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 |
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2,601 | Rules of thumb for minimum sample size for multiple regression | I have found this rather recent paper (2015) assessing that just 2 observations per variable are enough, as long as our interest is on the accuracy of estimated regression coefficients and standard errors (and on the empirical coverage of the resulting confidence intervals) and we use the adjusted $R^2$:
(pdf)
Of cours... | Rules of thumb for minimum sample size for multiple regression | I have found this rather recent paper (2015) assessing that just 2 observations per variable are enough, as long as our interest is on the accuracy of estimated regression coefficients and standard er | Rules of thumb for minimum sample size for multiple regression
I have found this rather recent paper (2015) assessing that just 2 observations per variable are enough, as long as our interest is on the accuracy of estimated regression coefficients and standard errors (and on the empirical coverage of the resulting conf... | Rules of thumb for minimum sample size for multiple regression
I have found this rather recent paper (2015) assessing that just 2 observations per variable are enough, as long as our interest is on the accuracy of estimated regression coefficients and standard er |
2,602 | Skills hard to find in machine learners? | I have seen multiple times developers use ML techniques. This is the usual pattern:
download library with fancy name;
spend 10 mins reading how to use it (skipping any statistics, maths, etc);
feed it with data (no preprocessing);
measure performance (e.g. accuracy even if classes are totally imbalanced) and tell ever... | Skills hard to find in machine learners? | I have seen multiple times developers use ML techniques. This is the usual pattern:
download library with fancy name;
spend 10 mins reading how to use it (skipping any statistics, maths, etc);
feed i | Skills hard to find in machine learners?
I have seen multiple times developers use ML techniques. This is the usual pattern:
download library with fancy name;
spend 10 mins reading how to use it (skipping any statistics, maths, etc);
feed it with data (no preprocessing);
measure performance (e.g. accuracy even if clas... | Skills hard to find in machine learners?
I have seen multiple times developers use ML techniques. This is the usual pattern:
download library with fancy name;
spend 10 mins reading how to use it (skipping any statistics, maths, etc);
feed i |
2,603 | Skills hard to find in machine learners? | What it's about
Just knowing about techniques is akin to knowing the animals in a zoo -- you can name them, describe their properties, perhaps identify them in the wild.
Understanding when to use them, formulating, building, testing, and deploying working mathematical models within an application area while avoiding th... | Skills hard to find in machine learners? | What it's about
Just knowing about techniques is akin to knowing the animals in a zoo -- you can name them, describe their properties, perhaps identify them in the wild.
Understanding when to use them | Skills hard to find in machine learners?
What it's about
Just knowing about techniques is akin to knowing the animals in a zoo -- you can name them, describe their properties, perhaps identify them in the wild.
Understanding when to use them, formulating, building, testing, and deploying working mathematical models wit... | Skills hard to find in machine learners?
What it's about
Just knowing about techniques is akin to knowing the animals in a zoo -- you can name them, describe their properties, perhaps identify them in the wild.
Understanding when to use them |
2,604 | Skills hard to find in machine learners? | I agree with everything that's been said. What stands out for me are:
How few machine learning "experts" are really interested in the subject matter to which they want to apply ML
How few truly understand predictive accuracy and proper scoring rules
How few understand principles of validation
How few know when to use... | Skills hard to find in machine learners? | I agree with everything that's been said. What stands out for me are:
How few machine learning "experts" are really interested in the subject matter to which they want to apply ML
How few truly unde | Skills hard to find in machine learners?
I agree with everything that's been said. What stands out for me are:
How few machine learning "experts" are really interested in the subject matter to which they want to apply ML
How few truly understand predictive accuracy and proper scoring rules
How few understand principl... | Skills hard to find in machine learners?
I agree with everything that's been said. What stands out for me are:
How few machine learning "experts" are really interested in the subject matter to which they want to apply ML
How few truly unde |
2,605 | Skills hard to find in machine learners? | Here are a couple of things to make you stand out from the crowd:
Understand the application domain or domains. That is, the business environment or other context.
Understand the big picture. This is very important! People who study machine learning often get lost in the details. Think about the overall picture that y... | Skills hard to find in machine learners? | Here are a couple of things to make you stand out from the crowd:
Understand the application domain or domains. That is, the business environment or other context.
Understand the big picture. This is | Skills hard to find in machine learners?
Here are a couple of things to make you stand out from the crowd:
Understand the application domain or domains. That is, the business environment or other context.
Understand the big picture. This is very important! People who study machine learning often get lost in the detail... | Skills hard to find in machine learners?
Here are a couple of things to make you stand out from the crowd:
Understand the application domain or domains. That is, the business environment or other context.
Understand the big picture. This is |
2,606 | Skills hard to find in machine learners? | I would put out there the notion of "soft skills".
recognising who the "expert" is for method X, and being able to tap into their knowledge (you shouldn't be able to or expected to know everything about erything). The ability and willingness to collaborate with others.
the ability to translate or represent "the real ... | Skills hard to find in machine learners? | I would put out there the notion of "soft skills".
recognising who the "expert" is for method X, and being able to tap into their knowledge (you shouldn't be able to or expected to know everything ab | Skills hard to find in machine learners?
I would put out there the notion of "soft skills".
recognising who the "expert" is for method X, and being able to tap into their knowledge (you shouldn't be able to or expected to know everything about erything). The ability and willingness to collaborate with others.
the abi... | Skills hard to find in machine learners?
I would put out there the notion of "soft skills".
recognising who the "expert" is for method X, and being able to tap into their knowledge (you shouldn't be able to or expected to know everything ab |
2,607 | Skills hard to find in machine learners? | Being able to generalize well
This is the essence of a good model. And it is the essence of what makes the best practitioners of the art of machine learning stand out from the crowd.
Understanding that the goal is to maximize performance on unseen data, i.e minimize generalization error, not to minimize training error... | Skills hard to find in machine learners? | Being able to generalize well
This is the essence of a good model. And it is the essence of what makes the best practitioners of the art of machine learning stand out from the crowd.
Understanding th | Skills hard to find in machine learners?
Being able to generalize well
This is the essence of a good model. And it is the essence of what makes the best practitioners of the art of machine learning stand out from the crowd.
Understanding that the goal is to maximize performance on unseen data, i.e minimize generalizat... | Skills hard to find in machine learners?
Being able to generalize well
This is the essence of a good model. And it is the essence of what makes the best practitioners of the art of machine learning stand out from the crowd.
Understanding th |
2,608 | Skills hard to find in machine learners? | The skill that sets one data miner apart from others is the ability to interpret machine learning models. Most build a machine, report the error and then stop. What are the mathematical relationships between the features? Are the effects additive or non-additive or both? Are any of the features irrelevant? Is the machi... | Skills hard to find in machine learners? | The skill that sets one data miner apart from others is the ability to interpret machine learning models. Most build a machine, report the error and then stop. What are the mathematical relationships | Skills hard to find in machine learners?
The skill that sets one data miner apart from others is the ability to interpret machine learning models. Most build a machine, report the error and then stop. What are the mathematical relationships between the features? Are the effects additive or non-additive or both? Are any... | Skills hard to find in machine learners?
The skill that sets one data miner apart from others is the ability to interpret machine learning models. Most build a machine, report the error and then stop. What are the mathematical relationships |
2,609 | Skills hard to find in machine learners? | Having done scientific research in Machine learning / Statistical pattern recognition for 17 years - I can come up with a few skills that make a wanted-for data scientist stand out from others.
Machine learning is about:
Achieving the algorithmic knowledge of learning algorithms out there, and getting the skill of how... | Skills hard to find in machine learners? | Having done scientific research in Machine learning / Statistical pattern recognition for 17 years - I can come up with a few skills that make a wanted-for data scientist stand out from others.
Machin | Skills hard to find in machine learners?
Having done scientific research in Machine learning / Statistical pattern recognition for 17 years - I can come up with a few skills that make a wanted-for data scientist stand out from others.
Machine learning is about:
Achieving the algorithmic knowledge of learning algorithm... | Skills hard to find in machine learners?
Having done scientific research in Machine learning / Statistical pattern recognition for 17 years - I can come up with a few skills that make a wanted-for data scientist stand out from others.
Machin |
2,610 | Skills hard to find in machine learners? | I see there are two parts while handling machine learning in practice
Engineering ( which covers all the algorithms, learning different packages, programming).
Curiosity/Reasoning (ability to ask better questions to data).
I think 'curiosity/reasoning' is the skill which distinguishes one from others.
For example, i... | Skills hard to find in machine learners? | I see there are two parts while handling machine learning in practice
Engineering ( which covers all the algorithms, learning different packages, programming).
Curiosity/Reasoning (ability to ask bet | Skills hard to find in machine learners?
I see there are two parts while handling machine learning in practice
Engineering ( which covers all the algorithms, learning different packages, programming).
Curiosity/Reasoning (ability to ask better questions to data).
I think 'curiosity/reasoning' is the skill which dist... | Skills hard to find in machine learners?
I see there are two parts while handling machine learning in practice
Engineering ( which covers all the algorithms, learning different packages, programming).
Curiosity/Reasoning (ability to ask bet |
2,611 | What is the advantages of Wasserstein metric compared to Kullback-Leibler divergence? | When considering the advantages of Wasserstein metric compared to KL divergence, then the most obvious one is that W is a metric whereas KL divergence is not, since KL is not symmetric (i.e. $D_{KL}(P||Q) \neq D_{KL}(Q||P)$ in general) and does not satisfy the triangle inequality (i.e. $D_{KL}(R||P) \leq D_{KL}(Q||P) +... | What is the advantages of Wasserstein metric compared to Kullback-Leibler divergence? | When considering the advantages of Wasserstein metric compared to KL divergence, then the most obvious one is that W is a metric whereas KL divergence is not, since KL is not symmetric (i.e. $D_{KL}(P | What is the advantages of Wasserstein metric compared to Kullback-Leibler divergence?
When considering the advantages of Wasserstein metric compared to KL divergence, then the most obvious one is that W is a metric whereas KL divergence is not, since KL is not symmetric (i.e. $D_{KL}(P||Q) \neq D_{KL}(Q||P)$ in general... | What is the advantages of Wasserstein metric compared to Kullback-Leibler divergence?
When considering the advantages of Wasserstein metric compared to KL divergence, then the most obvious one is that W is a metric whereas KL divergence is not, since KL is not symmetric (i.e. $D_{KL}(P |
2,612 | What is the advantages of Wasserstein metric compared to Kullback-Leibler divergence? | Wasserstein metric most commonly appears in optimal transport problems where the goal is to move things from a given configuration to a desired configuration in the minimum cost or minimum distance. The Kullback-Leibler (KL) is a divergence (not a metric) and shows up very often in statistics, machine learning, and inf... | What is the advantages of Wasserstein metric compared to Kullback-Leibler divergence? | Wasserstein metric most commonly appears in optimal transport problems where the goal is to move things from a given configuration to a desired configuration in the minimum cost or minimum distance. T | What is the advantages of Wasserstein metric compared to Kullback-Leibler divergence?
Wasserstein metric most commonly appears in optimal transport problems where the goal is to move things from a given configuration to a desired configuration in the minimum cost or minimum distance. The Kullback-Leibler (KL) is a dive... | What is the advantages of Wasserstein metric compared to Kullback-Leibler divergence?
Wasserstein metric most commonly appears in optimal transport problems where the goal is to move things from a given configuration to a desired configuration in the minimum cost or minimum distance. T |
2,613 | What is the advantages of Wasserstein metric compared to Kullback-Leibler divergence? | The Wasserstein metric is useful in validation of models as its units are that of the response itself. For example, if you are comparing two stochastic representations of the same system (e.g. a reduced-order-model), $P$ and $Q$, and the response is units of displacement, the Wasserstein metric is also in units of disp... | What is the advantages of Wasserstein metric compared to Kullback-Leibler divergence? | The Wasserstein metric is useful in validation of models as its units are that of the response itself. For example, if you are comparing two stochastic representations of the same system (e.g. a reduc | What is the advantages of Wasserstein metric compared to Kullback-Leibler divergence?
