |
3,988 | Does 10 heads in a row increase the chance of the next toss being a tail? | This isn't really an answer - your problem is psychological, not mathematical. But it may help.
I often face your "how the hell ..." question. The answers here - mostly correct, are too mathematical for the people you're addressing. One place I start is to try to convince them that flipping one coin 10 times is essenti... | Does 10 heads in a row increase the chance of the next toss being a tail? | This isn't really an answer - your problem is psychological, not mathematical. But it may help.
I often face your "how the hell ..." question. The answers here - mostly correct, are too mathematical f | Does 10 heads in a row increase the chance of the next toss being a tail?
This isn't really an answer - your problem is psychological, not mathematical. But it may help.
I often face your "how the hell ..." question. The answers here - mostly correct, are too mathematical for the people you're addressing. One place I s... | Does 10 heads in a row increase the chance of the next toss being a tail?
This isn't really an answer - your problem is psychological, not mathematical. But it may help.
I often face your "how the hell ..." question. The answers here - mostly correct, are too mathematical f |
3,989 | Does 10 heads in a row increase the chance of the next toss being a tail? | Assuming coin flips are independent, this is very easy to prove from one statistician to another. However, your friend seems to not believe that coin flips are independent. Other than throwing around words that are synonymous with independent (for example, the coin doesn't have a "memory") you can't prove to him that c... | Does 10 heads in a row increase the chance of the next toss being a tail? | Assuming coin flips are independent, this is very easy to prove from one statistician to another. However, your friend seems to not believe that coin flips are independent. Other than throwing around | Does 10 heads in a row increase the chance of the next toss being a tail?
Assuming coin flips are independent, this is very easy to prove from one statistician to another. However, your friend seems to not believe that coin flips are independent. Other than throwing around words that are synonymous with independent (fo... | Does 10 heads in a row increase the chance of the next toss being a tail?
Assuming coin flips are independent, this is very easy to prove from one statistician to another. However, your friend seems to not believe that coin flips are independent. Other than throwing around |
3,990 | Does 10 heads in a row increase the chance of the next toss being a tail? | To restate some of the explanations already given (by @TimB and @James K), once you've flipped a coin 10 times and got 10 heads, the probability of getting 10 heads in a row is exactly 1.0! It's already happened, so the probability of that happening is now fixed.
When you multiply that by the probability of getting he... | Does 10 heads in a row increase the chance of the next toss being a tail? | To restate some of the explanations already given (by @TimB and @James K), once you've flipped a coin 10 times and got 10 heads, the probability of getting 10 heads in a row is exactly 1.0! It's alre | Does 10 heads in a row increase the chance of the next toss being a tail?
To restate some of the explanations already given (by @TimB and @James K), once you've flipped a coin 10 times and got 10 heads, the probability of getting 10 heads in a row is exactly 1.0! It's already happened, so the probability of that happe... | Does 10 heads in a row increase the chance of the next toss being a tail?
To restate some of the explanations already given (by @TimB and @James K), once you've flipped a coin 10 times and got 10 heads, the probability of getting 10 heads in a row is exactly 1.0! It's alre |
3,991 | Does 10 heads in a row increase the chance of the next toss being a tail? | Let's say I'm convinced that the coin is fair. If the coin was fair then the probability of having 10 heads in a row is $$p_{10}=\left(\frac{1}{2}\right)^{10}=\frac{1}{1024}<0.1\%$$
So, as a frequentist at $\alpha=1\%$ significance, I must reject the $H_0$:coin is fair, and conclude that the $H_a$: "something's fishy" ... | Does 10 heads in a row increase the chance of the next toss being a tail? | Let's say I'm convinced that the coin is fair. If the coin was fair then the probability of having 10 heads in a row is $$p_{10}=\left(\frac{1}{2}\right)^{10}=\frac{1}{1024}<0.1\%$$
So, as a frequenti | Does 10 heads in a row increase the chance of the next toss being a tail?
Let's say I'm convinced that the coin is fair. If the coin was fair then the probability of having 10 heads in a row is $$p_{10}=\left(\frac{1}{2}\right)^{10}=\frac{1}{1024}<0.1\%$$
So, as a frequentist at $\alpha=1\%$ significance, I must reject... | Does 10 heads in a row increase the chance of the next toss being a tail?
Let's say I'm convinced that the coin is fair. If the coin was fair then the probability of having 10 heads in a row is $$p_{10}=\left(\frac{1}{2}\right)^{10}=\frac{1}{1024}<0.1\%$$
So, as a frequenti |
3,992 | Does 10 heads in a row increase the chance of the next toss being a tail? | Under ideal circumstances the answer is no. Each throw is independent of what came before. So if this is a truly fair coin then it does not matter. But if you unsure about whether the coin is faulty or not (which could happen in real life), a long sequence of tails may lead one to believe that it is unfair. | Does 10 heads in a row increase the chance of the next toss being a tail? | Under ideal circumstances the answer is no. Each throw is independent of what came before. So if this is a truly fair coin then it does not matter. But if you unsure about whether the coin is faulty o | Does 10 heads in a row increase the chance of the next toss being a tail?
