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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6,601 | Why is the mean function in Gaussian Process uninteresting? | I'll give you an explanation that probably wasn't meant by the speaker. In some applications means are always boring. For instance, let's say we're forecasting sales with autoregressive model $y_t=c+\gamma y_{t-1}+e_t$. The long run mean is obviously $E[y_t]\equiv\mu=\frac{c}{1-\gamma}$. Is it interesting?
It depends ... | Why is the mean function in Gaussian Process uninteresting? | I'll give you an explanation that probably wasn't meant by the speaker. In some applications means are always boring. For instance, let's say we're forecasting sales with autoregressive model $y_t=c+\ | Why is the mean function in Gaussian Process uninteresting?
I'll give you an explanation that probably wasn't meant by the speaker. In some applications means are always boring. For instance, let's say we're forecasting sales with autoregressive model $y_t=c+\gamma y_{t-1}+e_t$. The long run mean is obviously $E[y_t]\e... | Why is the mean function in Gaussian Process uninteresting?
I'll give you an explanation that probably wasn't meant by the speaker. In some applications means are always boring. For instance, let's say we're forecasting sales with autoregressive model $y_t=c+\ |
6,602 | How do you Interpret RMSLE (Root Mean Squared Logarithmic Error)? | I haven't seen RMSLE before, but I'm assuming it's $\sqrt{ \frac{1}{N} \sum_{i=1}^N (\log(x_i) - \log(y_i))^2 }$.
Thus exponentiating it won't give you RMSE, it'll give you
$e^\sqrt{ \frac{1}{N} \sum_{i=1}^N (\log(x_i) - \log(y_i))^2 } \ne \sqrt{\frac{1}{N} \sum_{i=1}^N (x_i - y_i)^2}$.
If we take the log of both sides... | How do you Interpret RMSLE (Root Mean Squared Logarithmic Error)? | I haven't seen RMSLE before, but I'm assuming it's $\sqrt{ \frac{1}{N} \sum_{i=1}^N (\log(x_i) - \log(y_i))^2 }$.
Thus exponentiating it won't give you RMSE, it'll give you
$e^\sqrt{ \frac{1}{N} \sum_ | How do you Interpret RMSLE (Root Mean Squared Logarithmic Error)?
I haven't seen RMSLE before, but I'm assuming it's $\sqrt{ \frac{1}{N} \sum_{i=1}^N (\log(x_i) - \log(y_i))^2 }$.
Thus exponentiating it won't give you RMSE, it'll give you
$e^\sqrt{ \frac{1}{N} \sum_{i=1}^N (\log(x_i) - \log(y_i))^2 } \ne \sqrt{\frac{1}... | How do you Interpret RMSLE (Root Mean Squared Logarithmic Error)?
I haven't seen RMSLE before, but I'm assuming it's $\sqrt{ \frac{1}{N} \sum_{i=1}^N (\log(x_i) - \log(y_i))^2 }$.
Thus exponentiating it won't give you RMSE, it'll give you
$e^\sqrt{ \frac{1}{N} \sum_ |
6,603 | How do you Interpret RMSLE (Root Mean Squared Logarithmic Error)? | I don't know if there is a straightforward generic interpretation, even analysing a particular case.
For example, you may be interested in evaluating what would be the error if you predict all the cases with the mean value and compare it to your approach.
Anyway, I believe RMSLE is usually used when you don't want to p... | How do you Interpret RMSLE (Root Mean Squared Logarithmic Error)? | I don't know if there is a straightforward generic interpretation, even analysing a particular case.
For example, you may be interested in evaluating what would be the error if you predict all the cas | How do you Interpret RMSLE (Root Mean Squared Logarithmic Error)?
I don't know if there is a straightforward generic interpretation, even analysing a particular case.
For example, you may be interested in evaluating what would be the error if you predict all the cases with the mean value and compare it to your approach... | How do you Interpret RMSLE (Root Mean Squared Logarithmic Error)?
I don't know if there is a straightforward generic interpretation, even analysing a particular case.
For example, you may be interested in evaluating what would be the error if you predict all the cas |
6,604 | How do you Interpret RMSLE (Root Mean Squared Logarithmic Error)? | There is an indirect way of measuring the performance of a loss function in terms of something more easily understandable, although it will not directly convert values as you have hoped.
Once the model has been trained and tested using RMSLE, simply take a new metric on it. Just because the model was trained on RMSLE, ... | How do you Interpret RMSLE (Root Mean Squared Logarithmic Error)? | There is an indirect way of measuring the performance of a loss function in terms of something more easily understandable, although it will not directly convert values as you have hoped.
Once the mode | How do you Interpret RMSLE (Root Mean Squared Logarithmic Error)?
There is an indirect way of measuring the performance of a loss function in terms of something more easily understandable, although it will not directly convert values as you have hoped.
Once the model has been trained and tested using RMSLE, simply take... | How do you Interpret RMSLE (Root Mean Squared Logarithmic Error)?
There is an indirect way of measuring the performance of a loss function in terms of something more easily understandable, although it will not directly convert values as you have hoped.
Once the mode |
6,605 | How do you Interpret RMSLE (Root Mean Squared Logarithmic Error)? | My understanding is, when we do logarithm both on prediction and actual numbers, we'll get much smoother results than original one. And reduce the impact of larger x, while emphasize of smaller x for $\log{x+1}$.
Also you'll get a intuitive impression by drawing a simple graph of $y=\log{x+1}$. | How do you Interpret RMSLE (Root Mean Squared Logarithmic Error)? | My understanding is, when we do logarithm both on prediction and actual numbers, we'll get much smoother results than original one. And reduce the impact of larger x, while emphasize of smaller x for | How do you Interpret RMSLE (Root Mean Squared Logarithmic Error)?
My understanding is, when we do logarithm both on prediction and actual numbers, we'll get much smoother results than original one. And reduce the impact of larger x, while emphasize of smaller x for $\log{x+1}$.
Also you'll get a intuitive impression by... | How do you Interpret RMSLE (Root Mean Squared Logarithmic Error)?
My understanding is, when we do logarithm both on prediction and actual numbers, we'll get much smoother results than original one. And reduce the impact of larger x, while emphasize of smaller x for |
6,606 | Brain-teaser: What is the expected length of an iid sequence that is monotonically increasing when drawn from a uniform [0,1] distribution? | Here are some general hints on solving this question:
You have a sequence of continuous IID random variables which means they are exchangeable. What does this imply about the probability of getting a particular order for the first $n$ values? Based on this, what is the probability of getting an increasing order for t... | Brain-teaser: What is the expected length of an iid sequence that is monotonically increasing when d | Here are some general hints on solving this question:
You have a sequence of continuous IID random variables which means they are exchangeable. What does this imply about the probability of getting a | Brain-teaser: What is the expected length of an iid sequence that is monotonically increasing when drawn from a uniform [0,1] distribution?
Here are some general hints on solving this question:
You have a sequence of continuous IID random variables which means they are exchangeable. What does this imply about the prob... | Brain-teaser: What is the expected length of an iid sequence that is monotonically increasing when d
Here are some general hints on solving this question:
You have a sequence of continuous IID random variables which means they are exchangeable. What does this imply about the probability of getting a |
6,607 | Brain-teaser: What is the expected length of an iid sequence that is monotonically increasing when drawn from a uniform [0,1] distribution? | Another solving method which gets you the solution for a more general case.
Suppose $F(x)$ is the expected length of a monotonic sequence $\{x_1, x_2, ...\}$, such that $x\leq x_1\leq x_2\leq\cdots$. The value we want to calculate is $F(0)$. And we know $F(1)=0$. Conditioning on the next value,
$$F(x) = \int_0^x \pi(y)... | Brain-teaser: What is the expected length of an iid sequence that is monotonically increasing when d | Another solving method which gets you the solution for a more general case.
Suppose $F(x)$ is the expected length of a monotonic sequence $\{x_1, x_2, ...\}$, such that $x\leq x_1\leq x_2\leq\cdots$. | Brain-teaser: What is the expected length of an iid sequence that is monotonically increasing when drawn from a uniform [0,1] distribution?
Another solving method which gets you the solution for a more general case.
Suppose $F(x)$ is the expected length of a monotonic sequence $\{x_1, x_2, ...\}$, such that $x\leq x_1\... | Brain-teaser: What is the expected length of an iid sequence that is monotonically increasing when d
Another solving method which gets you the solution for a more general case.
Suppose $F(x)$ is the expected length of a monotonic sequence $\{x_1, x_2, ...\}$, such that $x\leq x_1\leq x_2\leq\cdots$. |
6,608 | Brain-teaser: What is the expected length of an iid sequence that is monotonically increasing when drawn from a uniform [0,1] distribution? | Another solving method is to calculate the integral directly.
The probability of generating a sequence whose increasing part has length of $\geq n$ is $f^n(0)$, where $f^n(x) = \int_{x}^{1}\int_{x_1}^{1}\int_{x_2}^{1}...\int_{x_{n-2}}^{1}\int_{x_{n-1}}^{1}dx_ndx_{n-1}...dx_2dx_1$.
What we need to do is to calculate $f^... | Brain-teaser: What is the expected length of an iid sequence that is monotonically increasing when d | Another solving method is to calculate the integral directly.
The probability of generating a sequence whose increasing part has length of $\geq n$ is $f^n(0)$, where $f^n(x) = \int_{x}^{1}\int_{x_1}^ | Brain-teaser: What is the expected length of an iid sequence that is monotonically increasing when drawn from a uniform [0,1] distribution?
Another solving method is to calculate the integral directly.
The probability of generating a sequence whose increasing part has length of $\geq n$ is $f^n(0)$, where $f^n(x) = \in... | Brain-teaser: What is the expected length of an iid sequence that is monotonically increasing when d
Another solving method is to calculate the integral directly.
The probability of generating a sequence whose increasing part has length of $\geq n$ is $f^n(0)$, where $f^n(x) = \int_{x}^{1}\int_{x_1}^ |
6,609 | Do working statisticians care about the difference between frequentist and Bayesian inference? | I don't think it matters very much, as long as the interpretation of the results is performed within the same framework as the analysis. The main problem with frequentist statistics is that there is a natural tendency to treat the p-value of a frequentist significance test as if it was a Bayesian a-posteriori probabil... | Do working statisticians care about the difference between frequentist and Bayesian inference? | I don't think it matters very much, as long as the interpretation of the results is performed within the same framework as the analysis. The main problem with frequentist statistics is that there is | Do working statisticians care about the difference between frequentist and Bayesian inference?
I don't think it matters very much, as long as the interpretation of the results is performed within the same framework as the analysis. The main problem with frequentist statistics is that there is a natural tendency to tre... | Do working statisticians care about the difference between frequentist and Bayesian inference?
I don't think it matters very much, as long as the interpretation of the results is performed within the same framework as the analysis. The main problem with frequentist statistics is that there is |
6,610 | Do working statisticians care about the difference between frequentist and Bayesian inference? | Adding to what Shane says, I think the continuum comprises:
Firm philosophical standing in the Bayes camp
Both considered valid, with one approach more or less preferable for a given problem
I'd use a Bayesian approach (at all or more often) but I don't have the time.
Firm philosophical standing in the frequentist cam... | Do working statisticians care about the difference between frequentist and Bayesian inference? | Adding to what Shane says, I think the continuum comprises:
Firm philosophical standing in the Bayes camp
Both considered valid, with one approach more or less preferable for a given problem
I'd use | Do working statisticians care about the difference between frequentist and Bayesian inference?
Adding to what Shane says, I think the continuum comprises:
Firm philosophical standing in the Bayes camp
Both considered valid, with one approach more or less preferable for a given problem
I'd use a Bayesian approach (at a... | Do working statisticians care about the difference between frequentist and Bayesian inference?
Adding to what Shane says, I think the continuum comprises:
Firm philosophical standing in the Bayes camp
Both considered valid, with one approach more or less preferable for a given problem
I'd use |
6,611 | Do working statisticians care about the difference between frequentist and Bayesian inference? | I think Bayesian statistics come into play in two different contexts.
On the one hand, some researchers/statisticians are definitely convinced of the "Bayesian spirit" and, acknowledging the limit of the classical frequentist hypothesis framework, have decided to concentrate on Bayesian thinking. Studies in experiment... | Do working statisticians care about the difference between frequentist and Bayesian inference? | I think Bayesian statistics come into play in two different contexts.
On the one hand, some researchers/statisticians are definitely convinced of the "Bayesian spirit" and, acknowledging the limit of | Do working statisticians care about the difference between frequentist and Bayesian inference?
I think Bayesian statistics come into play in two different contexts.
On the one hand, some researchers/statisticians are definitely convinced of the "Bayesian spirit" and, acknowledging the limit of the classical frequentis... | Do working statisticians care about the difference between frequentist and Bayesian inference?