The Wasserstein metric is useful in validation of models as its units are that of the response itself. For example, if you are comparing two stochastic representations of the same system (e.g. a reduced-order-model), $P$ and $Q$, and ... | What is the advantages of Wasserstein metric compared to Kullback-Leibler divergence?
The Wasserstein metric is useful in validation of models as its units are that of the response itself. For example, if you are comparing two stochastic representations of the same system (e.g. a reduc |
2,614 | What is the advantages of Wasserstein metric compared to Kullback-Leibler divergence? | As an extension for the answer from antiquity regarding scipy.stats.wasserstein_distance: If you have already binned data with given bin-distances, you can use u_weights and v_weights. Assuming your data is equidistant binned:
from scipy.stats import wasserstein_distance
wasserstein_distance(sampP, sampQ)
>> 2.0
wass... | What is the advantages of Wasserstein metric compared to Kullback-Leibler divergence? | As an extension for the answer from antiquity regarding scipy.stats.wasserstein_distance: If you have already binned data with given bin-distances, you can use u_weights and v_weights. Assuming your d | What is the advantages of Wasserstein metric compared to Kullback-Leibler divergence?
As an extension for the answer from antiquity regarding scipy.stats.wasserstein_distance: If you have already binned data with given bin-distances, you can use u_weights and v_weights. Assuming your data is equidistant binned:
from sc... | What is the advantages of Wasserstein metric compared to Kullback-Leibler divergence?
As an extension for the answer from antiquity regarding scipy.stats.wasserstein_distance: If you have already binned data with given bin-distances, you can use u_weights and v_weights. Assuming your d |
2,615 | What is the advantages of Wasserstein metric compared to Kullback-Leibler divergence? | Wasserstein metric has a main drawback relative to invariance.
For instance, for homogeneous domains as simple as Poincaré upper half plane, wasserstein metric is not invariant wrt the automorphism of this space . Then, only Fisher metric from Information Geometry is valid and its extension by Jean-Louis Koszul and Je... | What is the advantages of Wasserstein metric compared to Kullback-Leibler divergence? | Wasserstein metric has a main drawback relative to invariance.
For instance, for homogeneous domains as simple as Poincaré upper half plane, wasserstein metric is not invariant wrt the automorphism of | What is the advantages of Wasserstein metric compared to Kullback-Leibler divergence?
Wasserstein metric has a main drawback relative to invariance.
For instance, for homogeneous domains as simple as Poincaré upper half plane, wasserstein metric is not invariant wrt the automorphism of this space . Then, only Fisher m... | What is the advantages of Wasserstein metric compared to Kullback-Leibler divergence?
Wasserstein metric has a main drawback relative to invariance.
For instance, for homogeneous domains as simple as Poincaré upper half plane, wasserstein metric is not invariant wrt the automorphism of |
2,616 | Reduce Classification Probability Threshold | Frank Harrell has written about this on his blog: Classification vs. Prediction, which I agree with wholeheartedly.
Essentially, his argument is that the statistical component of your exercise ends when you output a probability for each class of your new sample. Choosing a threshold beyond which you classify a new obse... | Reduce Classification Probability Threshold | Frank Harrell has written about this on his blog: Classification vs. Prediction, which I agree with wholeheartedly.
Essentially, his argument is that the statistical component of your exercise ends wh | Reduce Classification Probability Threshold
Frank Harrell has written about this on his blog: Classification vs. Prediction, which I agree with wholeheartedly.
Essentially, his argument is that the statistical component of your exercise ends when you output a probability for each class of your new sample. Choosing a th... | Reduce Classification Probability Threshold
Frank Harrell has written about this on his blog: Classification vs. Prediction, which I agree with wholeheartedly.
Essentially, his argument is that the statistical component of your exercise ends wh |
2,617 | Reduce Classification Probability Threshold | Stephan's answer is great. It fundamentally depends on what you want to do with the classifier.
Just adding a few examples.
A way to find the best threshold is to define an objective function. For binary classification, this can be accuracy or F1-score for example. Depending on which you choose, the best threshold will... | Reduce Classification Probability Threshold | Stephan's answer is great. It fundamentally depends on what you want to do with the classifier.
Just adding a few examples.
A way to find the best threshold is to define an objective function. For bin | Reduce Classification Probability Threshold
Stephan's answer is great. It fundamentally depends on what you want to do with the classifier.
Just adding a few examples.
A way to find the best threshold is to define an objective function. For binary classification, this can be accuracy or F1-score for example. Depending ... | Reduce Classification Probability Threshold
Stephan's answer is great. It fundamentally depends on what you want to do with the classifier.
Just adding a few examples.
A way to find the best threshold is to define an objective function. For bin |
2,618 | Reduce Classification Probability Threshold | There is possibly some value in considering how the probability is calculated. These days, Classifiers use a bias vector, which is multiplied by a matrix (linear algebra). As long as there are any non-zero values in the vector, the probability (the product of the vector and the matrix) will never be 0.
This causes con... | Reduce Classification Probability Threshold | There is possibly some value in considering how the probability is calculated. These days, Classifiers use a bias vector, which is multiplied by a matrix (linear algebra). As long as there are any no | Reduce Classification Probability Threshold
There is possibly some value in considering how the probability is calculated. These days, Classifiers use a bias vector, which is multiplied by a matrix (linear algebra). As long as there are any non-zero values in the vector, the probability (the product of the vector and ... | Reduce Classification Probability Threshold
There is possibly some value in considering how the probability is calculated. These days, Classifiers use a bias vector, which is multiplied by a matrix (linear algebra). As long as there are any no |
2,619 | Reduce Classification Probability Threshold | There is no wrong threshold. The threshold you choose depends of your objective in your prediction, or rather what you want to favor, for example precision versus recall (try to graph it and measure its associated AUC to compare different classification models of your choosing).
I am giving you this example of precisi... | Reduce Classification Probability Threshold | There is no wrong threshold. The threshold you choose depends of your objective in your prediction, or rather what you want to favor, for example precision versus recall (try to graph it and measure i | Reduce Classification Probability Threshold
There is no wrong threshold. The threshold you choose depends of your objective in your prediction, or rather what you want to favor, for example precision versus recall (try to graph it and measure its associated AUC to compare different classification models of your choosin... | Reduce Classification Probability Threshold
There is no wrong threshold. The threshold you choose depends of your objective in your prediction, or rather what you want to favor, for example precision versus recall (try to graph it and measure i |
2,620 | XKCD's modified Bayes theorem: actually kinda reasonable? | Well by distributing the $P(H)$ term, we obtain
$$
P(H|X) = \frac{P(X|H)P(H)}{P(X)} P(C) + P(H) [1 - P(C)],
$$
which we can interpret as the Law of Total Probability applied to the event $C =$ "you are using Bayesian statistics correctly." So if you are using Bayesian statistics correctly, then you recover Bayes' law (... | XKCD's modified Bayes theorem: actually kinda reasonable? | Well by distributing the $P(H)$ term, we obtain
$$
P(H|X) = \frac{P(X|H)P(H)}{P(X)} P(C) + P(H) [1 - P(C)],
$$
which we can interpret as the Law of Total Probability applied to the event $C =$ "you ar | XKCD's modified Bayes theorem: actually kinda reasonable?
Well by distributing the $P(H)$ term, we obtain
$$
P(H|X) = \frac{P(X|H)P(H)}{P(X)} P(C) + P(H) [1 - P(C)],
$$
which we can interpret as the Law of Total Probability applied to the event $C =$ "you are using Bayesian statistics correctly." So if you are using Ba... | XKCD's modified Bayes theorem: actually kinda reasonable?
Well by distributing the $P(H)$ term, we obtain
$$
P(H|X) = \frac{P(X|H)P(H)}{P(X)} P(C) + P(H) [1 - P(C)],
$$
which we can interpret as the Law of Total Probability applied to the event $C =$ "you ar |
2,621 | XKCD's modified Bayes theorem: actually kinda reasonable? | Believe it or not, this type of model does pop up every now and then in very serious statistical models, especially when dealing with data fusion, i.e., trying to combine inference from multiple sensors trying to make inference on a single event.
If a sensor malfunctions, it can greatly bias the inference made when tr... | XKCD's modified Bayes theorem: actually kinda reasonable? | Believe it or not, this type of model does pop up every now and then in very serious statistical models, especially when dealing with data fusion, i.e., trying to combine inference from multiple senso | XKCD's modified Bayes theorem: actually kinda reasonable?
Believe it or not, this type of model does pop up every now and then in very serious statistical models, especially when dealing with data fusion, i.e., trying to combine inference from multiple sensors trying to make inference on a single event.
If a sensor ma... | XKCD's modified Bayes theorem: actually kinda reasonable?
Believe it or not, this type of model does pop up every now and then in very serious statistical models, especially when dealing with data fusion, i.e., trying to combine inference from multiple senso |
2,622 | How to use Pearson correlation correctly with time series | Pearson correlation is used to look at correlation between series ... but being time series the correlation is looked at across different lags -- the cross-correlation function.
The cross-correlation is impacted by dependence within-series, so in many cases the within-series dependence should be removed first. So to us... | How to use Pearson correlation correctly with time series | Pearson correlation is used to look at correlation between series ... but being time series the correlation is looked at across different lags -- the cross-correlation function.
The cross-correlation | How to use Pearson correlation correctly with time series
Pearson correlation is used to look at correlation between series ... but being time series the correlation is looked at across different lags -- the cross-correlation function.
The cross-correlation is impacted by dependence within-series, so in many cases the ... | How to use Pearson correlation correctly with time series
Pearson correlation is used to look at correlation between series ... but being time series the correlation is looked at across different lags -- the cross-correlation function.
The cross-correlation |
2,623 | How to use Pearson correlation correctly with time series | To complete the answer of Glen_b and his/her example on random walks, if you really want to use Pearson correlation on this kind of time series $(S_t)_{1 \leq t \leq T}$, you should first differentiate them, then work out the correlation coefficient on the increments ($X_t = S_t - S_{t-1}$) which are (in the case of ra... | How to use Pearson correlation correctly with time series | To complete the answer of Glen_b and his/her example on random walks, if you really want to use Pearson correlation on this kind of time series $(S_t)_{1 \leq t \leq T}$, you should first differentiat | How to use Pearson correlation correctly with time series
To complete the answer of Glen_b and his/her example on random walks, if you really want to use Pearson correlation on this kind of time series $(S_t)_{1 \leq t \leq T}$, you should first differentiate them, then work out the correlation coefficient on the incre... | How to use Pearson correlation correctly with time series
To complete the answer of Glen_b and his/her example on random walks, if you really want to use Pearson correlation on this kind of time series $(S_t)_{1 \leq t \leq T}$, you should first differentiat |
2,624 | How to use Pearson correlation correctly with time series | Time series data is usually dependent on time. Pearson correlation, however, is appropriate for independent data. This problem is similar to the so called spurious regression. The coefficient is likely to be highly significant but this comes only from the time trend of the data that affects both series. I recommend to ... | How to use Pearson correlation correctly with time series | Time series data is usually dependent on time. Pearson correlation, however, is appropriate for independent data. This problem is similar to the so called spurious regression. The coefficient is likel | How to use Pearson correlation correctly with time series
Time series data is usually dependent on time. Pearson correlation, however, is appropriate for independent data. This problem is similar to the so called spurious regression. The coefficient is likely to be highly significant but this comes only from the time t... | How to use Pearson correlation correctly with time series
Time series data is usually dependent on time. Pearson correlation, however, is appropriate for independent data. This problem is similar to the so called spurious regression. The coefficient is likel |
2,625 | What is the difference between ZCA whitening and PCA whitening? | Let your (centered) data be stored in a $n\times d$ matrix $\mathbf X$ with $d$ features (variables) in columns and $n$ data points in rows. Let the covariance matrix $\mathbf C=\mathbf X^\top \mathbf X/n$ have eigenvectors in columns of $\mathbf E$ and eigenvalues on the diagonal of $\mathbf D$, so that $\mathbf C = \... | What is the difference between ZCA whitening and PCA whitening? | Let your (centered) data be stored in a $n\times d$ matrix $\mathbf X$ with $d$ features (variables) in columns and $n$ data points in rows. Let the covariance matrix $\mathbf C=\mathbf X^\top \mathbf | What is the difference between ZCA whitening and PCA whitening?
