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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4,801 | How to assess the similarity of two histograms? | As David's answer points out, the chi-squared test is necessary for binned data as the KS test assumes continuous distributions. Regarding why the KS test is inappropriate (naught101's comment), there has been some discussion of the issue in the applied statistics literature that is worth raising here.
An amusing exch... | How to assess the similarity of two histograms? | As David's answer points out, the chi-squared test is necessary for binned data as the KS test assumes continuous distributions. Regarding why the KS test is inappropriate (naught101's comment), there | How to assess the similarity of two histograms?
As David's answer points out, the chi-squared test is necessary for binned data as the KS test assumes continuous distributions. Regarding why the KS test is inappropriate (naught101's comment), there has been some discussion of the issue in the applied statistics literat... | How to assess the similarity of two histograms?
As David's answer points out, the chi-squared test is necessary for binned data as the KS test assumes continuous distributions. Regarding why the KS test is inappropriate (naught101's comment), there |
4,802 | Dynamic Time Warping Clustering | Do not use k-means for timeseries.
DTW is not minimized by the mean; k-means may not converge and even if it converges it will not yield a very good result. The mean is an least-squares estimator on the coordinates. It minimizes variance, not arbitrary distances, and k-means is designed for minimizing variance, not ar... | Dynamic Time Warping Clustering | Do not use k-means for timeseries.
DTW is not minimized by the mean; k-means may not converge and even if it converges it will not yield a very good result. The mean is an least-squares estimator on | Dynamic Time Warping Clustering
Do not use k-means for timeseries.
DTW is not minimized by the mean; k-means may not converge and even if it converges it will not yield a very good result. The mean is an least-squares estimator on the coordinates. It minimizes variance, not arbitrary distances, and k-means is designed... | Dynamic Time Warping Clustering
Do not use k-means for timeseries.
DTW is not minimized by the mean; k-means may not converge and even if it converges it will not yield a very good result. The mean is an least-squares estimator on |
4,803 | Dynamic Time Warping Clustering | Yes, you can use DTW approach for classification and clustering of time series. I've compiled the following resources, which are focused on this very topic (I've recently answered a similar question, but not on this site, so I'm copying the contents here for everybody's convenience):
UCR Time Series Classification/Clu... | Dynamic Time Warping Clustering | Yes, you can use DTW approach for classification and clustering of time series. I've compiled the following resources, which are focused on this very topic (I've recently answered a similar question, | Dynamic Time Warping Clustering
Yes, you can use DTW approach for classification and clustering of time series. I've compiled the following resources, which are focused on this very topic (I've recently answered a similar question, but not on this site, so I'm copying the contents here for everybody's convenience):
UC... | Dynamic Time Warping Clustering
Yes, you can use DTW approach for classification and clustering of time series. I've compiled the following resources, which are focused on this very topic (I've recently answered a similar question, |
4,804 | Dynamic Time Warping Clustering | A recent method DTW Barycenter Averaging (DBA) has been proposed by Petitjean et al. to average time series.
In an other paper they proved empirically and theoretically how it can be used to cluster time series with k-means.
An implementation is provided on GitHub by the authors (link to code).
1 F. Petitjean, G. Fo... | Dynamic Time Warping Clustering | A recent method DTW Barycenter Averaging (DBA) has been proposed by Petitjean et al. to average time series.
In an other paper they proved empirically and theoretically how it can be used to cluster | Dynamic Time Warping Clustering
A recent method DTW Barycenter Averaging (DBA) has been proposed by Petitjean et al. to average time series.
In an other paper they proved empirically and theoretically how it can be used to cluster time series with k-means.
An implementation is provided on GitHub by the authors (link ... | Dynamic Time Warping Clustering
A recent method DTW Barycenter Averaging (DBA) has been proposed by Petitjean et al. to average time series.
In an other paper they proved empirically and theoretically how it can be used to cluster |
4,805 | Dynamic Time Warping Clustering | Dynamic Time Warp compares the realized data points, which may or may not work. A more rigorous approach is to compare the distribution of the time series by way of a metric called telescope distance.