I think Bayesian statistics come into play in two different contexts.
On the one hand, some researchers/statisticians are definitely convinced of the "Bayesian spirit" and, acknowledging the limit of |
6,612 | Do working statisticians care about the difference between frequentist and Bayesian inference? | I would imagine that in applied fields the divide is not paid that much attention as researchers/practitioners tend to be pragmatic in applied works. You choose the tool that works given the context.
However, the debate is alive and well among those who care about the philosophical issues underlying these two approach... | Do working statisticians care about the difference between frequentist and Bayesian inference? | I would imagine that in applied fields the divide is not paid that much attention as researchers/practitioners tend to be pragmatic in applied works. You choose the tool that works given the context. | Do working statisticians care about the difference between frequentist and Bayesian inference?
I would imagine that in applied fields the divide is not paid that much attention as researchers/practitioners tend to be pragmatic in applied works. You choose the tool that works given the context.
However, the debate is a... | Do working statisticians care about the difference between frequentist and Bayesian inference?
I would imagine that in applied fields the divide is not paid that much attention as researchers/practitioners tend to be pragmatic in applied works. You choose the tool that works given the context. |
6,613 | Do working statisticians care about the difference between frequentist and Bayesian inference? | While this is subjective, I would say:
It is called the Bayesian/frequentist "debate" for a reason. There is a clear philosophical difference between the two approaches.
But as with most things, it's a spectrum. Some people are very much in one camp or the other and completely reject the alternative. Most people p... | Do working statisticians care about the difference between frequentist and Bayesian inference? | While this is subjective, I would say:
It is called the Bayesian/frequentist "debate" for a reason. There is a clear philosophical difference between the two approaches.
But as with most things, it | Do working statisticians care about the difference between frequentist and Bayesian inference?
While this is subjective, I would say:
It is called the Bayesian/frequentist "debate" for a reason. There is a clear philosophical difference between the two approaches.
But as with most things, it's a spectrum. Some peop... | Do working statisticians care about the difference between frequentist and Bayesian inference?
While this is subjective, I would say:
It is called the Bayesian/frequentist "debate" for a reason. There is a clear philosophical difference between the two approaches.
But as with most things, it |
6,614 | Why use vector error correction model? | The foremost advantage of VECM is that it has nice interpretation with long term and short term equations.
In theory VECM is just a representation of cointegrated VAR. This representation is courtesy of Granger's representation theorem. So if you have cointegrated VAR it has VECM representation and vice versa.
In pra... | Why use vector error correction model? | The foremost advantage of VECM is that it has nice interpretation with long term and short term equations.
In theory VECM is just a representation of cointegrated VAR. This representation is courtesy | Why use vector error correction model?
The foremost advantage of VECM is that it has nice interpretation with long term and short term equations.
In theory VECM is just a representation of cointegrated VAR. This representation is courtesy of Granger's representation theorem. So if you have cointegrated VAR it has VECM... | Why use vector error correction model?
The foremost advantage of VECM is that it has nice interpretation with long term and short term equations.
In theory VECM is just a representation of cointegrated VAR. This representation is courtesy |
6,615 | Why use vector error correction model? | I agree with mpiktas that the greatest interest of a VECM lies in the interpretation of the result, by introducing concepts such as long-term relationship between variables, and the associated concept of error correction, whereas one studies how deviations from the long-run are "corrected". Besides of this, indeed, if ... | Why use vector error correction model? | I agree with mpiktas that the greatest interest of a VECM lies in the interpretation of the result, by introducing concepts such as long-term relationship between variables, and the associated concept | Why use vector error correction model?
I agree with mpiktas that the greatest interest of a VECM lies in the interpretation of the result, by introducing concepts such as long-term relationship between variables, and the associated concept of error correction, whereas one studies how deviations from the long-run are "c... | Why use vector error correction model?
I agree with mpiktas that the greatest interest of a VECM lies in the interpretation of the result, by introducing concepts such as long-term relationship between variables, and the associated concept |
6,616 | Why use vector error correction model? | One description I've found (http://eco.uc3m.es/~jgonzalo/teaching/timeseriesMA/eviewsvar.pdf) says:
A vector error correction (VEC) model is a restricted VAR that has cointegration restrictions built into the specification, so that it is designed for use with nonstationary series that are known to be cointegrated. The... | Why use vector error correction model? | One description I've found (http://eco.uc3m.es/~jgonzalo/teaching/timeseriesMA/eviewsvar.pdf) says:
A vector error correction (VEC) model is a restricted VAR that has cointegration restrictions built | Why use vector error correction model?
One description I've found (http://eco.uc3m.es/~jgonzalo/teaching/timeseriesMA/eviewsvar.pdf) says:
A vector error correction (VEC) model is a restricted VAR that has cointegration restrictions built into the specification, so that it is designed for use with nonstationary series... | Why use vector error correction model?
One description I've found (http://eco.uc3m.es/~jgonzalo/teaching/timeseriesMA/eviewsvar.pdf) says:
A vector error correction (VEC) model is a restricted VAR that has cointegration restrictions built |
6,617 | Why use vector error correction model? | My understanding may be incorrect, but isn't the first step is just fitting a regression between time series using OLS - and it shows you if time series are really cointegrated (if residuals from this regression are stationary). But then cointegration is kind of a long-term relation between time-series and your residua... | Why use vector error correction model? | My understanding may be incorrect, but isn't the first step is just fitting a regression between time series using OLS - and it shows you if time series are really cointegrated (if residuals from this | Why use vector error correction model?
My understanding may be incorrect, but isn't the first step is just fitting a regression between time series using OLS - and it shows you if time series are really cointegrated (if residuals from this regression are stationary). But then cointegration is kind of a long-term relati... | Why use vector error correction model?
My understanding may be incorrect, but isn't the first step is just fitting a regression between time series using OLS - and it shows you if time series are really cointegrated (if residuals from this |
6,618 | Why use vector error correction model? | 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.
We can selection time series models based on whether t... | Why use vector error correction model? | 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.
| Why use vector error correction model?
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.
We can selectio... | Why use vector error correction model?
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.
|
6,619 | Why use vector error correction model? | You can't use VAR if the dependent variables are not stationary (that would be spurious regression). To solve for these issues, we have to test if the variables are cointegrated. In this case if we have a variable I(1), or all dependent variables are cointegrated at the same level, you can do VECM. | Why use vector error correction model? | You can't use VAR if the dependent variables are not stationary (that would be spurious regression). To solve for these issues, we have to test if the variables are cointegrated. In this case if we | Why use vector error correction model?
You can't use VAR if the dependent variables are not stationary (that would be spurious regression). To solve for these issues, we have to test if the variables are cointegrated. In this case if we have a variable I(1), or all dependent variables are cointegrated at the same lev... | Why use vector error correction model?
You can't use VAR if the dependent variables are not stationary (that would be spurious regression). To solve for these issues, we have to test if the variables are cointegrated. In this case if we |
6,620 | Why use vector error correction model? | What I observed in VAR was that it is used to capture short-run relationship between the variables employed while VECM tests for the long-run relationship. For instance, in a topic where shock is being applied, I think the appropriate estimation technique should be VAR. Meanwhile, when testing through the process of un... | Why use vector error correction model? | What I observed in VAR was that it is used to capture short-run relationship between the variables employed while VECM tests for the long-run relationship. For instance, in a topic where shock is bein | Why use vector error correction model?
What I observed in VAR was that it is used to capture short-run relationship between the variables employed while VECM tests for the long-run relationship. For instance, in a topic where shock is being applied, I think the appropriate estimation technique should be VAR. Meanwhile,... | Why use vector error correction model?
What I observed in VAR was that it is used to capture short-run relationship between the variables employed while VECM tests for the long-run relationship. For instance, in a topic where shock is bein |
6,621 | Why use vector error correction model? | If someone pops up here with the same question, here is the answer why one needs VECM instead of VAR. If your data is non stationary (finance data + some macro variables) you cannot forecast with VAR because it assume stationarity thus MLE (or OLS in this case) will produce forecasts that mean revert to quickly. VECM c... | Why use vector error correction model? | If someone pops up here with the same question, here is the answer why one needs VECM instead of VAR. If your data is non stationary (finance data + some macro variables) you cannot forecast with VAR | Why use vector error correction model?
If someone pops up here with the same question, here is the answer why one needs VECM instead of VAR. If your data is non stationary (finance data + some macro variables) you cannot forecast with VAR because it assume stationarity thus MLE (or OLS in this case) will produce foreca... | Why use vector error correction model?
If someone pops up here with the same question, here is the answer why one needs VECM instead of VAR. If your data is non stationary (finance data + some macro variables) you cannot forecast with VAR |
6,622 | Why use vector error correction model? | As has been rightly pointed out in the earlier posts , A VECM enables you to use non stationary data ( but cointegrated) for intepretation. This helps retain the relevant information in the data ( which would otherwise get missed on differencing of the same) | Why use vector error correction model? | As has been rightly pointed out in the earlier posts , A VECM enables you to use non stationary data ( but cointegrated) for intepretation. This helps retain the relevant information in the data ( wh | Why use vector error correction model?
As has been rightly pointed out in the earlier posts , A VECM enables you to use non stationary data ( but cointegrated) for intepretation. This helps retain the relevant information in the data ( which would otherwise get missed on differencing of the same) | Why use vector error correction model?
As has been rightly pointed out in the earlier posts , A VECM enables you to use non stationary data ( but cointegrated) for intepretation. This helps retain the relevant information in the data ( wh |
6,623 | Explanation of finite population correction factor? | The threshold is chosen such that it ensures convergence of the hypergeometric distribution ($\sqrt{\frac{N-n}{N-1}}$ is its SD), instead of a binomial distribution (for sampling with replacement), to a normal distribution (this is the Central Limit Theorem, see e.g., The Normal Curve, the Central Limit Theorem, and Ma... | Explanation of finite population correction factor? | The threshold is chosen such that it ensures convergence of the hypergeometric distribution ($\sqrt{\frac{N-n}{N-1}}$ is its SD), instead of a binomial distribution (for sampling with replacement), to | Explanation of finite population correction factor?
The threshold is chosen such that it ensures convergence of the hypergeometric distribution ($\sqrt{\frac{N-n}{N-1}}$ is its SD), instead of a binomial distribution (for sampling with replacement), to a normal distribution (this is the Central Limit Theorem, see e.g.,... | Explanation of finite population correction factor?
The threshold is chosen such that it ensures convergence of the hypergeometric distribution ($\sqrt{\frac{N-n}{N-1}}$ is its SD), instead of a binomial distribution (for sampling with replacement), to |
6,624 | Explanation of finite population correction factor? | As for the derivation, the setup goes as follows. Suppose we have a population of size $N$, with mean $\mu$ and variance $\sigma^2$, where each element can assume values $v_k$ for $k = 1, 2, \dots, m$. Let $n_k$ be the number of times that the value $v_k$ occurs in the population, such that the probability that we draw... | Explanation of finite population correction factor? | As for the derivation, the setup goes as follows. Suppose we have a population of size $N$, with mean $\mu$ and variance $\sigma^2$, where each element can assume values $v_k$ for $k = 1, 2, \dots, m$ | Explanation of finite population correction factor?
As for the derivation, the setup goes as follows. Suppose we have a population of size $N$, with mean $\mu$ and variance $\sigma^2$, where each element can assume values $v_k$ for $k = 1, 2, \dots, m$. Let $n_k$ be the number of times that the value $v_k$ occurs in th... | Explanation of finite population correction factor?
As for the derivation, the setup goes as follows. Suppose we have a population of size $N$, with mean $\mu$ and variance $\sigma^2$, where each element can assume values $v_k$ for $k = 1, 2, \dots, m$ |
6,625 | Explanation of finite population correction factor? | Here is an alternative setup within the framework of the superpopulation model of sampling theory. It differs in notation and conception to classical sampling theory, but I think it is quite simple and intuitive.
Let $X_1,X_2,X_3,...$ be an exchangeable "superpopulation" of values. Take the first $N$ values to be the... | Explanation of finite population correction factor? | Here is an alternative setup within the framework of the superpopulation model of sampling theory. It differs in notation and conception to classical sampling theory, but I think it is quite simple a | Explanation of finite population correction factor?
Here is an alternative setup within the framework of the superpopulation model of sampling theory. It differs in notation and conception to classical sampling theory, but I think it is quite simple and intuitive.
Let $X_1,X_2,X_3,...$ be an exchangeable "superpopulat... | Explanation of finite population correction factor?