Let your (centered) data be stored in a $n\times d$ matrix $\mathbf X$ with $d$ features (variables) in columns and $n$ data points in rows. Let the covariance matrix $\mathbf C=\mathbf X^\top \mathbf X/n$ have eigenvectors in columns of $\mathbf E$ and ei... | What is the difference between ZCA whitening and PCA whitening?
Let your (centered) data be stored in a $n\times d$ matrix $\mathbf X$ with $d$ features (variables) in columns and $n$ data points in rows. Let the covariance matrix $\mathbf C=\mathbf X^\top \mathbf |
2,626 | What is the difference between ZCA whitening and PCA whitening? | Given an Eigendecomposition of a covariance matrix
$$
\bar{X}\bar{X}^T = LDL^T
$$
where $D = \text{diag}(\lambda_1, \lambda_2, \dots, \lambda_n)$ is the diagonal matrix of Eigenvalues, ordinary whitening resorts to transforming the data into a space where the covariance matrix is diagonal:
$$\sqrt{D^{-1}}L^{-1}\bar{X}\... | What is the difference between ZCA whitening and PCA whitening? | Given an Eigendecomposition of a covariance matrix
$$
\bar{X}\bar{X}^T = LDL^T
$$
where $D = \text{diag}(\lambda_1, \lambda_2, \dots, \lambda_n)$ is the diagonal matrix of Eigenvalues, ordinary whiten | What is the difference between ZCA whitening and PCA whitening?
Given an Eigendecomposition of a covariance matrix
$$
\bar{X}\bar{X}^T = LDL^T
$$
where $D = \text{diag}(\lambda_1, \lambda_2, \dots, \lambda_n)$ is the diagonal matrix of Eigenvalues, ordinary whitening resorts to transforming the data into a space where ... | What is the difference between ZCA whitening and PCA whitening?
Given an Eigendecomposition of a covariance matrix
$$
\bar{X}\bar{X}^T = LDL^T
$$
where $D = \text{diag}(\lambda_1, \lambda_2, \dots, \lambda_n)$ is the diagonal matrix of Eigenvalues, ordinary whiten |
2,627 | What is the difference between ZCA whitening and PCA whitening? | I'll add the following plot to illustrate visually the difference between PCA-whitening and ZCA-whitening : the only thing you need to understand is what a rotation matrix is (aka orthonormal matrix), and that PCA-whitening and ZCA-whitening are just one rotation appart.
First plot is the raw data, along 2 arrows on X... | What is the difference between ZCA whitening and PCA whitening? | I'll add the following plot to illustrate visually the difference between PCA-whitening and ZCA-whitening : the only thing you need to understand is what a rotation matrix is (aka orthonormal matrix), | What is the difference between ZCA whitening and PCA whitening?
I'll add the following plot to illustrate visually the difference between PCA-whitening and ZCA-whitening : the only thing you need to understand is what a rotation matrix is (aka orthonormal matrix), and that PCA-whitening and ZCA-whitening are just one r... | What is the difference between ZCA whitening and PCA whitening?
I'll add the following plot to illustrate visually the difference between PCA-whitening and ZCA-whitening : the only thing you need to understand is what a rotation matrix is (aka orthonormal matrix), |
2,628 | What is regularization in plain english? | In simple terms, regularization is tuning or selecting the preferred level of model complexity so your models are better at predicting (generalizing). If you don't do this your models may be too complex and overfit or too simple and underfit, either way giving poor predictions.
If you least-squares fit a complex model ... | What is regularization in plain english? | In simple terms, regularization is tuning or selecting the preferred level of model complexity so your models are better at predicting (generalizing). If you don't do this your models may be too compl | What is regularization in plain english?
In simple terms, regularization is tuning or selecting the preferred level of model complexity so your models are better at predicting (generalizing). If you don't do this your models may be too complex and overfit or too simple and underfit, either way giving poor predictions.
... | What is regularization in plain english?
In simple terms, regularization is tuning or selecting the preferred level of model complexity so your models are better at predicting (generalizing). If you don't do this your models may be too compl |
2,629 | What is regularization in plain english? | Suppose you perform learning via empirical risk minimization.
More precisely:
you have got your non-negative loss function $L(\text{actual value},\text{ predicted value})$ which characterize how bad your predictions are
you want to fit your model in a such way that its predictions minimize mean of loss function, cal... | What is regularization in plain english? | Suppose you perform learning via empirical risk minimization.
More precisely:
you have got your non-negative loss function $L(\text{actual value},\text{ predicted value})$ which characterize how ba | What is regularization in plain english?
Suppose you perform learning via empirical risk minimization.
More precisely:
you have got your non-negative loss function $L(\text{actual value},\text{ predicted value})$ which characterize how bad your predictions are
you want to fit your model in a such way that its predic... | What is regularization in plain english?
Suppose you perform learning via empirical risk minimization.
More precisely:
you have got your non-negative loss function $L(\text{actual value},\text{ predicted value})$ which characterize how ba |
2,630 | What is regularization in plain english? | Put in simple terms, regularization is about benefiting the solutions you'd expect to get. As you mention, for example you can benefit "simple" solutions, for some definition of simplicity. If your problem has rules, one definition can be fewer rules. But this is problem-dependent.
You're asking the right question, how... | What is regularization in plain english? | Put in simple terms, regularization is about benefiting the solutions you'd expect to get. As you mention, for example you can benefit "simple" solutions, for some definition of simplicity. If your pr | What is regularization in plain english?
Put in simple terms, regularization is about benefiting the solutions you'd expect to get. As you mention, for example you can benefit "simple" solutions, for some definition of simplicity. If your problem has rules, one definition can be fewer rules. But this is problem-depende... | What is regularization in plain english?
Put in simple terms, regularization is about benefiting the solutions you'd expect to get. As you mention, for example you can benefit "simple" solutions, for some definition of simplicity. If your pr |
2,631 | What is regularization in plain english? | Regularization techniques are techniques applied to machine learning models which make the decision boundary / fitted model smoother. Those techniques help to prevent overfitting.
Examples: L1, L2, Dropout, Weight Decay in Neural Networks. Parameter $C$ in SVMs. | What is regularization in plain english? | Regularization techniques are techniques applied to machine learning models which make the decision boundary / fitted model smoother. Those techniques help to prevent overfitting.
Examples: L1, L2, Dr | What is regularization in plain english?
Regularization techniques are techniques applied to machine learning models which make the decision boundary / fitted model smoother. Those techniques help to prevent overfitting.
Examples: L1, L2, Dropout, Weight Decay in Neural Networks. Parameter $C$ in SVMs. | What is regularization in plain english?
Regularization techniques are techniques applied to machine learning models which make the decision boundary / fitted model smoother. Those techniques help to prevent overfitting.
Examples: L1, L2, Dr |
2,632 | What is regularization in plain english? | In simple term, Regularization is a technique to avoid over-fitting when training machine learning algorithms.
If you have an algorithm with enough free parameters you can interpolate with great detail your sample, but examples coming outside the sample might not follow this detail interpolation as it just captured no... | What is regularization in plain english? | In simple term, Regularization is a technique to avoid over-fitting when training machine learning algorithms.
If you have an algorithm with enough free parameters you can interpolate with great deta | What is regularization in plain english?
In simple term, Regularization is a technique to avoid over-fitting when training machine learning algorithms.
If you have an algorithm with enough free parameters you can interpolate with great detail your sample, but examples coming outside the sample might not follow this de... | What is regularization in plain english?
In simple term, Regularization is a technique to avoid over-fitting when training machine learning algorithms.
If you have an algorithm with enough free parameters you can interpolate with great deta |
2,633 | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a linear algebra problem (with eigenvectors)? | Problem statement
The geometric problem that PCA is trying to optimize is clear to me: PCA tries to find the first principal component by minimizing the reconstruction (projection) error, which simultaneously maximizes the variance of the projected data.
That's right. I explain the connection between these two formul... | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a li | Problem statement
The geometric problem that PCA is trying to optimize is clear to me: PCA tries to find the first principal component by minimizing the reconstruction (projection) error, which simul | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a linear algebra problem (with eigenvectors)?
Problem statement
The geometric problem that PCA is trying to optimize is clear to me: PCA tries to find the first principal component by minimizing the reconstruction (projecti... | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a li
Problem statement
The geometric problem that PCA is trying to optimize is clear to me: PCA tries to find the first principal component by minimizing the reconstruction (projection) error, which simul |
2,634 | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a linear algebra problem (with eigenvectors)? | This is my take on the linear algebra behind PCA. In linear algebra, one of the key theorems is the Spectral Theorem. It states if S is any symmetric n by n matrix with real coefficients, then S has n eigenvectors with all the eigenvalues being real. That means we can write $S = ADA^{-1} $ with D a diagonal matrix ... | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a li | This is my take on the linear algebra behind PCA. In linear algebra, one of the key theorems is the Spectral Theorem. It states if S is any symmetric n by n matrix with real coefficients, then S ha | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a linear algebra problem (with eigenvectors)?
This is my take on the linear algebra behind PCA. In linear algebra, one of the key theorems is the Spectral Theorem. It states if S is any symmetric n by n matrix with real c... | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a li
This is my take on the linear algebra behind PCA. In linear algebra, one of the key theorems is the Spectral Theorem. It states if S is any symmetric n by n matrix with real coefficients, then S ha |
2,635 | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a linear algebra problem (with eigenvectors)? | There is a result from 1936 by Eckart and Young (https://ccrma.stanford.edu/~dattorro/eckart%26young.1936.pdf), which states the following
$\sum_1^r d_k u_k v_k^T = arg min_{\hat{X} \epsilon M(r)} ||X-\hat{X}||_F^2$
where M(r) is the set of rank-r matrices, which basically means first r components of SVD of X gives the... | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a li | There is a result from 1936 by Eckart and Young (https://ccrma.stanford.edu/~dattorro/eckart%26young.1936.pdf), which states the following
$\sum_1^r d_k u_k v_k^T = arg min_{\hat{X} \epsilon M(r)} ||X | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a linear algebra problem (with eigenvectors)?
There is a result from 1936 by Eckart and Young (https://ccrma.stanford.edu/~dattorro/eckart%26young.1936.pdf), which states the following
$\sum_1^r d_k u_k v_k^T = arg min_{\hat... | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a li
There is a result from 1936 by Eckart and Young (https://ccrma.stanford.edu/~dattorro/eckart%26young.1936.pdf), which states the following
$\sum_1^r d_k u_k v_k^T = arg min_{\hat{X} \epsilon M(r)} ||X |
2,636 | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a linear algebra problem (with eigenvectors)? | " which simultaneously maximizes the variance of the projected data." Have you hear of Rayleigh quotient? Maybe that's one way of seeing this. Namely the rayleigh quotient of the covariance matrix gives you the variance of the projected data. (and the wiki page explains why eigenvectors maximise the Rayleigh quotient... | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a li | " which simultaneously maximizes the variance of the projected data." Have you hear of Rayleigh quotient? Maybe that's one way of seeing this. Namely the rayleigh quotient of the covariance matrix g | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a linear algebra problem (with eigenvectors)?