Under ideal circumstances the answer is no. Each throw is independent of what came before. So if this is a truly fair coin then it does not matter. But if you unsure about whether the coin is faulty or not (which could happen in real life), a lon... | Does 10 heads in a row increase the chance of the next toss being a tail?
Under ideal circumstances the answer is no. Each throw is independent of what came before. So if this is a truly fair coin then it does not matter. But if you unsure about whether the coin is faulty o |
3,993 | Does 10 heads in a row increase the chance of the next toss being a tail? | This answer will work for all questions of this sort, including the Monty Hall problem. Simply ask them what they think the odds are of getting a tail after ten heads. Offer to play them for slightly better (to them) but still under 50-50 odds. With any luck they will agree to let a computer do the flipping in which... | Does 10 heads in a row increase the chance of the next toss being a tail? | This answer will work for all questions of this sort, including the Monty Hall problem. Simply ask them what they think the odds are of getting a tail after ten heads. Offer to play them for slightl | Does 10 heads in a row increase the chance of the next toss being a tail?
This answer will work for all questions of this sort, including the Monty Hall problem. Simply ask them what they think the odds are of getting a tail after ten heads. Offer to play them for slightly better (to them) but still under 50-50 odds.... | Does 10 heads in a row increase the chance of the next toss being a tail?
This answer will work for all questions of this sort, including the Monty Hall problem. Simply ask them what they think the odds are of getting a tail after ten heads. Offer to play them for slightl |
3,994 | Does 10 heads in a row increase the chance of the next toss being a tail? | How would you convince them? One way is to show the distribution of outcomes from the exact problem described.
#1,000,000 observations
numObservations <- 1e+6
#11 coin tosses per sample
numCoinTosses <- 11
sampledCoinTosses <- matrix(sample(c(-1,1),numObservations*numCoinTosses,replace=TRUE),
n... | Does 10 heads in a row increase the chance of the next toss being a tail? | How would you convince them? One way is to show the distribution of outcomes from the exact problem described.
#1,000,000 observations
numObservations <- 1e+6
#11 coin tosses per sample
numCoinTosses | Does 10 heads in a row increase the chance of the next toss being a tail?
How would you convince them? One way is to show the distribution of outcomes from the exact problem described.
#1,000,000 observations
numObservations <- 1e+6
#11 coin tosses per sample
numCoinTosses <- 11
sampledCoinTosses <- matrix(sample(c(-1... | Does 10 heads in a row increase the chance of the next toss being a tail?
How would you convince them? One way is to show the distribution of outcomes from the exact problem described.
#1,000,000 observations
numObservations <- 1e+6
#11 coin tosses per sample
numCoinTosses |
3,995 | Does 10 heads in a row increase the chance of the next toss being a tail? | Try like this:
Assume that we already have $10$ heads tosses -- a very very rare event with probability of "being there" of $0.5^{10}$. Now we prepare for one more toss, and think ahead what might happen next:
if tails, we still end up with recording an extremely rare series of events with probability of $0.5^{10}$;
... | Does 10 heads in a row increase the chance of the next toss being a tail? | Try like this:
Assume that we already have $10$ heads tosses -- a very very rare event with probability of "being there" of $0.5^{10}$. Now we prepare for one more toss, and think ahead what might hap | Does 10 heads in a row increase the chance of the next toss being a tail?
Try like this:
Assume that we already have $10$ heads tosses -- a very very rare event with probability of "being there" of $0.5^{10}$. Now we prepare for one more toss, and think ahead what might happen next:
if tails, we still end up with rec... | Does 10 heads in a row increase the chance of the next toss being a tail?
Try like this:
Assume that we already have $10$ heads tosses -- a very very rare event with probability of "being there" of $0.5^{10}$. Now we prepare for one more toss, and think ahead what might hap |
3,996 | How to derive the ridge regression solution? | It suffices to modify the loss function by adding the penalty. In matrix terms, the initial quadratic loss function becomes
$$ (Y - X\beta)^{T}(Y-X\beta) + \lambda \beta^T\beta.$$
Deriving with respect to $\beta$ leads to the normal equation
$$ X^{T}Y = \left(X^{T}X + \lambda I\right)\beta $$
which leads to the Ridge e... | How to derive the ridge regression solution? | It suffices to modify the loss function by adding the penalty. In matrix terms, the initial quadratic loss function becomes
$$ (Y - X\beta)^{T}(Y-X\beta) + \lambda \beta^T\beta.$$
Deriving with respec | How to derive the ridge regression solution?
It suffices to modify the loss function by adding the penalty. In matrix terms, the initial quadratic loss function becomes
$$ (Y - X\beta)^{T}(Y-X\beta) + \lambda \beta^T\beta.$$
Deriving with respect to $\beta$ leads to the normal equation
$$ X^{T}Y = \left(X^{T}X + \lambd... | How to derive the ridge regression solution?