Here is an alternative setup within the framework of the superpopulation model of sampling theory. It differs in notation and conception to classical sampling theory, but I think it is quite simple a |
6,626 | Meaning (and proof) of "RNN can approximate any algorithm" | Background
We first have to go over some concepts from the theory of computation. An algorithm is a procedure for calculating a function. Given the input, the algorithm must produce the correct output in a finite number of steps and then terminate. To say that a function is computable means that there exists an algorit... | Meaning (and proof) of "RNN can approximate any algorithm" | Background
We first have to go over some concepts from the theory of computation. An algorithm is a procedure for calculating a function. Given the input, the algorithm must produce the correct output | Meaning (and proof) of "RNN can approximate any algorithm"
Background
We first have to go over some concepts from the theory of computation. An algorithm is a procedure for calculating a function. Given the input, the algorithm must produce the correct output in a finite number of steps and then terminate. To say that ... | Meaning (and proof) of "RNN can approximate any algorithm"
Background
We first have to go over some concepts from the theory of computation. An algorithm is a procedure for calculating a function. Given the input, the algorithm must produce the correct output |
6,627 | Meaning (and proof) of "RNN can approximate any algorithm" | I think this is what you're looking for. This guy proved that a multilayer, or even a single layer feedforward network could approximate any function, provided that the net has enough hidden units.
Hornik, K. (1991). Approximation capabilities of multilayer feedforward networks. Neural networks, 4(2), 251-257. | Meaning (and proof) of "RNN can approximate any algorithm" | I think this is what you're looking for. This guy proved that a multilayer, or even a single layer feedforward network could approximate any function, provided that the net has enough hidden units.
Ho | Meaning (and proof) of "RNN can approximate any algorithm"
I think this is what you're looking for. This guy proved that a multilayer, or even a single layer feedforward network could approximate any function, provided that the net has enough hidden units.
Hornik, K. (1991). Approximation capabilities of multilayer fee... | Meaning (and proof) of "RNN can approximate any algorithm"
I think this is what you're looking for. This guy proved that a multilayer, or even a single layer feedforward network could approximate any function, provided that the net has enough hidden units.
Ho |
6,628 | Meaning (and proof) of "RNN can approximate any algorithm" | RNN also means Random Neural Network. Its approximation capability was proved in two papers:
Erol Gelenbe, Zhi-Hong Mao, Yan-Da Li: Function approximation with spiked random networks. IEEE Trans. Neural Networks 10(1): 3-9 (1999)
Erol Gelenbe, Zhi-Hong Mao and Yan-Da Li: Function Approximation by Random Neural Networks... | Meaning (and proof) of "RNN can approximate any algorithm" | RNN also means Random Neural Network. Its approximation capability was proved in two papers:
Erol Gelenbe, Zhi-Hong Mao, Yan-Da Li: Function approximation with spiked random networks. IEEE Trans. Neur | Meaning (and proof) of "RNN can approximate any algorithm"
RNN also means Random Neural Network. Its approximation capability was proved in two papers:
Erol Gelenbe, Zhi-Hong Mao, Yan-Da Li: Function approximation with spiked random networks. IEEE Trans. Neural Networks 10(1): 3-9 (1999)
Erol Gelenbe, Zhi-Hong Mao and ... | Meaning (and proof) of "RNN can approximate any algorithm"
RNN also means Random Neural Network. Its approximation capability was proved in two papers:
Erol Gelenbe, Zhi-Hong Mao, Yan-Da Li: Function approximation with spiked random networks. IEEE Trans. Neur |
6,629 | When do Poisson and negative binomial regressions fit the same coefficients? | You have discovered an intimate, but generic, property of GLMs fit by maximum likelihood. The result drops out once one considers the simplest case of all: Fitting a single parameter to a single observation!
One sentence answer: If all we care about is fitting separate means to disjoint subsets of our sample, then GLM... | When do Poisson and negative binomial regressions fit the same coefficients? | You have discovered an intimate, but generic, property of GLMs fit by maximum likelihood. The result drops out once one considers the simplest case of all: Fitting a single parameter to a single obser | When do Poisson and negative binomial regressions fit the same coefficients?
You have discovered an intimate, but generic, property of GLMs fit by maximum likelihood. The result drops out once one considers the simplest case of all: Fitting a single parameter to a single observation!
One sentence answer: If all we car... | When do Poisson and negative binomial regressions fit the same coefficients?
You have discovered an intimate, but generic, property of GLMs fit by maximum likelihood. The result drops out once one considers the simplest case of all: Fitting a single parameter to a single obser |
6,630 | When do Poisson and negative binomial regressions fit the same coefficients? | In order to see what is going on here, it is useful first to do the regression without the intercept, since an intercept in a categorical regression with just one predictor is meaningless:
> rs1 = glm(breaks ~ tension-1, data=warpbreaks, family="poisson")
> rs2 = glm.nb(breaks ~ tension-1, data=warpbreaks)
Since Poiss... | When do Poisson and negative binomial regressions fit the same coefficients? | In order to see what is going on here, it is useful first to do the regression without the intercept, since an intercept in a categorical regression with just one predictor is meaningless:
> rs1 = glm | When do Poisson and negative binomial regressions fit the same coefficients?
In order to see what is going on here, it is useful first to do the regression without the intercept, since an intercept in a categorical regression with just one predictor is meaningless:
> rs1 = glm(breaks ~ tension-1, data=warpbreaks, famil... | When do Poisson and negative binomial regressions fit the same coefficients?
In order to see what is going on here, it is useful first to do the regression without the intercept, since an intercept in a categorical regression with just one predictor is meaningless:
> rs1 = glm |
6,631 | Theory behind partial least squares regression | Section 3.5.2 in The Elements of Statistical Learning is useful because it puts PLS regression in the right context (of other regularization methods), but is indeed very brief, and leaves some important statements as exercises. In addition, it only considers a case of a univariate dependent variable $\mathbf y$.
The... | Theory behind partial least squares regression | Section 3.5.2 in The Elements of Statistical Learning is useful because it puts PLS regression in the right context (of other regularization methods), but is indeed very brief, and leaves some importa | Theory behind partial least squares regression
Section 3.5.2 in The Elements of Statistical Learning is useful because it puts PLS regression in the right context (of other regularization methods), but is indeed very brief, and leaves some important statements as exercises. In addition, it only considers a case of a... | Theory behind partial least squares regression
Section 3.5.2 in The Elements of Statistical Learning is useful because it puts PLS regression in the right context (of other regularization methods), but is indeed very brief, and leaves some importa |
6,632 | Theory behind partial least squares regression | Yes. Herman Wold's book Theoretical Empiricism: A general rationale for scientific model-building is the single best exposition of PLS that I'm aware of, especially given that Wold is an originator of the approach. Not to mention that it's simply an interesting book to read and know about. In addition based on a search... | Theory behind partial least squares regression | Yes. Herman Wold's book Theoretical Empiricism: A general rationale for scientific model-building is the single best exposition of PLS that I'm aware of, especially given that Wold is an originator of | Theory behind partial least squares regression
Yes. Herman Wold's book Theoretical Empiricism: A general rationale for scientific model-building is the single best exposition of PLS that I'm aware of, especially given that Wold is an originator of the approach. Not to mention that it's simply an interesting book to rea... | Theory behind partial least squares regression
Yes. Herman Wold's book Theoretical Empiricism: A general rationale for scientific model-building is the single best exposition of PLS that I'm aware of, especially given that Wold is an originator of |
6,633 | Theory behind partial least squares regression | I recommend this lecture: https://www.youtube.com/watch?v=Px2otK2nZ1c by Prof Asada who explains that PLS consists of the follwoing three steps which are iterated for k times (when k components are used):
finding the directions v,w which maximize the correlation E[(xv)(yw)]
finding the parameter beta of the linear mod... | Theory behind partial least squares regression | I recommend this lecture: https://www.youtube.com/watch?v=Px2otK2nZ1c by Prof Asada who explains that PLS consists of the follwoing three steps which are iterated for k times (when k components are us | Theory behind partial least squares regression
I recommend this lecture: https://www.youtube.com/watch?v=Px2otK2nZ1c by Prof Asada who explains that PLS consists of the follwoing three steps which are iterated for k times (when k components are used):
finding the directions v,w which maximize the correlation E[(xv)(yw... | Theory behind partial least squares regression
I recommend this lecture: https://www.youtube.com/watch?v=Px2otK2nZ1c by Prof Asada who explains that PLS consists of the follwoing three steps which are iterated for k times (when k components are us |
6,634 | Inclusion of lagged dependent variable in regression | The decision to include a lagged dependent variable in your model is really a theoretical question. It makes sense to include a lagged DV if you expect that the current level of the DV is heavily determined by its past level. In that case, not including the lagged DV will lead to omitted variable bias and your results ... | Inclusion of lagged dependent variable in regression | The decision to include a lagged dependent variable in your model is really a theoretical question. It makes sense to include a lagged DV if you expect that the current level of the DV is heavily dete | Inclusion of lagged dependent variable in regression
The decision to include a lagged dependent variable in your model is really a theoretical question. It makes sense to include a lagged DV if you expect that the current level of the DV is heavily determined by its past level. In that case, not including the lagged DV... | Inclusion of lagged dependent variable in regression
The decision to include a lagged dependent variable in your model is really a theoretical question. It makes sense to include a lagged DV if you expect that the current level of the DV is heavily dete |
6,635 | Inclusion of lagged dependent variable in regression | I recommend two articles:
Achen C. H. (2001) Why lagged dependent variables can suppress the explanatory power of other independent variables (link)
Keele, L. and Kelly N. J. (2005) Dynamic models for dynamic theories: the ins and outs of lagged dependent variables (link).
The upshot is that including a lagged depend... | Inclusion of lagged dependent variable in regression | I recommend two articles:
Achen C. H. (2001) Why lagged dependent variables can suppress the explanatory power of other independent variables (link)
Keele, L. and Kelly N. J. (2005) Dynamic models fo | Inclusion of lagged dependent variable in regression
I recommend two articles:
Achen C. H. (2001) Why lagged dependent variables can suppress the explanatory power of other independent variables (link)
Keele, L. and Kelly N. J. (2005) Dynamic models for dynamic theories: the ins and outs of lagged dependent variables ... | Inclusion of lagged dependent variable in regression
I recommend two articles:
Achen C. H. (2001) Why lagged dependent variables can suppress the explanatory power of other independent variables (link)
Keele, L. and Kelly N. J. (2005) Dynamic models fo |
6,636 | Inclusion of lagged dependent variable in regression | Including lagged dependent variables can reduce the occurrence of autocorrelation arising from model misspecification. Thus accounting for lagged dependent variables helps you to defend the existence of autocorrelation in the model. The past value affects the present in the model, requires theoretical foundation, and b... | Inclusion of lagged dependent variable in regression | Including lagged dependent variables can reduce the occurrence of autocorrelation arising from model misspecification. Thus accounting for lagged dependent variables helps you to defend the existence | Inclusion of lagged dependent variable in regression
Including lagged dependent variables can reduce the occurrence of autocorrelation arising from model misspecification. Thus accounting for lagged dependent variables helps you to defend the existence of autocorrelation in the model. The past value affects the present... | Inclusion of lagged dependent variable in regression
Including lagged dependent variables can reduce the occurrence of autocorrelation arising from model misspecification. Thus accounting for lagged dependent variables helps you to defend the existence |
6,637 | Inclusion of lagged dependent variable in regression | Some say that the inclusion of LDV will biase downward the coefficient of other IVs.
To be more specific, using OLS with the inclusion of a LDV can bias your coefficient downwards. Consider the model $Y_t=\alpha + \lambda Y_{t-1} + U_t$ for $t=1,...,T$ with $-1<\lambda<1$ and the $U_t$s are identically distributed nor... | Inclusion of lagged dependent variable in regression | Some say that the inclusion of LDV will biase downward the coefficient of other IVs.
To be more specific, using OLS with the inclusion of a LDV can bias your coefficient downwards. Consider the model | Inclusion of lagged dependent variable in regression
Some say that the inclusion of LDV will biase downward the coefficient of other IVs.
To be more specific, using OLS with the inclusion of a LDV can bias your coefficient downwards. Consider the model $Y_t=\alpha + \lambda Y_{t-1} + U_t$ for $t=1,...,T$ with $-1<\lam... | Inclusion of lagged dependent variable in regression
Some say that the inclusion of LDV will biase downward the coefficient of other IVs.
To be more specific, using OLS with the inclusion of a LDV can bias your coefficient downwards. Consider the model |
6,638 | Inclusion of lagged dependent variable in regression | Yes, you should be wary of Nickell bias in a small T large N situation (Nickell, S. (1981). Biases in dynamic models with fixed effects. Econometrica: Journal of the Econometric Society, 1417-1426.)