" which simultaneously maximizes the variance of the projected data." Have you hear of Rayleigh quotient? Maybe that's one way of seeing this. Namely the rayleigh quotient of t... | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a li
" which simultaneously maximizes the variance of the projected data." Have you hear of Rayleigh quotient? Maybe that's one way of seeing this. Namely the rayleigh quotient of the covariance matrix g |
2,637 | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a linear algebra problem (with eigenvectors)? | Lagrange multipliers are fine but you don't actually need that to get a decent intuitive picture of why eigenvectors maximize the variance (the projected lengths).
So we want to find the unit length $w$ such that $\|Aw\|$ is maximal, where $A$ is the centered data matrix and $\frac{A^TA}{n} = C$ is our covariance matri... | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a li | Lagrange multipliers are fine but you don't actually need that to get a decent intuitive picture of why eigenvectors maximize the variance (the projected lengths).
So we want to find the unit length $ | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a linear algebra problem (with eigenvectors)?
Lagrange multipliers are fine but you don't actually need that to get a decent intuitive picture of why eigenvectors maximize the variance (the projected lengths).
So we want to ... | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a li
Lagrange multipliers are fine but you don't actually need that to get a decent intuitive picture of why eigenvectors maximize the variance (the projected lengths).
So we want to find the unit length $ |
2,638 | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a linear algebra problem (with eigenvectors)? | @amoeba gives neat formalization and proof of:
We can formalize it as follows: given the covariance matrix C, we are looking for a vector w having unit length, ‖w‖=1, such that wTCw is maximal.
But I think there is one intuitive proof to:
It turns out that the first principal direction is given by the eigenvector wi... | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a li | @amoeba gives neat formalization and proof of:
We can formalize it as follows: given the covariance matrix C, we are looking for a vector w having unit length, ‖w‖=1, such that wTCw is maximal.
But | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a linear algebra problem (with eigenvectors)?
@amoeba gives neat formalization and proof of:
We can formalize it as follows: given the covariance matrix C, we are looking for a vector w having unit length, ‖w‖=1, such that ... | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a li
@amoeba gives neat formalization and proof of:
We can formalize it as follows: given the covariance matrix C, we are looking for a vector w having unit length, ‖w‖=1, such that wTCw is maximal.
But |
2,639 | How to interpret coefficients in a Poisson regression? | The exponentiated numberofdrugs coefficient is the multiplicative term to use for the goal of calculating the estimated healthvalue when numberofdrugs increases by 1 unit. In the case of categorical (factor) variables, the exponentiated coefficient is the multiplicative term relative to the base (first factor) level fo... | How to interpret coefficients in a Poisson regression? | The exponentiated numberofdrugs coefficient is the multiplicative term to use for the goal of calculating the estimated healthvalue when numberofdrugs increases by 1 unit. In the case of categorical ( | How to interpret coefficients in a Poisson regression?
The exponentiated numberofdrugs coefficient is the multiplicative term to use for the goal of calculating the estimated healthvalue when numberofdrugs increases by 1 unit. In the case of categorical (factor) variables, the exponentiated coefficient is the multiplic... | How to interpret coefficients in a Poisson regression?
The exponentiated numberofdrugs coefficient is the multiplicative term to use for the goal of calculating the estimated healthvalue when numberofdrugs increases by 1 unit. In the case of categorical ( |
2,640 | Using principal component analysis (PCA) for feature selection | The basic idea when using PCA as a tool for feature selection is to select variables according to the magnitude (from largest to smallest in absolute values) of their coefficients (loadings). You may recall that PCA seeks to replace $p$ (more or less correlated) variables by $k<p$ uncorrelated linear combinations (proj... | Using principal component analysis (PCA) for feature selection | The basic idea when using PCA as a tool for feature selection is to select variables according to the magnitude (from largest to smallest in absolute values) of their coefficients (loadings). You may | Using principal component analysis (PCA) for feature selection
The basic idea when using PCA as a tool for feature selection is to select variables according to the magnitude (from largest to smallest in absolute values) of their coefficients (loadings). You may recall that PCA seeks to replace $p$ (more or less correl... | Using principal component analysis (PCA) for feature selection
The basic idea when using PCA as a tool for feature selection is to select variables according to the magnitude (from largest to smallest in absolute values) of their coefficients (loadings). You may |
2,641 | Using principal component analysis (PCA) for feature selection | Given a set of N features a PCA analysis will produce (1) the linear combination of the features with the highest variance (first PCA component), (2) the linear combination with the highest variance in the subspace orthogonal to the first PCA component etcetera (under the constraint that the coefficients of the combina... | Using principal component analysis (PCA) for feature selection | Given a set of N features a PCA analysis will produce (1) the linear combination of the features with the highest variance (first PCA component), (2) the linear combination with the highest variance i | Using principal component analysis (PCA) for feature selection
Given a set of N features a PCA analysis will produce (1) the linear combination of the features with the highest variance (first PCA component), (2) the linear combination with the highest variance in the subspace orthogonal to the first PCA component etce... | Using principal component analysis (PCA) for feature selection
Given a set of N features a PCA analysis will produce (1) the linear combination of the features with the highest variance (first PCA component), (2) the linear combination with the highest variance i |
2,642 | Using principal component analysis (PCA) for feature selection | I skim read through the comments above and I believe quite a few have pointed out that PCA is not a good approach to feature selection. PCA offers dimensionality reduction but it is often misconceived with feature selection (as both tend to reduce the feature space in a sense). I would like to point out the key differe... | Using principal component analysis (PCA) for feature selection | I skim read through the comments above and I believe quite a few have pointed out that PCA is not a good approach to feature selection. PCA offers dimensionality reduction but it is often misconceived | Using principal component analysis (PCA) for feature selection
I skim read through the comments above and I believe quite a few have pointed out that PCA is not a good approach to feature selection. PCA offers dimensionality reduction but it is often misconceived with feature selection (as both tend to reduce the featu... | Using principal component analysis (PCA) for feature selection
I skim read through the comments above and I believe quite a few have pointed out that PCA is not a good approach to feature selection. PCA offers dimensionality reduction but it is often misconceived |
2,643 | Using principal component analysis (PCA) for feature selection | You can not order features according to their variance, as the variance used in PCA is basically a multidimensional entity. You can only order features by the projection of the variance to certain direction you choose (which is normally the first principal compnonet.)
So, in other word, whether a feature has more varia... | Using principal component analysis (PCA) for feature selection | You can not order features according to their variance, as the variance used in PCA is basically a multidimensional entity. You can only order features by the projection of the variance to certain dir | Using principal component analysis (PCA) for feature selection
You can not order features according to their variance, as the variance used in PCA is basically a multidimensional entity. You can only order features by the projection of the variance to certain direction you choose (which is normally the first principal ... | Using principal component analysis (PCA) for feature selection
You can not order features according to their variance, as the variance used in PCA is basically a multidimensional entity. You can only order features by the projection of the variance to certain dir |
2,644 | Using principal component analysis (PCA) for feature selection | PCA tells us what features are more important, how?
In short:
We find the first principal component one (PC1). Now PC1 is a linear combination of the variables (features). The variable with the highest weight (coefficient)(loading scores) in the linear equation is the most important feature.
Don't miss this wonderful ... | Using principal component analysis (PCA) for feature selection | PCA tells us what features are more important, how?
In short:
We find the first principal component one (PC1). Now PC1 is a linear combination of the variables (features). The variable with the highes | Using principal component analysis (PCA) for feature selection
PCA tells us what features are more important, how?
In short:
We find the first principal component one (PC1). Now PC1 is a linear combination of the variables (features). The variable with the highest weight (coefficient)(loading scores) in the linear equa... | Using principal component analysis (PCA) for feature selection
PCA tells us what features are more important, how?
In short:
We find the first principal component one (PC1). Now PC1 is a linear combination of the variables (features). The variable with the highes |
2,645 | Using principal component analysis (PCA) for feature selection | From my perspective, I agree with Sidharth Gurbani's answer.
"The pca is not suitable for variable selection."
You can even construct a dataset in which linear model works well but the performs badly with respect to the first principle component:
df <- data.frame(y=c(1,2,2,2,3),
x1=c(-.87, -1.22, 0, 1.22, .87),
x2=c(-... | Using principal component analysis (PCA) for feature selection | From my perspective, I agree with Sidharth Gurbani's answer.
"The pca is not suitable for variable selection."
You can even construct a dataset in which linear model works well but the performs badly | Using principal component analysis (PCA) for feature selection
From my perspective, I agree with Sidharth Gurbani's answer.
"The pca is not suitable for variable selection."
You can even construct a dataset in which linear model works well but the performs badly with respect to the first principle component:
df <- data... | Using principal component analysis (PCA) for feature selection
From my perspective, I agree with Sidharth Gurbani's answer.
"The pca is not suitable for variable selection."
You can even construct a dataset in which linear model works well but the performs badly |
2,646 | Using principal component analysis (PCA) for feature selection | Some really great thoughts in the answers so far, and do a good job of explaining that the main job of PCA is to provide a few variables which are linear combinations of our original ones, not to select individual features of our original space. But it is actually possible to do something like that with the CUR decompo... | Using principal component analysis (PCA) for feature selection | Some really great thoughts in the answers so far, and do a good job of explaining that the main job of PCA is to provide a few variables which are linear combinations of our original ones, not to sele | Using principal component analysis (PCA) for feature selection
Some really great thoughts in the answers so far, and do a good job of explaining that the main job of PCA is to provide a few variables which are linear combinations of our original ones, not to select individual features of our original space. But it is a... | Using principal component analysis (PCA) for feature selection
Some really great thoughts in the answers so far, and do a good job of explaining that the main job of PCA is to provide a few variables which are linear combinations of our original ones, not to sele |
2,647 | What are i.i.d. random variables? | It means "Independent and identically distributed".
A good example is a succession of throws of a fair coin: The coin has no memory, so all the throws are "independent".
And every throw is 50:50 (heads:tails), so the coin is and stays fair - the distribution from which every throw is drawn, so to speak, is and stays th... | What are i.i.d. random variables? | It means "Independent and identically distributed".
A good example is a succession of throws of a fair coin: The coin has no memory, so all the throws are "independent".
And every throw is 50:50 (head | What are i.i.d. random variables?
It means "Independent and identically distributed".
A good example is a succession of throws of a fair coin: The coin has no memory, so all the throws are "independent".
And every throw is 50:50 (heads:tails), so the coin is and stays fair - the distribution from which every throw is d... | What are i.i.d. random variables?
It means "Independent and identically distributed".
A good example is a succession of throws of a fair coin: The coin has no memory, so all the throws are "independent".
And every throw is 50:50 (head |
2,648 | What are i.i.d. random variables? | Nontechnical explanation:
Independence is a very general notion. Two events are said to be independent if the occurrence of one does not give you any information as to whether the other event occurred or not. In particular,
the probability that we ascribe to the second event is not affected
by the knowledge that the f... | What are i.i.d. random variables? | Nontechnical explanation:
Independence is a very general notion. Two events are said to be independent if the occurrence of one does not give you any information as to whether the other event occurred | What are i.i.d. random variables?
Nontechnical explanation:
Independence is a very general notion. Two events are said to be independent if the occurrence of one does not give you any information as to whether the other event occurred or not. In particular,
the probability that we ascribe to the second event is not af... | What are i.i.d. random variables?