It suffices to modify the loss function by adding the penalty. In matrix terms, the initial quadratic loss function becomes
$$ (Y - X\beta)^{T}(Y-X\beta) + \lambda \beta^T\beta.$$
Deriving with respec |
3,997 | How to derive the ridge regression solution? | Let's build on what we know, which is that whenever the $n\times p$ model matrix is $X$, the response $n$-vector is $y$, and the parameter $p$-vector is $\beta$, the objective function
$$f(\beta) = (y - X\beta)^\prime(y - X\beta)$$
(which is the sum of squares of residuals) is minimized when $\beta$ solves the Normal e... | How to derive the ridge regression solution? | Let's build on what we know, which is that whenever the $n\times p$ model matrix is $X$, the response $n$-vector is $y$, and the parameter $p$-vector is $\beta$, the objective function
$$f(\beta) = (y | How to derive the ridge regression solution?
Let's build on what we know, which is that whenever the $n\times p$ model matrix is $X$, the response $n$-vector is $y$, and the parameter $p$-vector is $\beta$, the objective function
$$f(\beta) = (y - X\beta)^\prime(y - X\beta)$$
(which is the sum of squares of residuals) ... | How to derive the ridge regression solution?
Let's build on what we know, which is that whenever the $n\times p$ model matrix is $X$, the response $n$-vector is $y$, and the parameter $p$-vector is $\beta$, the objective function
$$f(\beta) = (y |
3,998 | How to derive the ridge regression solution? | The derivation includes matrix calculus, which can be quite tedious. We would like solve the following problem:
\begin{equation}
\min_\beta (Y-\beta^T X)^T(Y-\beta^T X)+\lambda \beta^T \beta
\end{equation}
Now note that
\begin{equation}
\frac{\partial (Y-\beta^T X)^T (Y-\beta^T X)}{\partial \beta}=-2X^T(Y-\beta^T X)
\... | How to derive the ridge regression solution? | The derivation includes matrix calculus, which can be quite tedious. We would like solve the following problem:
\begin{equation}
\min_\beta (Y-\beta^T X)^T(Y-\beta^T X)+\lambda \beta^T \beta
\end{equa | How to derive the ridge regression solution?
The derivation includes matrix calculus, which can be quite tedious. We would like solve the following problem:
\begin{equation}
\min_\beta (Y-\beta^T X)^T(Y-\beta^T X)+\lambda \beta^T \beta
\end{equation}
Now note that
\begin{equation}
\frac{\partial (Y-\beta^T X)^T (Y-\be... | How to derive the ridge regression solution?
The derivation includes matrix calculus, which can be quite tedious. We would like solve the following problem:
\begin{equation}
\min_\beta (Y-\beta^T X)^T(Y-\beta^T X)+\lambda \beta^T \beta
\end{equa |
3,999 | How to derive the ridge regression solution? | I have recently stumbled upon the same question in the context of P-Splines and as the concept is the same I want to give a more detailed answer on the derivation of the ridge estimator.
We start with a penalized criterion function that differs from the classic OLS-criterion function by its penalization term in the la... | How to derive the ridge regression solution? | I have recently stumbled upon the same question in the context of P-Splines and as the concept is the same I want to give a more detailed answer on the derivation of the ridge estimator.
We start wit | How to derive the ridge regression solution?
I have recently stumbled upon the same question in the context of P-Splines and as the concept is the same I want to give a more detailed answer on the derivation of the ridge estimator.
We start with a penalized criterion function that differs from the classic OLS-criterio... | How to derive the ridge regression solution?
I have recently stumbled upon the same question in the context of P-Splines and as the concept is the same I want to give a more detailed answer on the derivation of the ridge estimator.
We start wit |
4,000 | How to derive the ridge regression solution? | There are a few important things that are missing in the answers given.
The solution for $\beta$ is derived from the first-order necessary condition: $\frac{\partial f_{ridge}(\beta, \lambda)}{\partial \beta} = 0$ which yields $\beta = (X^TX+ \lambda I )^{-1}X^T Y$. But is this sufficient? That is, the solution is a ... | How to derive the ridge regression solution? | There are a few important things that are missing in the answers given.
The solution for $\beta$ is derived from the first-order necessary condition: $\frac{\partial f_{ridge}(\beta, \lambda)}{\part | How to derive the ridge regression solution?
There are a few important things that are missing in the answers given.
The solution for $\beta$ is derived from the first-order necessary condition: $\frac{\partial f_{ridge}(\beta, \lambda)}{\partial \beta} = 0$ which yields $\beta = (X^TX+ \lambda I )^{-1}X^T Y$. But is... | How to derive the ridge regression solution?
There are a few important things that are missing in the answers given.
The solution for $\beta$ is derived from the first-order necessary condition: $\frac{\partial f_{ridge}(\beta, \lambda)}{\part |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.