You might wish to look at Dynamic Panel Data models like Arellano-Bond or Blundell-Bond estimators. | Inclusion of lagged dependent variable in regression | Yes, you should be wary of Nickell bias in a small T large N situation (Nickell, S. (1981). Biases in dynamic models with fixed effects. Econometrica: Journal of the Econometric Society, 1417-1426.)
Y | Inclusion of lagged dependent variable in regression
Yes, you should be wary of Nickell bias in a small T large N situation (Nickell, S. (1981). Biases in dynamic models with fixed effects. Econometrica: Journal of the Econometric Society, 1417-1426.)
You might wish to look at Dynamic Panel Data models like Arellano-Bo... | Inclusion of lagged dependent variable in regression
Yes, you should be wary of Nickell bias in a small T large N situation (Nickell, S. (1981). Biases in dynamic models with fixed effects. Econometrica: Journal of the Econometric Society, 1417-1426.)
Y |
6,639 | Inclusion of lagged dependent variable in regression | What makes me intrigued about this question is not knowing more about the specification of the model or the estimation technique for it. I mention that because although using a lagged DV among the IVs may be theoretically important and methodologically necessary, it may also introduce a risky amount of endongeneity in ... | Inclusion of lagged dependent variable in regression | What makes me intrigued about this question is not knowing more about the specification of the model or the estimation technique for it. I mention that because although using a lagged DV among the IVs | Inclusion of lagged dependent variable in regression
What makes me intrigued about this question is not knowing more about the specification of the model or the estimation technique for it. I mention that because although using a lagged DV among the IVs may be theoretically important and methodologically necessary, it ... | Inclusion of lagged dependent variable in regression
What makes me intrigued about this question is not knowing more about the specification of the model or the estimation technique for it. I mention that because although using a lagged DV among the IVs |
6,640 | Measures of similarity or distance between two covariance matrices | You can use any of the norms $\| A-B \|_p $ (see Wikipedia on a variety of norms; note that the square-root of the sum of squared distances, $\sqrt{\sum_{i,j} (a_{ij}-b_{ij})^2}$, is called Frobenius norm, and is different from $L_2$ norm, which is the square root of the largest eigenvalue of $(A-B)^2$, although of cou... | Measures of similarity or distance between two covariance matrices | You can use any of the norms $\| A-B \|_p $ (see Wikipedia on a variety of norms; note that the square-root of the sum of squared distances, $\sqrt{\sum_{i,j} (a_{ij}-b_{ij})^2}$, is called Frobenius | Measures of similarity or distance between two covariance matrices
You can use any of the norms $\| A-B \|_p $ (see Wikipedia on a variety of norms; note that the square-root of the sum of squared distances, $\sqrt{\sum_{i,j} (a_{ij}-b_{ij})^2}$, is called Frobenius norm, and is different from $L_2$ norm, which is the ... | Measures of similarity or distance between two covariance matrices
You can use any of the norms $\| A-B \|_p $ (see Wikipedia on a variety of norms; note that the square-root of the sum of squared distances, $\sqrt{\sum_{i,j} (a_{ij}-b_{ij})^2}$, is called Frobenius |
6,641 | Measures of similarity or distance between two covariance matrices | A measure introduced by Herdin (2005) Correlation Matrix Distance, a Meaningful Measure
for Evaluation of Non-Stationary MIMO Channels is
$$d = 1 - \frac{\text{tr}(R_1 \cdot R_2)}{\|R_1\| \cdot \|R_2\|},$$
where the norm is the Frobenius norm. | Measures of similarity or distance between two covariance matrices | A measure introduced by Herdin (2005) Correlation Matrix Distance, a Meaningful Measure
for Evaluation of Non-Stationary MIMO Channels is
$$d = 1 - \frac{\text{tr}(R_1 \cdot R_2)}{\|R_1\| \cdot \|R_2\ | Measures of similarity or distance between two covariance matrices
A measure introduced by Herdin (2005) Correlation Matrix Distance, a Meaningful Measure
for Evaluation of Non-Stationary MIMO Channels is
$$d = 1 - \frac{\text{tr}(R_1 \cdot R_2)}{\|R_1\| \cdot \|R_2\|},$$
where the norm is the Frobenius norm. | Measures of similarity or distance between two covariance matrices
A measure introduced by Herdin (2005) Correlation Matrix Distance, a Meaningful Measure
for Evaluation of Non-Stationary MIMO Channels is
$$d = 1 - \frac{\text{tr}(R_1 \cdot R_2)}{\|R_1\| \cdot \|R_2\ |
6,642 | Measures of similarity or distance between two covariance matrices | Denote $\varSigma_1$ and $\varSigma_2$ your matrices both of dimension $p$.
Cond number:
$\log(\lambda_1)-\log(\lambda_p)$ where $\lambda_1$ ($\lambda_p$) is the largest
(smallest) eigenvalue of $\varSigma^*$, where $\varSigma^*$ is defined as:
$\varSigma^*:=\varSigma_1^{-1/2}\varSigma_2\varSigma_1^{-1/2}$
Edit: I ... | Measures of similarity or distance between two covariance matrices | Denote $\varSigma_1$ and $\varSigma_2$ your matrices both of dimension $p$.
Cond number:
$\log(\lambda_1)-\log(\lambda_p)$ where $\lambda_1$ ($\lambda_p$) is the largest
(smallest) eigenvalue of $\ | Measures of similarity or distance between two covariance matrices
Denote $\varSigma_1$ and $\varSigma_2$ your matrices both of dimension $p$.
Cond number:
$\log(\lambda_1)-\log(\lambda_p)$ where $\lambda_1$ ($\lambda_p$) is the largest
(smallest) eigenvalue of $\varSigma^*$, where $\varSigma^*$ is defined as:
$\var... | Measures of similarity or distance between two covariance matrices
Denote $\varSigma_1$ and $\varSigma_2$ your matrices both of dimension $p$.
Cond number:
$\log(\lambda_1)-\log(\lambda_p)$ where $\lambda_1$ ($\lambda_p$) is the largest
(smallest) eigenvalue of $\ |
6,643 | Measures of similarity or distance between two covariance matrices | 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.
The covariance matrix distance is used for tracking ob... | Measures of similarity or distance between two covariance matrices | 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.
| Measures of similarity or distance between two covariance matrices
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.
... | Measures of similarity or distance between two covariance matrices
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.
|
6,644 | Is a "hurdle model" really one model? Or just two separate, sequential models? | Separating the log-likelihood
It is correct that most hurdle models can be estimated separately (I would say, instead of sequentially). The reason is that the log-likelihood can be decomposed into two parts that can be maximized separately. This is because $\hat \pi$ is a just a scaling factor in (5.34) that becomes an... | Is a "hurdle model" really one model? Or just two separate, sequential models? | Separating the log-likelihood
It is correct that most hurdle models can be estimated separately (I would say, instead of sequentially). The reason is that the log-likelihood can be decomposed into two | Is a "hurdle model" really one model? Or just two separate, sequential models?
Separating the log-likelihood
It is correct that most hurdle models can be estimated separately (I would say, instead of sequentially). The reason is that the log-likelihood can be decomposed into two parts that can be maximized separately. ... | Is a "hurdle model" really one model? Or just two separate, sequential models?
Separating the log-likelihood
It is correct that most hurdle models can be estimated separately (I would say, instead of sequentially). The reason is that the log-likelihood can be decomposed into two |
6,645 | Is a "hurdle model" really one model? Or just two separate, sequential models? | I agree the difference between zero-inflated and hurdle models is hard to understand. Both are a kind of mixture model. From what I can tell, the important difference is, in a zero-inflated model, you mix a mass at zero with a distribution \textit{that can also take the value zero}. For a hurdle model, you mix a mas... | Is a "hurdle model" really one model? Or just two separate, sequential models? | I agree the difference between zero-inflated and hurdle models is hard to understand. Both are a kind of mixture model. From what I can tell, the important difference is, in a zero-inflated model, y | Is a "hurdle model" really one model? Or just two separate, sequential models?
I agree the difference between zero-inflated and hurdle models is hard to understand. Both are a kind of mixture model. From what I can tell, the important difference is, in a zero-inflated model, you mix a mass at zero with a distribution... | Is a "hurdle model" really one model? Or just two separate, sequential models?
I agree the difference between zero-inflated and hurdle models is hard to understand. Both are a kind of mixture model. From what I can tell, the important difference is, in a zero-inflated model, y |
6,646 | Is a "hurdle model" really one model? Or just two separate, sequential models? | Regarding the philosophical aspect, "when should we consider something a single model and when two separate models", it may be interesting to note that the sample estimates of the model-parameters are correlated.
In the plot below with a simulation you mostly see the correlation between the slope and the intercept of t... | Is a "hurdle model" really one model? Or just two separate, sequential models? | Regarding the philosophical aspect, "when should we consider something a single model and when two separate models", it may be interesting to note that the sample estimates of the model-parameters are | Is a "hurdle model" really one model? Or just two separate, sequential models?
Regarding the philosophical aspect, "when should we consider something a single model and when two separate models", it may be interesting to note that the sample estimates of the model-parameters are correlated.
In the plot below with a sim... | Is a "hurdle model" really one model? Or just two separate, sequential models?
Regarding the philosophical aspect, "when should we consider something a single model and when two separate models", it may be interesting to note that the sample estimates of the model-parameters are |
6,647 | Do we need gradient descent to find the coefficients of a linear regression model? | Linear Least squares can be solved by
0) Using high quality linear least squares solver, based on either SVD or QR, as described below, for unconstrained linear least squares, or based on a version of Quadratic Programming or Conic Optimization for bound or linearly constrained least squares, as described below. Such a... | Do we need gradient descent to find the coefficients of a linear regression model? | Linear Least squares can be solved by
0) Using high quality linear least squares solver, based on either SVD or QR, as described below, for unconstrained linear least squares, or based on a version of | Do we need gradient descent to find the coefficients of a linear regression model?
Linear Least squares can be solved by
0) Using high quality linear least squares solver, based on either SVD or QR, as described below, for unconstrained linear least squares, or based on a version of Quadratic Programming or Conic Optim... | Do we need gradient descent to find the coefficients of a linear regression model?
Linear Least squares can be solved by
0) Using high quality linear least squares solver, based on either SVD or QR, as described below, for unconstrained linear least squares, or based on a version of |
6,648 | Do we need gradient descent to find the coefficients of a linear regression model? | Finding coefficients of a linear model is technically the process of finding solutions to a set of Linear Equations.
For computing such solutions, a lot of optimization techniques have been developed and Gradient Descent is one of them.
Thus, Gradient Descent is not the only way to do that.
Andrew Ng uses it in the cou... | Do we need gradient descent to find the coefficients of a linear regression model? | Finding coefficients of a linear model is technically the process of finding solutions to a set of Linear Equations.
For computing such solutions, a lot of optimization techniques have been developed | Do we need gradient descent to find the coefficients of a linear regression model?
Finding coefficients of a linear model is technically the process of finding solutions to a set of Linear Equations.
For computing such solutions, a lot of optimization techniques have been developed and Gradient Descent is one of them.
... | Do we need gradient descent to find the coefficients of a linear regression model?
Finding coefficients of a linear model is technically the process of finding solutions to a set of Linear Equations.
For computing such solutions, a lot of optimization techniques have been developed |
6,649 | Do we need gradient descent to find the coefficients of a linear regression model? | Yes you can.
To solve the Ax=B problem you can use the QR or other matrix decomposition based least squares solvers. However, I tried to do it by Gradient Descent with L2 norm regularization. And I think GD is better.
The first picture is the result of numpy.nnls, orange line is ground truth, blue line is numpy.nnls re... | Do we need gradient descent to find the coefficients of a linear regression model? | Yes you can.
To solve the Ax=B problem you can use the QR or other matrix decomposition based least squares solvers. However, I tried to do it by Gradient Descent with L2 norm regularization. And I th | Do we need gradient descent to find the coefficients of a linear regression model?
Yes you can.
To solve the Ax=B problem you can use the QR or other matrix decomposition based least squares solvers. However, I tried to do it by Gradient Descent with L2 norm regularization. And I think GD is better.
The first picture i... | Do we need gradient descent to find the coefficients of a linear regression model?
Yes you can.
To solve the Ax=B problem you can use the QR or other matrix decomposition based least squares solvers. However, I tried to do it by Gradient Descent with L2 norm regularization. And I th |
6,650 | Variance of a function of one random variable | Update
I've underestimated Taylor expansions. They actually work. I assumed that integral of the remainder term can be unbounded, but with a little work it can be shown that this is not the case.
The Taylor expansion works for functions in bounded closed interval. For random variables with finite variance Chebyshev in... | Variance of a function of one random variable | Update
I've underestimated Taylor expansions. They actually work. I assumed that integral of the remainder term can be unbounded, but with a little work it can be shown that this is not the case.