Nontechnical explanation:
Independence is a very general notion. Two events are said to be independent if the occurrence of one does not give you any information as to whether the other event occurred |
2,649 | What are i.i.d. random variables? | A random variable is variable which contains the probability of all possible events in a scenario. For example, lets create a random variable which represents the number of heads in 100 coin tosses. The random variable will contain the probability of getting 1 heads, 2 heads, 3 heads.....all the way to 100 heads. Lets ... | What are i.i.d. random variables? | A random variable is variable which contains the probability of all possible events in a scenario. For example, lets create a random variable which represents the number of heads in 100 coin tosses. T | What are i.i.d. random variables?
A random variable is variable which contains the probability of all possible events in a scenario. For example, lets create a random variable which represents the number of heads in 100 coin tosses. The random variable will contain the probability of getting 1 heads, 2 heads, 3 heads..... | What are i.i.d. random variables?
A random variable is variable which contains the probability of all possible events in a scenario. For example, lets create a random variable which represents the number of heads in 100 coin tosses. T |
2,650 | What are i.i.d. random variables? | That two dependent variables can have the same distribution can be shown with this example:
Assume two successive experiments involving each 100 tosses of a biased coin, where the total number of Head is modeled as a random variable X1 for the first experiment and X2 for the second experiment. X1 and X2 are binomial... | What are i.i.d. random variables? | That two dependent variables can have the same distribution can be shown with this example:
Assume two successive experiments involving each 100 tosses of a biased coin, where the total number of He | What are i.i.d. random variables?
That two dependent variables can have the same distribution can be shown with this example:
Assume two successive experiments involving each 100 tosses of a biased coin, where the total number of Head is modeled as a random variable X1 for the first experiment and X2 for the second e... | What are i.i.d. random variables?
That two dependent variables can have the same distribution can be shown with this example:
Assume two successive experiments involving each 100 tosses of a biased coin, where the total number of He |
2,651 | What are i.i.d. random variables? | An aggregation of several random draws from the same distribution. An example being pulling a marble out of bag 10,000 times and counting the times you pull the red marble out. | What are i.i.d. random variables? | An aggregation of several random draws from the same distribution. An example being pulling a marble out of bag 10,000 times and counting the times you pull the red marble out. | What are i.i.d. random variables?
An aggregation of several random draws from the same distribution. An example being pulling a marble out of bag 10,000 times and counting the times you pull the red marble out. | What are i.i.d. random variables?
An aggregation of several random draws from the same distribution. An example being pulling a marble out of bag 10,000 times and counting the times you pull the red marble out. |
2,652 | What are i.i.d. random variables? | If a random variable $X$ comes from a population having (say) a normal distribution, that is its pdf (probability density function) is that of normal distribution, with a population average $\mu=3$ and population variance $\sigma^2=4$ (the numbers are hypothetical and are just for your understanding and to simplify com... | What are i.i.d. random variables? | If a random variable $X$ comes from a population having (say) a normal distribution, that is its pdf (probability density function) is that of normal distribution, with a population average $\mu=3$ an | What are i.i.d. random variables?
If a random variable $X$ comes from a population having (say) a normal distribution, that is its pdf (probability density function) is that of normal distribution, with a population average $\mu=3$ and population variance $\sigma^2=4$ (the numbers are hypothetical and are just for your... | What are i.i.d. random variables?
If a random variable $X$ comes from a population having (say) a normal distribution, that is its pdf (probability density function) is that of normal distribution, with a population average $\mu=3$ an |
2,653 | Why do neural network researchers care about epochs? | In addition to Franck's answer about practicalities, and David's answer about looking at small subgroups – both of which are important points – there are in fact some theoretical reasons to prefer sampling without replacement. The reason is perhaps related to David's point (which is essentially the coupon collector's p... | Why do neural network researchers care about epochs? | In addition to Franck's answer about practicalities, and David's answer about looking at small subgroups – both of which are important points – there are in fact some theoretical reasons to prefer sam | Why do neural network researchers care about epochs?
In addition to Franck's answer about practicalities, and David's answer about looking at small subgroups – both of which are important points – there are in fact some theoretical reasons to prefer sampling without replacement. The reason is perhaps related to David's... | Why do neural network researchers care about epochs?
In addition to Franck's answer about practicalities, and David's answer about looking at small subgroups – both of which are important points – there are in fact some theoretical reasons to prefer sam |
2,654 | Why do neural network researchers care about epochs? | It is indeed quite unnecessary from a performance standpoint with a large training set, but using epochs can be convenient, e.g.:
it gives a pretty good metric: "the neural network was trained for 10 epochs" is a clearer statement than "the neural network was trained for 18942 iterations" or "the neural network was tr... | Why do neural network researchers care about epochs? | It is indeed quite unnecessary from a performance standpoint with a large training set, but using epochs can be convenient, e.g.:
it gives a pretty good metric: "the neural network was trained for 10 | Why do neural network researchers care about epochs?
It is indeed quite unnecessary from a performance standpoint with a large training set, but using epochs can be convenient, e.g.:
it gives a pretty good metric: "the neural network was trained for 10 epochs" is a clearer statement than "the neural network was traine... | Why do neural network researchers care about epochs?
It is indeed quite unnecessary from a performance standpoint with a large training set, but using epochs can be convenient, e.g.:
it gives a pretty good metric: "the neural network was trained for 10 |
2,655 | Why do neural network researchers care about epochs? | I disagree somewhat that it clearly won't matter. Let's say there are a million training examples, and we take ten million samples.
In R, we can quickly see what the distribution looks like with
plot(dbinom(0:40, size = 10 * 1E6, prob = 1E-6), type = "h")
Some examples will be visited 20+ times, while 1% of them wi... | Why do neural network researchers care about epochs? | I disagree somewhat that it clearly won't matter. Let's say there are a million training examples, and we take ten million samples.
In R, we can quickly see what the distribution looks like with
pl | Why do neural network researchers care about epochs?
I disagree somewhat that it clearly won't matter. Let's say there are a million training examples, and we take ten million samples.
In R, we can quickly see what the distribution looks like with
plot(dbinom(0:40, size = 10 * 1E6, prob = 1E-6), type = "h")
Some ex... | Why do neural network researchers care about epochs?
I disagree somewhat that it clearly won't matter. Let's say there are a million training examples, and we take ten million samples.
In R, we can quickly see what the distribution looks like with
pl |
2,656 | How does a simple logistic regression model achieve a 92% classification accuracy on MNIST? | tl;dr Even though this is an image classification dataset, it remains a very easy task, for which one can easily find a direct mapping from inputs to predictions.
Answer:
This is a very interesting question and thanks to the simplicity of logistic regression you can actually find out the answer.
What logistic regress... | How does a simple logistic regression model achieve a 92% classification accuracy on MNIST? | tl;dr Even though this is an image classification dataset, it remains a very easy task, for which one can easily find a direct mapping from inputs to predictions.
Answer:
This is a very interesting q | How does a simple logistic regression model achieve a 92% classification accuracy on MNIST?
tl;dr Even though this is an image classification dataset, it remains a very easy task, for which one can easily find a direct mapping from inputs to predictions.
Answer:
This is a very interesting question and thanks to the si... | How does a simple logistic regression model achieve a 92% classification accuracy on MNIST?
tl;dr Even though this is an image classification dataset, it remains a very easy task, for which one can easily find a direct mapping from inputs to predictions.
Answer:
This is a very interesting q |
2,657 | What is the difference between R functions prcomp and princomp? | The difference between them is nothing to do with the type of PCA they perform, just the method they use. As the help page for prcomp says:
The calculation is done by a singular value decomposition of the (centered and possibly scaled) data matrix, not by using eigen on the covariance matrix. This is generally the pre... | What is the difference between R functions prcomp and princomp? | The difference between them is nothing to do with the type of PCA they perform, just the method they use. As the help page for prcomp says:
The calculation is done by a singular value decomposition o | What is the difference between R functions prcomp and princomp?
The difference between them is nothing to do with the type of PCA they perform, just the method they use. As the help page for prcomp says:
The calculation is done by a singular value decomposition of the (centered and possibly scaled) data matrix, not by... | What is the difference between R functions prcomp and princomp?
The difference between them is nothing to do with the type of PCA they perform, just the method they use. As the help page for prcomp says:
The calculation is done by a singular value decomposition o |
2,658 | What is the difference between R functions prcomp and princomp? | Usually a multivariate analysis (computing correlations, extracting latents, etc.) is done of data columns which are features or questions, - while sample units, the rows, are respondents. Hence this way is called R way analysis. Sometimes, though, you may want to do multivariate analysis of responsents, while question... | What is the difference between R functions prcomp and princomp? | Usually a multivariate analysis (computing correlations, extracting latents, etc.) is done of data columns which are features or questions, - while sample units, the rows, are respondents. Hence this | What is the difference between R functions prcomp and princomp?
Usually a multivariate analysis (computing correlations, extracting latents, etc.) is done of data columns which are features or questions, - while sample units, the rows, are respondents. Hence this way is called R way analysis. Sometimes, though, you may... | What is the difference between R functions prcomp and princomp?
Usually a multivariate analysis (computing correlations, extracting latents, etc.) is done of data columns which are features or questions, - while sample units, the rows, are respondents. Hence this |
2,659 | What is the difference between R functions prcomp and princomp? | A useful and specific documentation from Gregory B. Anderson, titled PRINCIPAL COMPONENT ANALYSIS IN R AN EXAMINATION OF THE DIFFERENT FUNCTIONS AND METHODS TO PERFORM PCA has given more information on this topic. Updated link (7 Jan 2021).
The following two paragraph were extracted from the introduction:
In R there a... | What is the difference between R functions prcomp and princomp? | A useful and specific documentation from Gregory B. Anderson, titled PRINCIPAL COMPONENT ANALYSIS IN R AN EXAMINATION OF THE DIFFERENT FUNCTIONS AND METHODS TO PERFORM PCA has given more information o | What is the difference between R functions prcomp and princomp?
A useful and specific documentation from Gregory B. Anderson, titled PRINCIPAL COMPONENT ANALYSIS IN R AN EXAMINATION OF THE DIFFERENT FUNCTIONS AND METHODS TO PERFORM PCA has given more information on this topic. Updated link (7 Jan 2021).
The following t... | What is the difference between R functions prcomp and princomp?
A useful and specific documentation from Gregory B. Anderson, titled PRINCIPAL COMPONENT ANALYSIS IN R AN EXAMINATION OF THE DIFFERENT FUNCTIONS AND METHODS TO PERFORM PCA has given more information o |
2,660 | What is the difference between R functions prcomp and princomp? | They are different when both using covariance matrix. When scaling (normalizing) the training data, prcomp uses $n-1$ as denominator but princomp uses $n$ as its denominator. Difference of these two denominators is explained in this tutorial on principal component analysis.
Below are my test results:
> job<-read.table(... | What is the difference between R functions prcomp and princomp? | They are different when both using covariance matrix. When scaling (normalizing) the training data, prcomp uses $n-1$ as denominator but princomp uses $n$ as its denominator. Difference of these two d | What is the difference between R functions prcomp and princomp?
They are different when both using covariance matrix. When scaling (normalizing) the training data, prcomp uses $n-1$ as denominator but princomp uses $n$ as its denominator. Difference of these two denominators is explained in this tutorial on principal c... | What is the difference between R functions prcomp and princomp?
They are different when both using covariance matrix. When scaling (normalizing) the training data, prcomp uses $n-1$ as denominator but princomp uses $n$ as its denominator. Difference of these two d |
2,661 | Variable selection for predictive modeling really needed in 2016? | There have been rumors for years that Google uses all available features in building its predictive algorithms. To date however, no disclaimers, explanations or white papers have emerged that clarify and/or dispute this rumor. Not even their published patents help in the understanding. As a result, no one external to G... | Variable selection for predictive modeling really needed in 2016? | There have been rumors for years that Google uses all available features in building its predictive algorithms. To date however, no disclaimers, explanations or white papers have emerged that clarify | Variable selection for predictive modeling really needed in 2016?