The | Variance of a function of one random variable
Update
I've underestimated Taylor expansions. They actually work. I assumed that integral of the remainder term can be unbounded, but with a little work it can be shown that this is not the case.
The Taylor expansion works for functions in bounded closed interval. For rando... | Variance of a function of one random variable
Update
I've underestimated Taylor expansions. They actually work. I assumed that integral of the remainder term can be unbounded, but with a little work it can be shown that this is not the case.
The |
6,651 | Variance of a function of one random variable | To know the first two moments of X (mean and variance) is not enough, if the function f(x) is arbitrary (non linear). Not only for computing the variance of the transformed variable Y, but also for its mean.
To see this -and perhaps to attack your problem- you can assume that your transformation function has a Taylor e... | Variance of a function of one random variable | To know the first two moments of X (mean and variance) is not enough, if the function f(x) is arbitrary (non linear). Not only for computing the variance of the transformed variable Y, but also for it | Variance of a function of one random variable
To know the first two moments of X (mean and variance) is not enough, if the function f(x) is arbitrary (non linear). Not only for computing the variance of the transformed variable Y, but also for its mean.
To see this -and perhaps to attack your problem- you can assume th... | Variance of a function of one random variable
To know the first two moments of X (mean and variance) is not enough, if the function f(x) is arbitrary (non linear). Not only for computing the variance of the transformed variable Y, but also for it |
6,652 | Justification of one-tailed hypothesis testing | That's a thoughtful question. Many texts (perhaps for pedagogical reasons) paper over this issue. What's really going on is that $H_0$ is a composite "hypothesis" in your one-sided situation: it's actually a set of hypotheses, not a single one. It is necessary that for every possible hypothesis in $H_0$, the chance ... | Justification of one-tailed hypothesis testing | That's a thoughtful question. Many texts (perhaps for pedagogical reasons) paper over this issue. What's really going on is that $H_0$ is a composite "hypothesis" in your one-sided situation: it's a | Justification of one-tailed hypothesis testing
That's a thoughtful question. Many texts (perhaps for pedagogical reasons) paper over this issue. What's really going on is that $H_0$ is a composite "hypothesis" in your one-sided situation: it's actually a set of hypotheses, not a single one. It is necessary that for ... | Justification of one-tailed hypothesis testing
That's a thoughtful question. Many texts (perhaps for pedagogical reasons) paper over this issue. What's really going on is that $H_0$ is a composite "hypothesis" in your one-sided situation: it's a |
6,653 | Justification of one-tailed hypothesis testing | I see the $p$-value as the maximum probability of a type I error. If $\theta \ll \theta_0$, the probability of a type I error rate may be effectively zero, but so be it. When looking at the test from a minimax perspective, an adversary would never draw from deep in the 'interior' of the null hypothesis anyway, and the ... | Justification of one-tailed hypothesis testing | I see the $p$-value as the maximum probability of a type I error. If $\theta \ll \theta_0$, the probability of a type I error rate may be effectively zero, but so be it. When looking at the test from | Justification of one-tailed hypothesis testing
I see the $p$-value as the maximum probability of a type I error. If $\theta \ll \theta_0$, the probability of a type I error rate may be effectively zero, but so be it. When looking at the test from a minimax perspective, an adversary would never draw from deep in the 'in... | Justification of one-tailed hypothesis testing
I see the $p$-value as the maximum probability of a type I error. If $\theta \ll \theta_0$, the probability of a type I error rate may be effectively zero, but so be it. When looking at the test from |
6,654 | Justification of one-tailed hypothesis testing | You would use a one-sided hypothesis test if only results in one direction are supportive of the conclusion you are trying to reach.
Think of this in terms of the question you are asking. Suppose, for example, you want to see whether obesity leads to increased risk of heart attack. You gather your data, which might con... | Justification of one-tailed hypothesis testing | You would use a one-sided hypothesis test if only results in one direction are supportive of the conclusion you are trying to reach.
Think of this in terms of the question you are asking. Suppose, for | Justification of one-tailed hypothesis testing
You would use a one-sided hypothesis test if only results in one direction are supportive of the conclusion you are trying to reach.
Think of this in terms of the question you are asking. Suppose, for example, you want to see whether obesity leads to increased risk of hear... | Justification of one-tailed hypothesis testing
You would use a one-sided hypothesis test if only results in one direction are supportive of the conclusion you are trying to reach.
Think of this in terms of the question you are asking. Suppose, for |
6,655 | Justification of one-tailed hypothesis testing | The $p$-value is the probability of the respective event under the condition that $H_0$ is true. The simplest possible toy example are two coin tosses. The 2-sided $H_0$ would be that you consider the coin fair, i.e. you throw one head and one tail. The probability for that is $0.5$. $H_1$ in this case is that you cons... | Justification of one-tailed hypothesis testing | The $p$-value is the probability of the respective event under the condition that $H_0$ is true. The simplest possible toy example are two coin tosses. The 2-sided $H_0$ would be that you consider the | Justification of one-tailed hypothesis testing
The $p$-value is the probability of the respective event under the condition that $H_0$ is true. The simplest possible toy example are two coin tosses. The 2-sided $H_0$ would be that you consider the coin fair, i.e. you throw one head and one tail. The probability for tha... | Justification of one-tailed hypothesis testing
The $p$-value is the probability of the respective event under the condition that $H_0$ is true. The simplest possible toy example are two coin tosses. The 2-sided $H_0$ would be that you consider the |
6,656 | Why are Decision Trees not computationally expensive? | Decision trees algorithms do not compute all possible trees when they fit a tree. If they did they would be solving an NP-hard problem. Decision tree fitting algorithms typically make greedy decisions in the fitting process—at each stage they optimize the sub-problem for finding an optimal split with the data in the gi... | Why are Decision Trees not computationally expensive? | Decision trees algorithms do not compute all possible trees when they fit a tree. If they did they would be solving an NP-hard problem. Decision tree fitting algorithms typically make greedy decisions | Why are Decision Trees not computationally expensive?
Decision trees algorithms do not compute all possible trees when they fit a tree. If they did they would be solving an NP-hard problem. Decision tree fitting algorithms typically make greedy decisions in the fitting process—at each stage they optimize the sub-proble... | Why are Decision Trees not computationally expensive?
Decision trees algorithms do not compute all possible trees when they fit a tree. If they did they would be solving an NP-hard problem. Decision tree fitting algorithms typically make greedy decisions |
6,657 | Why are Decision Trees not computationally expensive? | There are some differences between the CART and C4.5 algorithms for building decision trees. For instance, CART uses Gini Impurity to pick features while C.4.5 uses Shannon Entropy. I don't think the differences are relevant for the answer, so I will not differentiate between those.
What makes decision trees faster tha... | Why are Decision Trees not computationally expensive? | There are some differences between the CART and C4.5 algorithms for building decision trees. For instance, CART uses Gini Impurity to pick features while C.4.5 uses Shannon Entropy. I don't think the | Why are Decision Trees not computationally expensive?
There are some differences between the CART and C4.5 algorithms for building decision trees. For instance, CART uses Gini Impurity to pick features while C.4.5 uses Shannon Entropy. I don't think the differences are relevant for the answer, so I will not differentia... | Why are Decision Trees not computationally expensive?
There are some differences between the CART and C4.5 algorithms for building decision trees. For instance, CART uses Gini Impurity to pick features while C.4.5 uses Shannon Entropy. I don't think the |
6,658 | Why are Decision Trees not computationally expensive? | Just to enrich the answers,
Hierarchic axis-parallel decision-trees are fast (CART, C4.5) but there are other alternatives such as non-hierarchic decision trees or those that perform oblique partitions that are not, although they can be more accurate. Check the following references if you are interested (They are not ... | Why are Decision Trees not computationally expensive? | Just to enrich the answers,
Hierarchic axis-parallel decision-trees are fast (CART, C4.5) but there are other alternatives such as non-hierarchic decision trees or those that perform oblique partitio | Why are Decision Trees not computationally expensive?
Just to enrich the answers,
Hierarchic axis-parallel decision-trees are fast (CART, C4.5) but there are other alternatives such as non-hierarchic decision trees or those that perform oblique partitions that are not, although they can be more accurate. Check the fol... | Why are Decision Trees not computationally expensive?
Just to enrich the answers,
Hierarchic axis-parallel decision-trees are fast (CART, C4.5) but there are other alternatives such as non-hierarchic decision trees or those that perform oblique partitio |
6,659 | What's the difference between logistic regression and perceptron? | In short, logistic regression has probabilistic connotations that go beyond the classifier use in ML. I have some notes on logistic regression here.
The hypothesis in logistic regression provides a measure of uncertainty in the occurrence of a binary outcome based on a linear model. The output is bounded asymptotically... | What's the difference between logistic regression and perceptron? | In short, logistic regression has probabilistic connotations that go beyond the classifier use in ML. I have some notes on logistic regression here.
The hypothesis in logistic regression provides a me | What's the difference between logistic regression and perceptron?
In short, logistic regression has probabilistic connotations that go beyond the classifier use in ML. I have some notes on logistic regression here.
The hypothesis in logistic regression provides a measure of uncertainty in the occurrence of a binary out... | What's the difference between logistic regression and perceptron?
In short, logistic regression has probabilistic connotations that go beyond the classifier use in ML. I have some notes on logistic regression here.
The hypothesis in logistic regression provides a me |
6,660 | What's the difference between logistic regression and perceptron? | There is some confusion that may arise here. Originally a perceptron was only referring to neural networks with a step function as the transfer function. In that case of course the difference is that the logistic regression uses a logistic function and the perceptron uses a step function. In general both algorithm shou... | What's the difference between logistic regression and perceptron? | There is some confusion that may arise here. Originally a perceptron was only referring to neural networks with a step function as the transfer function. In that case of course the difference is that | What's the difference between logistic regression and perceptron?
There is some confusion that may arise here. Originally a perceptron was only referring to neural networks with a step function as the transfer function. In that case of course the difference is that the logistic regression uses a logistic function and t... | What's the difference between logistic regression and perceptron?
There is some confusion that may arise here. Originally a perceptron was only referring to neural networks with a step function as the transfer function. In that case of course the difference is that |
6,661 | What's the difference between logistic regression and perceptron? | You can use logistic regression to build a perceptron. The logistic regression uses logistic function to build the output from a given inputs. Logistic function produces a smooth output between 0 and 1, so you need one more thing to make it a classifier, which is a threshold. Perceptrons can be built with other functio... | What's the difference between logistic regression and perceptron? | You can use logistic regression to build a perceptron. The logistic regression uses logistic function to build the output from a given inputs. Logistic function produces a smooth output between 0 and | What's the difference between logistic regression and perceptron?
You can use logistic regression to build a perceptron. The logistic regression uses logistic function to build the output from a given inputs. Logistic function produces a smooth output between 0 and 1, so you need one more thing to make it a classifier,... | What's the difference between logistic regression and perceptron?
You can use logistic regression to build a perceptron. The logistic regression uses logistic function to build the output from a given inputs. Logistic function produces a smooth output between 0 and |
6,662 | What's the difference between logistic regression and perceptron? | Suppose that our training observations are the feature vectors $x_1,\ldots, x_N \in \mathbb R^n$, and the corresponding labels are $y_1,\ldots,y_N \in \{-1, 1 \}$. For notational simplicity, let's append a $1$ to the end of each vector $x_i$.
The perceptron algorithm can be interpreted as using stochastic subgradient ... | What's the difference between logistic regression and perceptron? | Suppose that our training observations are the feature vectors $x_1,\ldots, x_N \in \mathbb R^n$, and the corresponding labels are $y_1,\ldots,y_N \in \{-1, 1 \}$. For notational simplicity, let's app | What's the difference between logistic regression and perceptron?
Suppose that our training observations are the feature vectors $x_1,\ldots, x_N \in \mathbb R^n$, and the corresponding labels are $y_1,\ldots,y_N \in \{-1, 1 \}$. For notational simplicity, let's append a $1$ to the end of each vector $x_i$.
The percep... | What's the difference between logistic regression and perceptron?
Suppose that our training observations are the feature vectors $x_1,\ldots, x_N \in \mathbb R^n$, and the corresponding labels are $y_1,\ldots,y_N \in \{-1, 1 \}$. For notational simplicity, let's app |
6,663 | What's the difference between logistic regression and perceptron? | They're both applying regression by estimating the parameters of the same logistic-transformed model. According to the properties of convex functions, the values of the parameters will be the same any way you choose to estimate them. To quote myself from a previous answer:
Logistic regression models a function of the m... | What's the difference between logistic regression and perceptron? | They're both applying regression by estimating the parameters of the same logistic-transformed model. According to the properties of convex functions, the values of the parameters will be the same any | What's the difference between logistic regression and perceptron?
They're both applying regression by estimating the parameters of the same logistic-transformed model. According to the properties of convex functions, the values of the parameters will be the same any way you choose to estimate them. To quote myself from... | What's the difference between logistic regression and perceptron?
They're both applying regression by estimating the parameters of the same logistic-transformed model. According to the properties of convex functions, the values of the parameters will be the same any |
6,664 | What's the difference between logistic regression and perceptron? | Andrew Ng used the term "logistic regression" as a model for solving the binary classification problem.
As you may saw in the paper he actually never draw the model itself.
Let me add few details to the bucket so you may find the reasoning on how I think he constructed the lectures.
The model used for the "logistic re... | What's the difference between logistic regression and perceptron? | Andrew Ng used the term "logistic regression" as a model for solving the binary classification problem.
As you may saw in the paper he actually never draw the model itself.
Let me add few details to | What's the difference between logistic regression and perceptron?
Andrew Ng used the term "logistic regression" as a model for solving the binary classification problem.
As you may saw in the paper he actually never draw the model itself.
Let me add few details to the bucket so you may find the reasoning on how I thin... | What's the difference between logistic regression and perceptron?
Andrew Ng used the term "logistic regression" as a model for solving the binary classification problem.
As you may saw in the paper he actually never draw the model itself.
Let me add few details to |
6,665 | MSE decomposition to Variance and Bias Squared | The trick is that $\mathbb{E}(\hat{\theta}) - \theta$ is a constant. | MSE decomposition to Variance and Bias Squared | The trick is that $\mathbb{E}(\hat{\theta}) - \theta$ is a constant. | MSE decomposition to Variance and Bias Squared
The trick is that $\mathbb{E}(\hat{\theta}) - \theta$ is a constant. | MSE decomposition to Variance and Bias Squared
The trick is that $\mathbb{E}(\hat{\theta}) - \theta$ is a constant. |
6,666 | MSE decomposition to Variance and Bias Squared | There has been some confusion about the question which was ambiguous being about the highlight and the step from line three to line four.
There are two terms that look a lot like each other.
$$\mathbb{E}\left[\hat{\theta}\right] - \theta \quad \text{vs} \quad \mathbb{E}\left[\hat{\theta}\right] - \hat\theta$$
The ques... | MSE decomposition to Variance and Bias Squared | There has been some confusion about the question which was ambiguous being about the highlight and the step from line three to line four.
There are two terms that look a lot like each other.
$$\mathb | MSE decomposition to Variance and Bias Squared
There has been some confusion about the question which was ambiguous being about the highlight and the step from line three to line four.
There are two terms that look a lot like each other.
$$\mathbb{E}\left[\hat{\theta}\right] - \theta \quad \text{vs} \quad \mathbb{E}\l... | MSE decomposition to Variance and Bias Squared
There has been some confusion about the question which was ambiguous being about the highlight and the step from line three to line four.
There are two terms that look a lot like each other.
$$\mathb |
6,667 | MSE decomposition to Variance and Bias Squared | $E(\hat{\theta}) - \theta$ is not a constant.
The comment of @user1158559 is actually the correct one:
$$
E[\hat{\theta} - E(\hat{\theta})] = E(\hat{\theta}) - E[E(\hat{\theta})]
= E(\hat{\theta}) - E(\hat{\theta}) = 0
$$ | MSE decomposition to Variance and Bias Squared | $E(\hat{\theta}) - \theta$ is not a constant.
The comment of @user1158559 is actually the correct one:
$$
E[\hat{\theta} - E(\hat{\theta})] = E(\hat{\theta}) - E[E(\hat{\theta})]
= E(\hat{\theta}) - | MSE decomposition to Variance and Bias Squared
$E(\hat{\theta}) - \theta$ is not a constant.
The comment of @user1158559 is actually the correct one:
$$
E[\hat{\theta} - E(\hat{\theta})] = E(\hat{\theta}) - E[E(\hat{\theta})]
= E(\hat{\theta}) - E(\hat{\theta}) = 0
$$ | MSE decomposition to Variance and Bias Squared
$E(\hat{\theta}) - \theta$ is not a constant.
The comment of @user1158559 is actually the correct one:
$$
E[\hat{\theta} - E(\hat{\theta})] = E(\hat{\theta}) - E[E(\hat{\theta})]
= E(\hat{\theta}) - |
6,668 | How does one measure the non-uniformity of a distribution? | If you have not only the frequencies but the actual counts, you can use a $\chi^2$ goodness-of-fit test for each data series. In particular, you wish to use the test for a discrete uniform distribution. This gives you a good test, which allows you to find out which data series are likely not to have been generated by a... | How does one measure the non-uniformity of a distribution? | If you have not only the frequencies but the actual counts, you can use a $\chi^2$ goodness-of-fit test for each data series. In particular, you wish to use the test for a discrete uniform distributio | How does one measure the non-uniformity of a distribution?
If you have not only the frequencies but the actual counts, you can use a $\chi^2$ goodness-of-fit test for each data series. In particular, you wish to use the test for a discrete uniform distribution. This gives you a good test, which allows you to find out w... | How does one measure the non-uniformity of a distribution?
If you have not only the frequencies but the actual counts, you can use a $\chi^2$ goodness-of-fit test for each data series. In particular, you wish to use the test for a discrete uniform distributio |
6,669 | How does one measure the non-uniformity of a distribution? | In addition to @MansT 's good ideas, you could come up with other measures, but it depends on what you mean by "non-uniformity". To keep it simple, let's look at 4 levels. Perfect uniformity is easy to define:
25 25 25 25
but which of the following is more non-uniform?
20 20 30 30
or
20 20 25 35
or are they equal... | How does one measure the non-uniformity of a distribution? | In addition to @MansT 's good ideas, you could come up with other measures, but it depends on what you mean by "non-uniformity". To keep it simple, let's look at 4 levels. Perfect uniformity is easy t | How does one measure the non-uniformity of a distribution?
In addition to @MansT 's good ideas, you could come up with other measures, but it depends on what you mean by "non-uniformity". To keep it simple, let's look at 4 levels. Perfect uniformity is easy to define:
25 25 25 25
but which of the following is more no... | How does one measure the non-uniformity of a distribution?
In addition to @MansT 's good ideas, you could come up with other measures, but it depends on what you mean by "non-uniformity". To keep it simple, let's look at 4 levels. Perfect uniformity is easy t |
6,670 | How does one measure the non-uniformity of a distribution? | Here is a simple heuristic: if you assume elements in any vector sum to $1$ (or simply normalize each element with the sum to achieve this), then uniformity can be represented by L2 norm, which ranges from $\frac{1}{\sqrt d}$ to $1$, with $d$ being the dimension of vectors.
The lower bound $\frac{1}{\sqrt d}$ correspon... | How does one measure the non-uniformity of a distribution? | Here is a simple heuristic: if you assume elements in any vector sum to $1$ (or simply normalize each element with the sum to achieve this), then uniformity can be represented by L2 norm, which ranges | How does one measure the non-uniformity of a distribution?
Here is a simple heuristic: if you assume elements in any vector sum to $1$ (or simply normalize each element with the sum to achieve this), then uniformity can be represented by L2 norm, which ranges from $\frac{1}{\sqrt d}$ to $1$, with $d$ being the dimensio... | How does one measure the non-uniformity of a distribution?
Here is a simple heuristic: if you assume elements in any vector sum to $1$ (or simply normalize each element with the sum to achieve this), then uniformity can be represented by L2 norm, which ranges |
6,671 | How does one measure the non-uniformity of a distribution? | Stumbled upon this recently, and to add to the answer from @user495285, as far as I understand it:
When the values are normalized and sum to one, then the uniform distribution is the unit sphere in $\mathbb{R}^n$, and what is being calculated by using an $L_p$ norm is the deviation from the unit sphere using a distance... | How does one measure the non-uniformity of a distribution? | Stumbled upon this recently, and to add to the answer from @user495285, as far as I understand it:
When the values are normalized and sum to one, then the uniform distribution is the unit sphere in $\ | How does one measure the non-uniformity of a distribution?
Stumbled upon this recently, and to add to the answer from @user495285, as far as I understand it:
When the values are normalized and sum to one, then the uniform distribution is the unit sphere in $\mathbb{R}^n$, and what is being calculated by using an $L_p$ ... | How does one measure the non-uniformity of a distribution?
Stumbled upon this recently, and to add to the answer from @user495285, as far as I understand it:
When the values are normalized and sum to one, then the uniform distribution is the unit sphere in $\ |
6,672 | Interpreting residual diagnostic plots for glm models? | I think this is one of the most challenging parts when doing regression analysis. I also struggle with most of the interpretations (in particular binomial diagnostics are crazy!).
I just stumbled on this post
http://www.r-bloggers.com/model-validation-interpreting-residual-plots/
who also linked
https://web.archive.org... | Interpreting residual diagnostic plots for glm models? | I think this is one of the most challenging parts when doing regression analysis. I also struggle with most of the interpretations (in particular binomial diagnostics are crazy!).
I just stumbled on t | Interpreting residual diagnostic plots for glm models?
I think this is one of the most challenging parts when doing regression analysis. I also struggle with most of the interpretations (in particular binomial diagnostics are crazy!).
I just stumbled on this post
http://www.r-bloggers.com/model-validation-interpreting-... | Interpreting residual diagnostic plots for glm models?
I think this is one of the most challenging parts when doing regression analysis. I also struggle with most of the interpretations (in particular binomial diagnostics are crazy!).
I just stumbled on t |
6,673 | Interpreting residual diagnostic plots for glm models? | I would suggest the methods described in:
Buja, A., Cook, D. Hofmann, H., Lawrence, M. Lee, E.-K., Swayne,
D.F and Wickham, H. (2009) Statistical Inference for exploratory
data analysis and model diagnostics Phil. Trans. R. Soc. A 2009
367, 4361-4383 doi: 10.1098/rsta.2009.0120
There are a few different ideas, b... | Interpreting residual diagnostic plots for glm models? | I would suggest the methods described in:
Buja, A., Cook, D. Hofmann, H., Lawrence, M. Lee, E.-K., Swayne,
D.F and Wickham, H. (2009) Statistical Inference for exploratory
data analysis and model | Interpreting residual diagnostic plots for glm models?
I would suggest the methods described in:
Buja, A., Cook, D. Hofmann, H., Lawrence, M. Lee, E.-K., Swayne,
D.F and Wickham, H. (2009) Statistical Inference for exploratory
data analysis and model diagnostics Phil. Trans. R. Soc. A 2009
367, 4361-4383 doi: 10.1... | Interpreting residual diagnostic plots for glm models?
I would suggest the methods described in:
Buja, A., Cook, D. Hofmann, H., Lawrence, M. Lee, E.-K., Swayne,
D.F and Wickham, H. (2009) Statistical Inference for exploratory
data analysis and model |
6,674 | Interpreting residual diagnostic plots for glm models? | This question is quite old, but I thought it would be useful to add that, since recently, you can use the DHARMa R package to transform the residuals of any GL(M)M into a standardized space. Once this is done, you can visually assess / test residual problems such as deviations from the distribution, residual dependency... | Interpreting residual diagnostic plots for glm models? | This question is quite old, but I thought it would be useful to add that, since recently, you can use the DHARMa R package to transform the residuals of any GL(M)M into a standardized space. Once this | Interpreting residual diagnostic plots for glm models?
This question is quite old, but I thought it would be useful to add that, since recently, you can use the DHARMa R package to transform the residuals of any GL(M)M into a standardized space. Once this is done, you can visually assess / test residual problems such a... | Interpreting residual diagnostic plots for glm models?
This question is quite old, but I thought it would be useful to add that, since recently, you can use the DHARMa R package to transform the residuals of any GL(M)M into a standardized space. Once this |
6,675 | Cross-validating time-series analysis | The "classical" k-times cross-validation technique is based on the fact that each sample in the available data set is used (k-1)-times to train a model and 1 time to test it. Since it is very important to validate time series models on "future" data, this approach will not contribute to the stability of the model.