There have been rumors for years that Google uses all available features in building its predictive algorithms. To date however, no disclaimers, explanations or white papers have emerged that clarify and/or dispute this rumor. Not even their published pa... | Variable selection for predictive modeling really needed in 2016?
There have been rumors for years that Google uses all available features in building its predictive algorithms. To date however, no disclaimers, explanations or white papers have emerged that clarify |
2,662 | Variable selection for predictive modeling really needed in 2016? | In terms of prediction, you probably need to think of the question of how quickly the model learns the important features. Even thinking of OLS, this will give you something like model selection given enough data. But we know that it doesn't converge to this solution quickly enough - so we search for something better... | Variable selection for predictive modeling really needed in 2016? | In terms of prediction, you probably need to think of the question of how quickly the model learns the important features. Even thinking of OLS, this will give you something like model selection give | Variable selection for predictive modeling really needed in 2016?
In terms of prediction, you probably need to think of the question of how quickly the model learns the important features. Even thinking of OLS, this will give you something like model selection given enough data. But we know that it doesn't converge t... | Variable selection for predictive modeling really needed in 2016?
In terms of prediction, you probably need to think of the question of how quickly the model learns the important features. Even thinking of OLS, this will give you something like model selection give |
2,663 | Variable selection for predictive modeling really needed in 2016? | I give you the perspective of industry.
Industries don't like to spend money on sensors and monitoring systems which they don't know how much they will benefit from.
For instance, I don't want to name, so imagine a component with 10 sensors gathering data every minute. The asset owner turns to me and asks me how well... | Variable selection for predictive modeling really needed in 2016? | I give you the perspective of industry.
Industries don't like to spend money on sensors and monitoring systems which they don't know how much they will benefit from.
For instance, I don't want to na | Variable selection for predictive modeling really needed in 2016?
I give you the perspective of industry.
Industries don't like to spend money on sensors and monitoring systems which they don't know how much they will benefit from.
For instance, I don't want to name, so imagine a component with 10 sensors gathering d... | Variable selection for predictive modeling really needed in 2016?
I give you the perspective of industry.
Industries don't like to spend money on sensors and monitoring systems which they don't know how much they will benefit from.
For instance, I don't want to na |
2,664 | Variable selection for predictive modeling really needed in 2016? | As part of an algorithm for learning a purely predictive model, variable selection is not necessarily bad from a performance viewpoint nor is it automatically dangerous. However, there are some issues that one should be aware of.
To make the question a little more concrete, let's consider the linear regression problem... | Variable selection for predictive modeling really needed in 2016? | As part of an algorithm for learning a purely predictive model, variable selection is not necessarily bad from a performance viewpoint nor is it automatically dangerous. However, there are some issues | Variable selection for predictive modeling really needed in 2016?
As part of an algorithm for learning a purely predictive model, variable selection is not necessarily bad from a performance viewpoint nor is it automatically dangerous. However, there are some issues that one should be aware of.
To make the question a ... | Variable selection for predictive modeling really needed in 2016?
As part of an algorithm for learning a purely predictive model, variable selection is not necessarily bad from a performance viewpoint nor is it automatically dangerous. However, there are some issues |
2,665 | Variable selection for predictive modeling really needed in 2016? | Allow me to comment on the statement: “... fitting k parameters to n < k observations is just not going to happen.”
In chemometrics we are often interested in predictive models, and the situation k >> n is frequently encountered (e.g. in spectroscopic data). This problem is typically solved simply by projecting the obs... | Variable selection for predictive modeling really needed in 2016? | Allow me to comment on the statement: “... fitting k parameters to n < k observations is just not going to happen.”
In chemometrics we are often interested in predictive models, and the situation k >> | Variable selection for predictive modeling really needed in 2016?
Allow me to comment on the statement: “... fitting k parameters to n < k observations is just not going to happen.”
In chemometrics we are often interested in predictive models, and the situation k >> n is frequently encountered (e.g. in spectroscopic da... | Variable selection for predictive modeling really needed in 2016?
Allow me to comment on the statement: “... fitting k parameters to n < k observations is just not going to happen.”
In chemometrics we are often interested in predictive models, and the situation k >> |
2,666 | Variable selection for predictive modeling really needed in 2016? | In several well known cases, yes, variable selection is not necessary. Deep learning has become a bit overhyped for precisely this reason.
For example, when a convoluted neural network (http://cs231n.github.io/convolutional-networks/) tries to predict if a centered image contains a human face, the corners of the image... | Variable selection for predictive modeling really needed in 2016? | In several well known cases, yes, variable selection is not necessary. Deep learning has become a bit overhyped for precisely this reason.
For example, when a convoluted neural network (http://cs231n | Variable selection for predictive modeling really needed in 2016?
In several well known cases, yes, variable selection is not necessary. Deep learning has become a bit overhyped for precisely this reason.
For example, when a convoluted neural network (http://cs231n.github.io/convolutional-networks/) tries to predict i... | Variable selection for predictive modeling really needed in 2016?
In several well known cases, yes, variable selection is not necessary. Deep learning has become a bit overhyped for precisely this reason.
For example, when a convoluted neural network (http://cs231n |
2,667 | Best way to present a random forest in a publication? | Regarding making it reproducible, the best way is to provide reproducible research (i.e. code and data) along with the paper. Make it available on your website, or on a hosting site (like github).
Regarding visualization, Leo Breiman has done some interesting work on this (see his homepage, in particular the section o... | Best way to present a random forest in a publication? | Regarding making it reproducible, the best way is to provide reproducible research (i.e. code and data) along with the paper. Make it available on your website, or on a hosting site (like github).
Re | Best way to present a random forest in a publication?
Regarding making it reproducible, the best way is to provide reproducible research (i.e. code and data) along with the paper. Make it available on your website, or on a hosting site (like github).
Regarding visualization, Leo Breiman has done some interesting work ... | Best way to present a random forest in a publication?
Regarding making it reproducible, the best way is to provide reproducible research (i.e. code and data) along with the paper. Make it available on your website, or on a hosting site (like github).
Re |
2,668 | Best way to present a random forest in a publication? | As Shane wrote; make it reproducible research + include random seeds, because RF is stochastic.
First of all, plotting single trees forming RF is nonsense; this is an ensemble classifier, it makes sense only as a whole. But even plotting the whole forest is nonsense -- it is a black-box classifier, so it is not intende... | Best way to present a random forest in a publication? | As Shane wrote; make it reproducible research + include random seeds, because RF is stochastic.
First of all, plotting single trees forming RF is nonsense; this is an ensemble classifier, it makes sen | Best way to present a random forest in a publication?
As Shane wrote; make it reproducible research + include random seeds, because RF is stochastic.
First of all, plotting single trees forming RF is nonsense; this is an ensemble classifier, it makes sense only as a whole. But even plotting the whole forest is nonsense... | Best way to present a random forest in a publication?
As Shane wrote; make it reproducible research + include random seeds, because RF is stochastic.
First of all, plotting single trees forming RF is nonsense; this is an ensemble classifier, it makes sen |
2,669 | Best way to present a random forest in a publication? | Keep in mind the caveats in the other answers about the plot necessarily being meaningful. But if you want a plot for illustrative/pedagogical purposes, the following snippet of R might be useful. Not hard to add "split point" to the edge text if you need it.
to.dendrogram <- function(dfrep,rownum=1,height.increment=... | Best way to present a random forest in a publication? | Keep in mind the caveats in the other answers about the plot necessarily being meaningful. But if you want a plot for illustrative/pedagogical purposes, the following snippet of R might be useful. N | Best way to present a random forest in a publication?
Keep in mind the caveats in the other answers about the plot necessarily being meaningful. But if you want a plot for illustrative/pedagogical purposes, the following snippet of R might be useful. Not hard to add "split point" to the edge text if you need it.
to.d... | Best way to present a random forest in a publication?
Keep in mind the caveats in the other answers about the plot necessarily being meaningful. But if you want a plot for illustrative/pedagogical purposes, the following snippet of R might be useful. N |
2,670 | What algorithm should I use to detect anomalies on time-series? | I think the key is "unexpected" qualifier in your graph. In order to detect the unexpected you need to have an idea of what's expected.
I would start with a simple time series model such as AR(p) or ARMA(p,q). Fit it to data, add seasonality as appropriate. For instance, your SAR(1)(24) model could be: $y_{t}=c+\phi y_... | What algorithm should I use to detect anomalies on time-series? | I think the key is "unexpected" qualifier in your graph. In order to detect the unexpected you need to have an idea of what's expected.
I would start with a simple time series model such as AR(p) or A | What algorithm should I use to detect anomalies on time-series?
I think the key is "unexpected" qualifier in your graph. In order to detect the unexpected you need to have an idea of what's expected.
I would start with a simple time series model such as AR(p) or ARMA(p,q). Fit it to data, add seasonality as appropriate... | What algorithm should I use to detect anomalies on time-series?
I think the key is "unexpected" qualifier in your graph. In order to detect the unexpected you need to have an idea of what's expected.
I would start with a simple time series model such as AR(p) or A |
2,671 | What algorithm should I use to detect anomalies on time-series? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
On the Netflix tech blog there is an article on their ... | What algorithm should I use to detect anomalies on time-series? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| What algorithm should I use to detect anomalies on time-series?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
... | What algorithm should I use to detect anomalies on time-series?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
|
2,672 | What algorithm should I use to detect anomalies on time-series? | Most outlier detection algorithms in open source package are for business time series data with low frequency, daily/weekly/monthly frequency data. This data appears to be for a specialized area that is captured in minutes, so I'm not sure if open source outlier detction would be helpful. You could try to adapt this ap... | What algorithm should I use to detect anomalies on time-series? | Most outlier detection algorithms in open source package are for business time series data with low frequency, daily/weekly/monthly frequency data. This data appears to be for a specialized area that | What algorithm should I use to detect anomalies on time-series?
Most outlier detection algorithms in open source package are for business time series data with low frequency, daily/weekly/monthly frequency data. This data appears to be for a specialized area that is captured in minutes, so I'm not sure if open source o... | What algorithm should I use to detect anomalies on time-series?
Most outlier detection algorithms in open source package are for business time series data with low frequency, daily/weekly/monthly frequency data. This data appears to be for a specialized area that |
2,673 | What algorithm should I use to detect anomalies on time-series? | What other answers didn't seems to mention is that your problem sounds like a changepoint detection. The idea of changapoint detection is that you are seeking for segments in your data that significantly differ in terms properties (e.g. mean, variance). This can be achieved my using maximum likelihood estimation, where... | What algorithm should I use to detect anomalies on time-series? | What other answers didn't seems to mention is that your problem sounds like a changepoint detection. The idea of changapoint detection is that you are seeking for segments in your data that significan | What algorithm should I use to detect anomalies on time-series?
What other answers didn't seems to mention is that your problem sounds like a changepoint detection. The idea of changapoint detection is that you are seeking for segments in your data that significantly differ in terms properties (e.g. mean, variance). Th... | What algorithm should I use to detect anomalies on time-series?
What other answers didn't seems to mention is that your problem sounds like a changepoint detection. The idea of changapoint detection is that you are seeking for segments in your data that significan |
2,674 | What algorithm should I use to detect anomalies on time-series? | Have you tried using Statistical Process Control rules (e.g. Western Electric http://en.wikipedia.org/wiki/Western_Electric_rules)?