One ... | Cross-validating time-series analysis | The "classical" k-times cross-validation technique is based on the fact that each sample in the available data set is used (k-1)-times to train a model and 1 time to test it. Since it is very importan | Cross-validating time-series analysis
The "classical" k-times cross-validation technique is based on the fact that each sample in the available data set is used (k-1)-times to train a model and 1 time to test it. Since it is very important to validate time series models on "future" data, this approach will not contribu... | Cross-validating time-series analysis
The "classical" k-times cross-validation technique is based on the fact that each sample in the available data set is used (k-1)-times to train a model and 1 time to test it. Since it is very importan |
6,676 | Cross-validating time-series analysis | http://robjhyndman.com/researchtips/crossvalidation/ contains a quick tip for cross validation of time series. Regarding using random forest for time series data....not sure although it seems like an odd choice given that the model is fitted using bootstrap samples. There are classic time series methods of course (e.g.... | Cross-validating time-series analysis | http://robjhyndman.com/researchtips/crossvalidation/ contains a quick tip for cross validation of time series. Regarding using random forest for time series data....not sure although it seems like an | Cross-validating time-series analysis
http://robjhyndman.com/researchtips/crossvalidation/ contains a quick tip for cross validation of time series. Regarding using random forest for time series data....not sure although it seems like an odd choice given that the model is fitted using bootstrap samples. There are class... | Cross-validating time-series analysis
http://robjhyndman.com/researchtips/crossvalidation/ contains a quick tip for cross validation of time series. Regarding using random forest for time series data....not sure although it seems like an |
6,677 | Cross-validating time-series analysis | Here is some example code for cross-validating time series models. I expanded on this code in my blog, incorporating the foreach package to speed things up and allowing for a possible xreg term in the cross-validation.
Here's a copy of the code from Rob Hyndman's blog:
library(fpp) # To load the data set a10
plot(a10,... | Cross-validating time-series analysis | Here is some example code for cross-validating time series models. I expanded on this code in my blog, incorporating the foreach package to speed things up and allowing for a possible xreg term in th | Cross-validating time-series analysis
Here is some example code for cross-validating time series models. I expanded on this code in my blog, incorporating the foreach package to speed things up and allowing for a possible xreg term in the cross-validation.
Here's a copy of the code from Rob Hyndman's blog:
library(fpp... | Cross-validating time-series analysis
Here is some example code for cross-validating time series models. I expanded on this code in my blog, incorporating the foreach package to speed things up and allowing for a possible xreg term in th |
6,678 | Cross-validating time-series analysis | If you have time series data then you might have a "degrees of freedom problem" . For example if you have 4 observations taken at hourly intervals and then decide to use 241 observations at 1minute intervals, you have 241 observations but they are not necessarily independent. When you submit these 241 values/measuremen... | Cross-validating time-series analysis | If you have time series data then you might have a "degrees of freedom problem" . For example if you have 4 observations taken at hourly intervals and then decide to use 241 observations at 1minute in | Cross-validating time-series analysis
If you have time series data then you might have a "degrees of freedom problem" . For example if you have 4 observations taken at hourly intervals and then decide to use 241 observations at 1minute intervals, you have 241 observations but they are not necessarily independent. When ... | Cross-validating time-series analysis
If you have time series data then you might have a "degrees of freedom problem" . For example if you have 4 observations taken at hourly intervals and then decide to use 241 observations at 1minute in |
6,679 | Cross-validating time-series analysis | I can recomend you 2 interesting papers to read that are online
1.Streamed Learning: One-Pass SVMs, by Piyush Rai, Hal Daum´e III, Suresh Venkatasubramanian
2.Streaming k-means approximation, by Nir Ailon
Hope it clarifies you a little your ideas | Cross-validating time-series analysis | I can recomend you 2 interesting papers to read that are online
1.Streamed Learning: One-Pass SVMs, by Piyush Rai, Hal Daum´e III, Suresh Venkatasubramanian
2.Streaming k-means approximation, by Nir A | Cross-validating time-series analysis
I can recomend you 2 interesting papers to read that are online
1.Streamed Learning: One-Pass SVMs, by Piyush Rai, Hal Daum´e III, Suresh Venkatasubramanian
2.Streaming k-means approximation, by Nir Ailon
Hope it clarifies you a little your ideas | Cross-validating time-series analysis
I can recomend you 2 interesting papers to read that are online
1.Streamed Learning: One-Pass SVMs, by Piyush Rai, Hal Daum´e III, Suresh Venkatasubramanian
2.Streaming k-means approximation, by Nir A |
6,680 | Is there a reliable nonparametric confidence interval for the mean of a skewed distribution? | I am somewhat pessimistic about a such non-parametric method, at least without the introduction of some sort of constraints on the underlying distribution.
My reasoning for this is that there will always be a distribution that breaks the true coverage probability for any finite $n$ (although as $n \rightarrow \infty$,... | Is there a reliable nonparametric confidence interval for the mean of a skewed distribution? | I am somewhat pessimistic about a such non-parametric method, at least without the introduction of some sort of constraints on the underlying distribution.
My reasoning for this is that there will al | Is there a reliable nonparametric confidence interval for the mean of a skewed distribution?
I am somewhat pessimistic about a such non-parametric method, at least without the introduction of some sort of constraints on the underlying distribution.
My reasoning for this is that there will always be a distribution that... | Is there a reliable nonparametric confidence interval for the mean of a skewed distribution?
I am somewhat pessimistic about a such non-parametric method, at least without the introduction of some sort of constraints on the underlying distribution.
My reasoning for this is that there will al |
6,681 | Is there a reliable nonparametric confidence interval for the mean of a skewed distribution? | One of the underlying assumptions of any sample is representativeness. The longer the tails of a distribution the less likely any small sample is going to be representative enough for any method to reliably solve for the CI because the sample won't be able to represent the distribution.
For example, running a simple pe... | Is there a reliable nonparametric confidence interval for the mean of a skewed distribution? | One of the underlying assumptions of any sample is representativeness. The longer the tails of a distribution the less likely any small sample is going to be representative enough for any method to re | Is there a reliable nonparametric confidence interval for the mean of a skewed distribution?
One of the underlying assumptions of any sample is representativeness. The longer the tails of a distribution the less likely any small sample is going to be representative enough for any method to reliably solve for the CI bec... | Is there a reliable nonparametric confidence interval for the mean of a skewed distribution?
One of the underlying assumptions of any sample is representativeness. The longer the tails of a distribution the less likely any small sample is going to be representative enough for any method to re |
6,682 | What are easy to interpret, goodness of fit measures for linear mixed effects models? | There is nothing such as an easy to interpret goodness of fit measure for linear mixed models :)
Random effect fit (mod1) can be measured by ICC and ICC2 (the ratio between variance accounted by random effects and the residual variance). psychometric R package includes a function to extract them form a lme object.
It i... | What are easy to interpret, goodness of fit measures for linear mixed effects models? | There is nothing such as an easy to interpret goodness of fit measure for linear mixed models :)
Random effect fit (mod1) can be measured by ICC and ICC2 (the ratio between variance accounted by rando | What are easy to interpret, goodness of fit measures for linear mixed effects models?
There is nothing such as an easy to interpret goodness of fit measure for linear mixed models :)
Random effect fit (mod1) can be measured by ICC and ICC2 (the ratio between variance accounted by random effects and the residual varianc... | What are easy to interpret, goodness of fit measures for linear mixed effects models?
There is nothing such as an easy to interpret goodness of fit measure for linear mixed models :)
Random effect fit (mod1) can be measured by ICC and ICC2 (the ratio between variance accounted by rando |
6,683 | Is overfitting "better" than underfitting? | Overfitting is likely to be worse than underfitting. The reason is that there is no real upper limit to the degradation of generalisation performance that can result from over-fitting, whereas there is for underfitting.
Consider a non-linear regression model, such as a neural network or polynomial model. Assume we ha... | Is overfitting "better" than underfitting? | Overfitting is likely to be worse than underfitting. The reason is that there is no real upper limit to the degradation of generalisation performance that can result from over-fitting, whereas there | Is overfitting "better" than underfitting?
Overfitting is likely to be worse than underfitting. The reason is that there is no real upper limit to the degradation of generalisation performance that can result from over-fitting, whereas there is for underfitting.
Consider a non-linear regression model, such as a neural... | Is overfitting "better" than underfitting?
Overfitting is likely to be worse than underfitting. The reason is that there is no real upper limit to the degradation of generalisation performance that can result from over-fitting, whereas there |
6,684 | Is overfitting "better" than underfitting? | Roughly, overfitting is fitting the model to noise, while underfitting is not fitting a model to the signal. In your prediction with overfitting you'll reproduce the noise, the underfitting will show the mean, at best. It's like choosing between diarrhea and constipation. I'd probably choose the latter, so I'd go with ... | Is overfitting "better" than underfitting? | Roughly, overfitting is fitting the model to noise, while underfitting is not fitting a model to the signal. In your prediction with overfitting you'll reproduce the noise, the underfitting will show | Is overfitting "better" than underfitting?
Roughly, overfitting is fitting the model to noise, while underfitting is not fitting a model to the signal. In your prediction with overfitting you'll reproduce the noise, the underfitting will show the mean, at best. It's like choosing between diarrhea and constipation. I'd ... | Is overfitting "better" than underfitting?
Roughly, overfitting is fitting the model to noise, while underfitting is not fitting a model to the signal. In your prediction with overfitting you'll reproduce the noise, the underfitting will show |
6,685 | Is overfitting "better" than underfitting? | The question of what is good and what is bad depends on the problem, the question and the circumstances.
Some thoughts: The most impressive proof of how underfitting is not generally rejected so much is the universal use of simple linear regression. Problems in social sciences, life sciences, psychology etc. are almost... | Is overfitting "better" than underfitting? | The question of what is good and what is bad depends on the problem, the question and the circumstances.
Some thoughts: The most impressive proof of how underfitting is not generally rejected so much | Is overfitting "better" than underfitting?
The question of what is good and what is bad depends on the problem, the question and the circumstances.
Some thoughts: The most impressive proof of how underfitting is not generally rejected so much is the universal use of simple linear regression. Problems in social sciences... | Is overfitting "better" than underfitting?
The question of what is good and what is bad depends on the problem, the question and the circumstances.
Some thoughts: The most impressive proof of how underfitting is not generally rejected so much |
6,686 | Is overfitting "better" than underfitting? | The "better" one is the one that performs better on the test set.
When you're running it in production, that's (ideally) going to be similar to the test set. It's not going to be data you've seen before, so the training set performance doesn't matter so much.
Although if they're roughly equal, underfitting is generally... | Is overfitting "better" than underfitting? | The "better" one is the one that performs better on the test set.
When you're running it in production, that's (ideally) going to be similar to the test set. It's not going to be data you've seen befo | Is overfitting "better" than underfitting?
The "better" one is the one that performs better on the test set.
When you're running it in production, that's (ideally) going to be similar to the test set. It's not going to be data you've seen before, so the training set performance doesn't matter so much.
Although if they'... | Is overfitting "better" than underfitting?
The "better" one is the one that performs better on the test set.
When you're running it in production, that's (ideally) going to be similar to the test set. It's not going to be data you've seen befo |
6,687 | Is overfitting "better" than underfitting? | I liked the question and the key concept to answer it is Bias–variance tradeoff. Both underfitted model and overfitted model have some valid use case.
For example my answer here
Is an overfitted model necessarily useless? | Is overfitting "better" than underfitting? | I liked the question and the key concept to answer it is Bias–variance tradeoff. Both underfitted model and overfitted model have some valid use case.
For example my answer here
Is an overfitted model | Is overfitting "better" than underfitting?
I liked the question and the key concept to answer it is Bias–variance tradeoff. Both underfitted model and overfitted model have some valid use case.
For example my answer here
Is an overfitted model necessarily useless? | Is overfitting "better" than underfitting?
I liked the question and the key concept to answer it is Bias–variance tradeoff. Both underfitted model and overfitted model have some valid use case.
For example my answer here
Is an overfitted model |
6,688 | Is overfitting "better" than underfitting? | The answers so far are reasonable in the context of linear regression. But in a deep-learning context we usually train to the point of overfitting (if we have the resources to); then we go back and use the model saved most recently before that. I.e. underfitting just means "not there yet, carry on".
You also have to co... | Is overfitting "better" than underfitting? | The answers so far are reasonable in the context of linear regression. But in a deep-learning context we usually train to the point of overfitting (if we have the resources to); then we go back and us | Is overfitting "better" than underfitting?
The answers so far are reasonable in the context of linear regression. But in a deep-learning context we usually train to the point of overfitting (if we have the resources to); then we go back and use the model saved most recently before that. I.e. underfitting just means "no... | Is overfitting "better" than underfitting?
The answers so far are reasonable in the context of linear regression. But in a deep-learning context we usually train to the point of overfitting (if we have the resources to); then we go back and us |
6,689 | Is overfitting "better" than underfitting? | Parsimony usually a desirable feature in a machine learning model - this relates to the idea of Occam's Razor, that among models that produce equally good (or bad) results, you should generally prefer the simpler one. This is explicitly performed in certain model selection approaches such as the Minimum Description Len... | Is overfitting "better" than underfitting? | Parsimony usually a desirable feature in a machine learning model - this relates to the idea of Occam's Razor, that among models that produce equally good (or bad) results, you should generally prefer | Is overfitting "better" than underfitting?
Parsimony usually a desirable feature in a machine learning model - this relates to the idea of Occam's Razor, that among models that produce equally good (or bad) results, you should generally prefer the simpler one. This is explicitly performed in certain model selection app... | Is overfitting "better" than underfitting?
Parsimony usually a desirable feature in a machine learning model - this relates to the idea of Occam's Razor, that among models that produce equally good (or bad) results, you should generally prefer |
6,690 | Is overfitting "better" than underfitting? | Imagine you're an ML algorithm that is supposed to do well on a test. You know the syllabus and hence, you have a set of example problems (with solutions) which you can practice from. Now, you have three options:
Overfit: Memorize solutions of practice problems without actually understanding how you arrived at the sol... | Is overfitting "better" than underfitting? | Imagine you're an ML algorithm that is supposed to do well on a test. You know the syllabus and hence, you have a set of example problems (with solutions) which you can practice from. Now, you have th | Is overfitting "better" than underfitting?
Imagine you're an ML algorithm that is supposed to do well on a test. You know the syllabus and hence, you have a set of example problems (with solutions) which you can practice from. Now, you have three options:
Overfit: Memorize solutions of practice problems without actual... | Is overfitting "better" than underfitting?
Imagine you're an ML algorithm that is supposed to do well on a test. You know the syllabus and hence, you have a set of example problems (with solutions) which you can practice from. Now, you have th |
6,691 | Is overfitting "better" than underfitting? | Probably not your situation, but you can use machine learning as a memory. Suppose you have some inputs where you can train on the entire domain of inputs. That is, there is no possible input that wasn't previously known and used for training. That way, you can always generate the correct output. If the concept you wis... | Is overfitting "better" than underfitting? | Probably not your situation, but you can use machine learning as a memory. Suppose you have some inputs where you can train on the entire domain of inputs. That is, there is no possible input that was | Is overfitting "better" than underfitting?
Probably not your situation, but you can use machine learning as a memory. Suppose you have some inputs where you can train on the entire domain of inputs. That is, there is no possible input that wasn't previously known and used for training. That way, you can always generate... | Is overfitting "better" than underfitting?
Probably not your situation, but you can use machine learning as a memory. Suppose you have some inputs where you can train on the entire domain of inputs. That is, there is no possible input that was |
6,692 | If we know A is independent of B, why isn't P(A|B,C) = P(A|C) necessarily true? | My favourite example is a chessboard: if you pick a point uniformly then the row, column, and colour are pairwise independent.
Suppose A is colour, B is row, and C is column. Then P(A="white"|B)=0.5 and P(A="white"|C)=0.5 for any value of B, but P(A="white"|B,C) is either 0 or 1 for any values of B and C. | If we know A is independent of B, why isn't P(A|B,C) = P(A|C) necessarily true? | My favourite example is a chessboard: if you pick a point uniformly then the row, column, and colour are pairwise independent.
Suppose A is colour, B is row, and C is column. Then P(A="white"|B)=0.5 a | If we know A is independent of B, why isn't P(A|B,C) = P(A|C) necessarily true?
My favourite example is a chessboard: if you pick a point uniformly then the row, column, and colour are pairwise independent.
Suppose A is colour, B is row, and C is column. Then P(A="white"|B)=0.5 and P(A="white"|C)=0.5 for any value of B... | If we know A is independent of B, why isn't P(A|B,C) = P(A|C) necessarily true?
My favourite example is a chessboard: if you pick a point uniformly then the row, column, and colour are pairwise independent.
Suppose A is colour, B is row, and C is column. Then P(A="white"|B)=0.5 a |
6,693 | If we know A is independent of B, why isn't P(A|B,C) = P(A|C) necessarily true? | Imagine $A$ and $B$ are independent Bernoulli random variables with success probability 1/2, and let $C = AB + (1 - A)(1 - B)$ (if you like, $A$ is the event that a coin lands heads, $B$ is the event that another coin lands heads, and $C$ is the event that both coins land the same side up). Then $P(A = 1 \mid C = 1) = ... | If we know A is independent of B, why isn't P(A|B,C) = P(A|C) necessarily true? | Imagine $A$ and $B$ are independent Bernoulli random variables with success probability 1/2, and let $C = AB + (1 - A)(1 - B)$ (if you like, $A$ is the event that a coin lands heads, $B$ is the event | If we know A is independent of B, why isn't P(A|B,C) = P(A|C) necessarily true?
Imagine $A$ and $B$ are independent Bernoulli random variables with success probability 1/2, and let $C = AB + (1 - A)(1 - B)$ (if you like, $A$ is the event that a coin lands heads, $B$ is the event that another coin lands heads, and $C$ i... | If we know A is independent of B, why isn't P(A|B,C) = P(A|C) necessarily true?
Imagine $A$ and $B$ are independent Bernoulli random variables with success probability 1/2, and let $C = AB + (1 - A)(1 - B)$ (if you like, $A$ is the event that a coin lands heads, $B$ is the event |
6,694 | If we know A is independent of B, why isn't P(A|B,C) = P(A|C) necessarily true? | Let's continue your example with two decks of cards, supposing that one card is chosen randomly from each deck.
You have proposed that $A$ is the event that the ace of spades is chosen from the first deck and that $B$ is the event that the ace of spades is chosen from the second deck.
Now let $C$ be the event that the ... | If we know A is independent of B, why isn't P(A|B,C) = P(A|C) necessarily true? | Let's continue your example with two decks of cards, supposing that one card is chosen randomly from each deck.
You have proposed that $A$ is the event that the ace of spades is chosen from the first | If we know A is independent of B, why isn't P(A|B,C) = P(A|C) necessarily true?
Let's continue your example with two decks of cards, supposing that one card is chosen randomly from each deck.
You have proposed that $A$ is the event that the ace of spades is chosen from the first deck and that $B$ is the event that the ... | If we know A is independent of B, why isn't P(A|B,C) = P(A|C) necessarily true?
Let's continue your example with two decks of cards, supposing that one card is chosen randomly from each deck.
You have proposed that $A$ is the event that the ace of spades is chosen from the first |
6,695 | If we know A is independent of B, why isn't P(A|B,C) = P(A|C) necessarily true? | There are two situations how this can happen.
Collider bias
A common way how the situation can occur is collider bias.
An example is in the image below. In this example, intelligence and appearance are statistically unrelated (there's not even an effect in this case as with the coin example below). But conditional on t... | If we know A is independent of B, why isn't P(A|B,C) = P(A|C) necessarily true? | There are two situations how this can happen.
Collider bias
A common way how the situation can occur is collider bias.
An example is in the image below. In this example, intelligence and appearance ar | If we know A is independent of B, why isn't P(A|B,C) = P(A|C) necessarily true?
There are two situations how this can happen.
Collider bias
A common way how the situation can occur is collider bias.
An example is in the image below. In this example, intelligence and appearance are statistically unrelated (there's not e... | If we know A is independent of B, why isn't P(A|B,C) = P(A|C) necessarily true?
There are two situations how this can happen.
Collider bias
A common way how the situation can occur is collider bias.
An example is in the image below. In this example, intelligence and appearance ar |
6,696 | If we know A is independent of B, why isn't P(A|B,C) = P(A|C) necessarily true? | I quote Joseph Blitzstein's Introduction to Probability (2019 2 edn), p. 65.
Example 2.5.11 (Independence doesn't imply conditional independence).
My
friends Alice and Bob are the only two people who ever call me on the phone. Each
day, they decide independently whether to call me that day. Let A be the event
that Ali... | If we know A is independent of B, why isn't P(A|B,C) = P(A|C) necessarily true? | I quote Joseph Blitzstein's Introduction to Probability (2019 2 edn), p. 65.
Example 2.5.11 (Independence doesn't imply conditional independence).
My
friends Alice and Bob are the only two people who | If we know A is independent of B, why isn't P(A|B,C) = P(A|C) necessarily true?
I quote Joseph Blitzstein's Introduction to Probability (2019 2 edn), p. 65.
Example 2.5.11 (Independence doesn't imply conditional independence).
My
friends Alice and Bob are the only two people who ever call me on the phone. Each
day, th... | If we know A is independent of B, why isn't P(A|B,C) = P(A|C) necessarily true?
I quote Joseph Blitzstein's Introduction to Probability (2019 2 edn), p. 65.
Example 2.5.11 (Independence doesn't imply conditional independence).
My
friends Alice and Bob are the only two people who |
6,697 | If we know A is independent of B, why isn't P(A|B,C) = P(A|C) necessarily true? | As @Sextus Empiricus (the ancient skeptic!) said, collider bias phenomenon in epidemiology is a great exemplar of why marginal independence of two random variables does not necessarily imply their conditional independence, given a third random variable.
Sackett (1978)'s example is a classic for the collider bias. In h... | If we know A is independent of B, why isn't P(A|B,C) = P(A|C) necessarily true? | As @Sextus Empiricus (the ancient skeptic!) said, collider bias phenomenon in epidemiology is a great exemplar of why marginal independence of two random variables does not necessarily imply their con | If we know A is independent of B, why isn't P(A|B,C) = P(A|C) necessarily true?
As @Sextus Empiricus (the ancient skeptic!) said, collider bias phenomenon in epidemiology is a great exemplar of why marginal independence of two random variables does not necessarily imply their conditional independence, given a third ran... | If we know A is independent of B, why isn't P(A|B,C) = P(A|C) necessarily true?
As @Sextus Empiricus (the ancient skeptic!) said, collider bias phenomenon in epidemiology is a great exemplar of why marginal independence of two random variables does not necessarily imply their con |
6,698 | What is the relationship between $Y$ and $X$ in this plot? | The question deals with several concepts: how to evaluate data given only in the form of a scatterplot, how to summarize a scatterplot, and whether (and to what degree) a relationship looks linear. Let's take them in order.
Evaluating graphical data
Use principles of exploratory data analysis (EDA). These (at least ... | What is the relationship between $Y$ and $X$ in this plot? | The question deals with several concepts: how to evaluate data given only in the form of a scatterplot, how to summarize a scatterplot, and whether (and to what degree) a relationship looks linear. | What is the relationship between $Y$ and $X$ in this plot?
The question deals with several concepts: how to evaluate data given only in the form of a scatterplot, how to summarize a scatterplot, and whether (and to what degree) a relationship looks linear. Let's take them in order.
Evaluating graphical data
Use princ... | What is the relationship between $Y$ and $X$ in this plot?
The question deals with several concepts: how to evaluate data given only in the form of a scatterplot, how to summarize a scatterplot, and whether (and to what degree) a relationship looks linear. |
6,699 | What is the relationship between $Y$ and $X$ in this plot? | Let's have some fun!
First of all, I scraped the data off your graph.
Then I used a running line smoother to produce the black regression line below with the dashed 95% CI bands in gray. The graph below shows a span in the smooth of one half the data, although tighter spans revealed more or less precisely the same rela... | What is the relationship between $Y$ and $X$ in this plot? | Let's have some fun!
First of all, I scraped the data off your graph.
Then I used a running line smoother to produce the black regression line below with the dashed 95% CI bands in gray. The graph bel | What is the relationship between $Y$ and $X$ in this plot?
Let's have some fun!
First of all, I scraped the data off your graph.
Then I used a running line smoother to produce the black regression line below with the dashed 95% CI bands in gray. The graph below shows a span in the smooth of one half the data, although ... | What is the relationship between $Y$ and $X$ in this plot?
Let's have some fun!
First of all, I scraped the data off your graph.
Then I used a running line smoother to produce the black regression line below with the dashed 95% CI bands in gray. The graph bel |
6,700 | What is the relationship between $Y$ and $X$ in this plot? | Here's my 2¢ 1.5¢. To me the most prominent feature is that the data abruptly stop and 'bunch up' at the bottom of the range of Y. I do see the two (potential) 'clusters' and the general negative association, but the most salient features are the (potential) floor effect and the fact that the top, low-density cluster... | What is the relationship between $Y$ and $X$ in this plot? | Here's my 2¢ 1.5¢. To me the most prominent feature is that the data abruptly stop and 'bunch up' at the bottom of the range of Y. I do see the two (potential) 'clusters' and the general negative as | What is the relationship between $Y$ and $X$ in this plot?
Here's my 2¢ 1.5¢. To me the most prominent feature is that the data abruptly stop and 'bunch up' at the bottom of the range of Y. I do see the two (potential) 'clusters' and the general negative association, but the most salient features are the (potential) ... | What is the relationship between $Y$ and $X$ in this plot?
Here's my 2¢ 1.5¢. To me the most prominent feature is that the data abruptly stop and 'bunch up' at the bottom of the range of Y. I do see the two (potential) 'clusters' and the general negative as |
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