I use them for time series data - often with a touch of intuition about the data - to assess whether the data is going somewhere I don't want it to go. Like your example, these rules say ... | What algorithm should I use to detect anomalies on time-series? | Have you tried using Statistical Process Control rules (e.g. Western Electric http://en.wikipedia.org/wiki/Western_Electric_rules)?
I use them for time series data - often with a touch of intuition ab | What algorithm should I use to detect anomalies on time-series?
Have you tried using Statistical Process Control rules (e.g. Western Electric http://en.wikipedia.org/wiki/Western_Electric_rules)?
I use them for time series data - often with a touch of intuition about the data - to assess whether the data is going somew... | What algorithm should I use to detect anomalies on time-series?
Have you tried using Statistical Process Control rules (e.g. Western Electric http://en.wikipedia.org/wiki/Western_Electric_rules)?
I use them for time series data - often with a touch of intuition ab |
2,675 | What algorithm should I use to detect anomalies on time-series? | Given that the periodicity of the time series should be well understood a simple, but effective, algorithm based on differencing can be devised.
A simple one-step differencing will detect a sudden drop from a previous value
$$y_t'= y_t - y_{t-1}$$
but if the series has a strong periodic component you'd expect that drop... | What algorithm should I use to detect anomalies on time-series? | Given that the periodicity of the time series should be well understood a simple, but effective, algorithm based on differencing can be devised.
A simple one-step differencing will detect a sudden dro | What algorithm should I use to detect anomalies on time-series?
Given that the periodicity of the time series should be well understood a simple, but effective, algorithm based on differencing can be devised.
A simple one-step differencing will detect a sudden drop from a previous value
$$y_t'= y_t - y_{t-1}$$
but if t... | What algorithm should I use to detect anomalies on time-series?
Given that the periodicity of the time series should be well understood a simple, but effective, algorithm based on differencing can be devised.
A simple one-step differencing will detect a sudden dro |
2,676 | What algorithm should I use to detect anomalies on time-series? | Would it be more useful to think of the changes in the time series as a beginning of a new trend rather than an anomaly? Taking the difference between adjacent points would help tell when the slope (derivative) is changing and might signal the beginning of a new trend in the date. Also taking the differences of the di... | What algorithm should I use to detect anomalies on time-series? | Would it be more useful to think of the changes in the time series as a beginning of a new trend rather than an anomaly? Taking the difference between adjacent points would help tell when the slope ( | What algorithm should I use to detect anomalies on time-series?
Would it be more useful to think of the changes in the time series as a beginning of a new trend rather than an anomaly? Taking the difference between adjacent points would help tell when the slope (derivative) is changing and might signal the beginning o... | What algorithm should I use to detect anomalies on time-series?
Would it be more useful to think of the changes in the time series as a beginning of a new trend rather than an anomaly? Taking the difference between adjacent points would help tell when the slope ( |
2,677 | What algorithm should I use to detect anomalies on time-series? | I was able to get some nice results for multiple-seasonality time series (daily, weekly) using two different algorithms:
Seasonal-trend decomposition using loess (or STL) to establish the midpoint series.
Nonlinear regression to establish thresholds around that midpoint, based on the relationship between the variance ... | What algorithm should I use to detect anomalies on time-series? | I was able to get some nice results for multiple-seasonality time series (daily, weekly) using two different algorithms:
Seasonal-trend decomposition using loess (or STL) to establish the midpoint se | What algorithm should I use to detect anomalies on time-series?
I was able to get some nice results for multiple-seasonality time series (daily, weekly) using two different algorithms:
Seasonal-trend decomposition using loess (or STL) to establish the midpoint series.
Nonlinear regression to establish thresholds aroun... | What algorithm should I use to detect anomalies on time-series?
I was able to get some nice results for multiple-seasonality time series (daily, weekly) using two different algorithms:
Seasonal-trend decomposition using loess (or STL) to establish the midpoint se |
2,678 | What algorithm should I use to detect anomalies on time-series? | Inspired by David, have you tried to use FFT? It might be able to spot sudden drops because those are indicating your anomalies. The anomalies might appear in a narrow spectrum. So you can easily capture them. | What algorithm should I use to detect anomalies on time-series? | Inspired by David, have you tried to use FFT? It might be able to spot sudden drops because those are indicating your anomalies. The anomalies might appear in a narrow spectrum. So you can easily cap | What algorithm should I use to detect anomalies on time-series?
Inspired by David, have you tried to use FFT? It might be able to spot sudden drops because those are indicating your anomalies. The anomalies might appear in a narrow spectrum. So you can easily capture them. | What algorithm should I use to detect anomalies on time-series?
Inspired by David, have you tried to use FFT? It might be able to spot sudden drops because those are indicating your anomalies. The anomalies might appear in a narrow spectrum. So you can easily cap |
2,679 | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests? | As Rob mentions, this occurs when you have highly correlated variables. The standard example I use is predicting weight from shoe size. You can predict weight equally well with the right or left shoe size. But together it doesn't work out.
Brief simulation example
RSS = 3:10 #Right shoe size
LSS = rnorm(RSS, RSS, 0.1) ... | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests? | As Rob mentions, this occurs when you have highly correlated variables. The standard example I use is predicting weight from shoe size. You can predict weight equally well with the right or left shoe | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests?
As Rob mentions, this occurs when you have highly correlated variables. The standard example I use is predicting weight from shoe size. You can predict weight equally well with the right or left shoe size. But together it ... | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests?
As Rob mentions, this occurs when you have highly correlated variables. The standard example I use is predicting weight from shoe size. You can predict weight equally well with the right or left shoe |
2,680 | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests? | It takes very little correlation among the independent variables to cause this.
To see why, try the following:
Draw 50 sets of ten vectors $(x_1, x_2, \ldots, x_{10})$ with coefficients iid standard normal.
Compute $y_i = (x_i + x_{i+1})/\sqrt{2}$ for $i = 1, 2, \ldots, 9$. This makes the $y_i$ individually standard ... | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests? | It takes very little correlation among the independent variables to cause this.
To see why, try the following:
Draw 50 sets of ten vectors $(x_1, x_2, \ldots, x_{10})$ with coefficients iid standard | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests?
It takes very little correlation among the independent variables to cause this.
To see why, try the following:
Draw 50 sets of ten vectors $(x_1, x_2, \ldots, x_{10})$ with coefficients iid standard normal.
Compute $y_i =... | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests?
It takes very little correlation among the independent variables to cause this.
To see why, try the following:
Draw 50 sets of ten vectors $(x_1, x_2, \ldots, x_{10})$ with coefficients iid standard |
2,681 | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests? | Multicollinearity
As you note, and as has been discussed in this previous question, high levels of multicollinearity is one major cause of a statistically significant $R^2$ but statically non-significant predictors.
Of course, multicollinearity is not just about an absolute threshold. Standard errors on regression co... | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests? | Multicollinearity
As you note, and as has been discussed in this previous question, high levels of multicollinearity is one major cause of a statistically significant $R^2$ but statically non-signif | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests?
Multicollinearity
As you note, and as has been discussed in this previous question, high levels of multicollinearity is one major cause of a statistically significant $R^2$ but statically non-significant predictors.
Of c... | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests?
Multicollinearity
As you note, and as has been discussed in this previous question, high levels of multicollinearity is one major cause of a statistically significant $R^2$ but statically non-signif |
2,682 | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests? | This happens when the predictors are highly correlated. Imagine a situation where there are only two predictors with very high correlation. Individually, they both also correlate closely with the response variable. Consequently, the F-test has a low p-value (it is saying that the predictors together are highly signific... | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests? | This happens when the predictors are highly correlated. Imagine a situation where there are only two predictors with very high correlation. Individually, they both also correlate closely with the resp | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests?
This happens when the predictors are highly correlated. Imagine a situation where there are only two predictors with very high correlation. Individually, they both also correlate closely with the response variable. Consequ... | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests?
This happens when the predictors are highly correlated. Imagine a situation where there are only two predictors with very high correlation. Individually, they both also correlate closely with the resp |
2,683 | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests? | Consider the following model: $ X_1 \sim N(0,1)$, $X_2 = a X_1 + \delta$, $Y = bX_1 + cX_2 + \epsilon$, $\delta$, $\epsilon$ and $X_1$ are all mutually independent $N(0,1)$.
Then $${\rm Cov}(X_2,Y) = {\rm E}[(aX_1+\delta)(bX_1+cX_2+\epsilon)]={\rm E}[(aX_1+\delta)(\{b+ac\}X_1+c\delta+\epsilon)]=a(b+ac)+c$$
We can set t... | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests? | Consider the following model: $ X_1 \sim N(0,1)$, $X_2 = a X_1 + \delta$, $Y = bX_1 + cX_2 + \epsilon$, $\delta$, $\epsilon$ and $X_1$ are all mutually independent $N(0,1)$.
Then $${\rm Cov}(X_2,Y) = | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests?
Consider the following model: $ X_1 \sim N(0,1)$, $X_2 = a X_1 + \delta$, $Y = bX_1 + cX_2 + \epsilon$, $\delta$, $\epsilon$ and $X_1$ are all mutually independent $N(0,1)$.
Then $${\rm Cov}(X_2,Y) = {\rm E}[(aX_1+\delta)(... | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests?
Consider the following model: $ X_1 \sim N(0,1)$, $X_2 = a X_1 + \delta$, $Y = bX_1 + cX_2 + \epsilon$, $\delta$, $\epsilon$ and $X_1$ are all mutually independent $N(0,1)$.
Then $${\rm Cov}(X_2,Y) = |
2,684 | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests? | A keyword to search for would be "collinearity" or "multicollinearity". This can be detected using diagnostics like Variance Inflation Factors (VIFs) or methods as described inthe textbook "Regression Diagnostics: Identifying Influential Data and Sources of Collinearity" by Belsley, Kuh and Welsch. VIFs are much easier... | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests? | A keyword to search for would be "collinearity" or "multicollinearity". This can be detected using diagnostics like Variance Inflation Factors (VIFs) or methods as described inthe textbook "Regression | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests?
A keyword to search for would be "collinearity" or "multicollinearity". This can be detected using diagnostics like Variance Inflation Factors (VIFs) or methods as described inthe textbook "Regression Diagnostics: Identify... | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests?
A keyword to search for would be "collinearity" or "multicollinearity". This can be detected using diagnostics like Variance Inflation Factors (VIFs) or methods as described inthe textbook "Regression |
2,685 | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests? | The answer you get depends on the question you ask. In addition to the points already made, the individual parameters F values and the overall model F values answer different questions, so they get different answers. I have seen this happen even when the individual F values are not that close to significant, especiall... | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests? | The answer you get depends on the question you ask. In addition to the points already made, the individual parameters F values and the overall model F values answer different questions, so they get d | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests?
The answer you get depends on the question you ask. In addition to the points already made, the individual parameters F values and the overall model F values answer different questions, so they get different answers. I ha... | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests?
The answer you get depends on the question you ask. In addition to the points already made, the individual parameters F values and the overall model F values answer different questions, so they get d |
2,686 | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests? | One other thing to keep in mind is that the tests on the individual coefficients each assume that all of the other predictors are in the model. In other words each predictor is not significant as long as all of the other predictors are in the model. There must be some interaction or interdependence between two or more ... | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests? | One other thing to keep in mind is that the tests on the individual coefficients each assume that all of the other predictors are in the model. In other words each predictor is not significant as long | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests?
One other thing to keep in mind is that the tests on the individual coefficients each assume that all of the other predictors are in the model. In other words each predictor is not significant as long as all of the other p... | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests?
One other thing to keep in mind is that the tests on the individual coefficients each assume that all of the other predictors are in the model. In other words each predictor is not significant as long |
2,687 | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests? | One way to understand this is the geometry of least squares as @StasK suggests.
Another is to realize it means that X is related to Y when controlling for the other variables, but not alone. You say X relates to unique variance in Y. This is right. The unique variance in Y, though, is different from the total variance... | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests? | One way to understand this is the geometry of least squares as @StasK suggests.
Another is to realize it means that X is related to Y when controlling for the other variables, but not alone. You say | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests?
One way to understand this is the geometry of least squares as @StasK suggests.
Another is to realize it means that X is related to Y when controlling for the other variables, but not alone. You say X relates to unique va... | Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests?
One way to understand this is the geometry of least squares as @StasK suggests.
Another is to realize it means that X is related to Y when controlling for the other variables, but not alone. You say |
2,688 | Famous statistical wins and horror stories for teaching purposes | Benford's law:
Described here. Digits do not appear with uniform frequency in front of numbers, but rather follow a specific pattern: digit 1 is the most likely to be the first digit, with 30% chance, followed by 2 (17.6% chance), and so on. The following picture (from Wikipedia) shows the frequency of each digit at th... | Famous statistical wins and horror stories for teaching purposes | Benford's law:
Described here. Digits do not appear with uniform frequency in front of numbers, but rather follow a specific pattern: digit 1 is the most likely to be the first digit, with 30% chance, | Famous statistical wins and horror stories for teaching purposes
Benford's law:
Described here. Digits do not appear with uniform frequency in front of numbers, but rather follow a specific pattern: digit 1 is the most likely to be the first digit, with 30% chance, followed by 2 (17.6% chance), and so on. The following... | Famous statistical wins and horror stories for teaching purposes
Benford's law:
Described here. Digits do not appear with uniform frequency in front of numbers, but rather follow a specific pattern: digit 1 is the most likely to be the first digit, with 30% chance, |
2,689 | Famous statistical wins and horror stories for teaching purposes | I really liked the German tank problem. It shows, how data which is usually considered as irrelevant becomes valuable information in the hand of a statistician. Furthermore, I liked the law of small numbers and the base rate fallacy. | Famous statistical wins and horror stories for teaching purposes | I really liked the German tank problem. It shows, how data which is usually considered as irrelevant becomes valuable information in the hand of a statistician. Furthermore, I liked the law of small n | Famous statistical wins and horror stories for teaching purposes
I really liked the German tank problem. It shows, how data which is usually considered as irrelevant becomes valuable information in the hand of a statistician. Furthermore, I liked the law of small numbers and the base rate fallacy. | Famous statistical wins and horror stories for teaching purposes
I really liked the German tank problem. It shows, how data which is usually considered as irrelevant becomes valuable information in the hand of a statistician. Furthermore, I liked the law of small n |
2,690 | Famous statistical wins and horror stories for teaching purposes | R vs Sally Clark is a famous case of a woman being convicted for murder because the court was unaware of statistics and probability base principles.
But if I have to say the thing that impressed me the most, when I begun studying statistics, that is regression to the mean, which also gave the name to statistical regres... | Famous statistical wins and horror stories for teaching purposes | R vs Sally Clark is a famous case of a woman being convicted for murder because the court was unaware of statistics and probability base principles.
But if I have to say the thing that impressed me th | Famous statistical wins and horror stories for teaching purposes
R vs Sally Clark is a famous case of a woman being convicted for murder because the court was unaware of statistics and probability base principles.
But if I have to say the thing that impressed me the most, when I begun studying statistics, that is regre... | Famous statistical wins and horror stories for teaching purposes
R vs Sally Clark is a famous case of a woman being convicted for murder because the court was unaware of statistics and probability base principles.
But if I have to say the thing that impressed me th |
2,691 | Famous statistical wins and horror stories for teaching purposes | To illustrate where ordinary intuition fails, the Monty Hall paradox is a great starter. | Famous statistical wins and horror stories for teaching purposes | To illustrate where ordinary intuition fails, the Monty Hall paradox is a great starter. | Famous statistical wins and horror stories for teaching purposes
To illustrate where ordinary intuition fails, the Monty Hall paradox is a great starter. | Famous statistical wins and horror stories for teaching purposes
To illustrate where ordinary intuition fails, the Monty Hall paradox is a great starter. |
2,692 | Famous statistical wins and horror stories for teaching purposes | If sampling is a part of your course then it's hard to beat Dewey beats Truman | Famous statistical wins and horror stories for teaching purposes | If sampling is a part of your course then it's hard to beat Dewey beats Truman | Famous statistical wins and horror stories for teaching purposes
If sampling is a part of your course then it's hard to beat Dewey beats Truman | Famous statistical wins and horror stories for teaching purposes
If sampling is a part of your course then it's hard to beat Dewey beats Truman |
2,693 | Famous statistical wins and horror stories for teaching purposes | Another interesting case as to how wrong gambling can go is the Monte Carlo Casino example.
In a game of roulette at the Monte Carlo Casino on August 18, 1913 the ball fell in black 26 times in a row. This was an extremely uncommon occurrence: the probability of a sequence of either red or black occurring 26 times in ... | Famous statistical wins and horror stories for teaching purposes | Another interesting case as to how wrong gambling can go is the Monte Carlo Casino example.
In a game of roulette at the Monte Carlo Casino on August 18, 1913 the ball fell in black 26 times in a row | Famous statistical wins and horror stories for teaching purposes
Another interesting case as to how wrong gambling can go is the Monte Carlo Casino example.
In a game of roulette at the Monte Carlo Casino on August 18, 1913 the ball fell in black 26 times in a row. This was an extremely uncommon occurrence: the probab... | Famous statistical wins and horror stories for teaching purposes
Another interesting case as to how wrong gambling can go is the Monte Carlo Casino example.
In a game of roulette at the Monte Carlo Casino on August 18, 1913 the ball fell in black 26 times in a row |
2,694 | Famous statistical wins and horror stories for teaching purposes | I find the false positive paradox remarkable because it is so counter-intuitive. A good example:
Cancer screening of the general population does not increase life expectancy, even though clearly lives are saved because some cancers are caught early and can be treated better. The U.S. Preventive Services Task Force acc... | Famous statistical wins and horror stories for teaching purposes | I find the false positive paradox remarkable because it is so counter-intuitive. A good example:
Cancer screening of the general population does not increase life expectancy, even though clearly live | Famous statistical wins and horror stories for teaching purposes
I find the false positive paradox remarkable because it is so counter-intuitive. A good example:
Cancer screening of the general population does not increase life expectancy, even though clearly lives are saved because some cancers are caught early and c... | Famous statistical wins and horror stories for teaching purposes
I find the false positive paradox remarkable because it is so counter-intuitive. A good example:
Cancer screening of the general population does not increase life expectancy, even though clearly live |
2,695 | Famous statistical wins and horror stories for teaching purposes | My favourite example, as an illustration of how faulty statistics can have long-term consequences when they are used to direct government policy, is the act of large-scale railway vandalism known as the Beeching Axe. It resulted from a Transport Minister with strong ties to the road-building industry (Ernest Marples) ... | Famous statistical wins and horror stories for teaching purposes | My favourite example, as an illustration of how faulty statistics can have long-term consequences when they are used to direct government policy, is the act of large-scale railway vandalism known as t | Famous statistical wins and horror stories for teaching purposes
My favourite example, as an illustration of how faulty statistics can have long-term consequences when they are used to direct government policy, is the act of large-scale railway vandalism known as the Beeching Axe. It resulted from a Transport Minister... | Famous statistical wins and horror stories for teaching purposes
My favourite example, as an illustration of how faulty statistics can have long-term consequences when they are used to direct government policy, is the act of large-scale railway vandalism known as t |
2,696 | Famous statistical wins and horror stories for teaching purposes | Nice QA! here my two cents: It is mainly about how correlation can be very suspicious and some traditional ways to work it out:
https://www.tylervigen.com/spurious-correlations
https://en.wikipedia.org/wiki/Anscombe%27s_quartet
https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient
To elaborate a littl... | Famous statistical wins and horror stories for teaching purposes | Nice QA! here my two cents: It is mainly about how correlation can be very suspicious and some traditional ways to work it out:
https://www.tylervigen.com/spurious-correlations
https://en.wikipedia.or | Famous statistical wins and horror stories for teaching purposes
Nice QA! here my two cents: It is mainly about how correlation can be very suspicious and some traditional ways to work it out:
https://www.tylervigen.com/spurious-correlations
https://en.wikipedia.org/wiki/Anscombe%27s_quartet
https://en.wikipedia.org/wi... | Famous statistical wins and horror stories for teaching purposes
Nice QA! here my two cents: It is mainly about how correlation can be very suspicious and some traditional ways to work it out:
https://www.tylervigen.com/spurious-correlations
https://en.wikipedia.or |
2,697 | Famous statistical wins and horror stories for teaching purposes | I don't know if this counts as "intuition falls short", but rather a "naive analysis gives a counter intuitive, and misleading, answer".
One of my stats professors introduced a study regarding the connection between smoking and FEV in young students.
FEV can be considered to be a measure of lung volume. When the prof... | Famous statistical wins and horror stories for teaching purposes | I don't know if this counts as "intuition falls short", but rather a "naive analysis gives a counter intuitive, and misleading, answer".
One of my stats professors introduced a study regarding the co | Famous statistical wins and horror stories for teaching purposes
I don't know if this counts as "intuition falls short", but rather a "naive analysis gives a counter intuitive, and misleading, answer".
One of my stats professors introduced a study regarding the connection between smoking and FEV in young students.
FE... | Famous statistical wins and horror stories for teaching purposes
I don't know if this counts as "intuition falls short", but rather a "naive analysis gives a counter intuitive, and misleading, answer".
One of my stats professors introduced a study regarding the co |
2,698 | Famous statistical wins and horror stories for teaching purposes | The failure to show the association between launch temperature, and the effect of launch temperature, on the space shuttle o-rings, leading to the catastrophic failure of the Columbia soon after launch. An overview of the problem is here. | Famous statistical wins and horror stories for teaching purposes | The failure to show the association between launch temperature, and the effect of launch temperature, on the space shuttle o-rings, leading to the catastrophic failure of the Columbia soon after launc | Famous statistical wins and horror stories for teaching purposes
The failure to show the association between launch temperature, and the effect of launch temperature, on the space shuttle o-rings, leading to the catastrophic failure of the Columbia soon after launch. An overview of the problem is here. | Famous statistical wins and horror stories for teaching purposes
The failure to show the association between launch temperature, and the effect of launch temperature, on the space shuttle o-rings, leading to the catastrophic failure of the Columbia soon after launc |
2,699 | Famous statistical wins and horror stories for teaching purposes | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
For the last year and a half Bloomberg News has made p... | Famous statistical wins and horror stories for teaching purposes | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| Famous statistical wins and horror stories for teaching purposes
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
... | Famous statistical wins and horror stories for teaching purposes
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
|
2,700 | Understanding ROC curve | I'm not sure I got the question, but since the title asks for explaining ROC curves, I'll try.
ROC Curves are used to see how well your classifier can separate positive and negative examples and to identify the best threshold for separating them.
To be able to use the ROC curve, your classifier has to be ranking - th... | Understanding ROC curve | I'm not sure I got the question, but since the title asks for explaining ROC curves, I'll try.
ROC Curves are used to see how well your classifier can separate positive and negative examples and to i | Understanding ROC curve
I'm not sure I got the question, but since the title asks for explaining ROC curves, I'll try.
ROC Curves are used to see how well your classifier can separate positive and negative examples and to identify the best threshold for separating them.
To be able to use the ROC curve, your classifie... | Understanding ROC curve
I'm not sure I got the question, but since the title asks for explaining ROC curves, I'll try.
ROC Curves are used to see how well your classifier can separate positive and negative examples and to i |
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