The cool thing about this metric is that the empirical calculation is done by fitting a series of binary classifiers s... | Dynamic Time Warping Clustering | Dynamic Time Warp compares the realized data points, which may or may not work. A more rigorous approach is to compare the distribution of the time series by way of a metric called telescope distance. | Dynamic Time Warping Clustering
Dynamic Time Warp compares the realized data points, which may or may not work. A more rigorous approach is to compare the distribution of the time series by way of a metric called telescope distance.
The cool thing about this metric is that the empirical calculation is done by fitting ... | Dynamic Time Warping Clustering
Dynamic Time Warp compares the realized data points, which may or may not work. A more rigorous approach is to compare the distribution of the time series by way of a metric called telescope distance. |
4,806 | Dynamic Time Warping Clustering | Yes. A naive and potentially slow approach might be,
Create your all cluster combinations. k is for cluster count and n is for number of series. The number of items returned should be n! / k! / (n-k)!. These would be something like potential centers.
For each series, calculate distances via DTW for each center in each... | Dynamic Time Warping Clustering | Yes. A naive and potentially slow approach might be,
Create your all cluster combinations. k is for cluster count and n is for number of series. The number of items returned should be n! / k! / (n-k) | Dynamic Time Warping Clustering
Yes. A naive and potentially slow approach might be,
Create your all cluster combinations. k is for cluster count and n is for number of series. The number of items returned should be n! / k! / (n-k)!. These would be something like potential centers.
For each series, calculate distances... | Dynamic Time Warping Clustering
Yes. A naive and potentially slow approach might be,
Create your all cluster combinations. k is for cluster count and n is for number of series. The number of items returned should be n! / k! / (n-k) |
4,807 | Is minimizing squared error equivalent to minimizing absolute error? Why squared error is more popular than the latter? | Minimizing square errors (MSE) is definitely not the same as minimizing absolute deviations (MAD) of errors. MSE provides the mean response of $y$ conditioned on $x$, while MAD provides the median response of $y$ conditioned on $x$.
Historically, Laplace originally considered the maximum observed error as a measure of ... | Is minimizing squared error equivalent to minimizing absolute error? Why squared error is more popul | Minimizing square errors (MSE) is definitely not the same as minimizing absolute deviations (MAD) of errors. MSE provides the mean response of $y$ conditioned on $x$, while MAD provides the median res | Is minimizing squared error equivalent to minimizing absolute error? Why squared error is more popular than the latter?
Minimizing square errors (MSE) is definitely not the same as minimizing absolute deviations (MAD) of errors. MSE provides the mean response of $y$ conditioned on $x$, while MAD provides the median res... | Is minimizing squared error equivalent to minimizing absolute error? Why squared error is more popul
Minimizing square errors (MSE) is definitely not the same as minimizing absolute deviations (MAD) of errors. MSE provides the mean response of $y$ conditioned on $x$, while MAD provides the median res |
4,808 | Is minimizing squared error equivalent to minimizing absolute error? Why squared error is more popular than the latter? | As an alternative explanation, consider the following intuition:
When minimizing an error, we must decide how to penalize these errors. Indeed, the most straightforward approach to penalizing errors would be to use a linearly proportional penalty function. With such a function, each deviation from the mean is given a p... | Is minimizing squared error equivalent to minimizing absolute error? Why squared error is more popul | As an alternative explanation, consider the following intuition:
When minimizing an error, we must decide how to penalize these errors. Indeed, the most straightforward approach to penalizing errors w | Is minimizing squared error equivalent to minimizing absolute error? Why squared error is more popular than the latter?
As an alternative explanation, consider the following intuition:
When minimizing an error, we must decide how to penalize these errors. Indeed, the most straightforward approach to penalizing errors w... | Is minimizing squared error equivalent to minimizing absolute error? Why squared error is more popul
As an alternative explanation, consider the following intuition:
When minimizing an error, we must decide how to penalize these errors. Indeed, the most straightforward approach to penalizing errors w |
4,809 | Is minimizing squared error equivalent to minimizing absolute error? Why squared error is more popular than the latter? | In theory you could use any kind of loss function. The absolute and the squared loss functions just happen to be the most popular and the most intuitive loss functions. According to this wikipedia entry,
A common example involves estimating "location." Under typical statistical assumptions, the mean or average is th... | Is minimizing squared error equivalent to minimizing absolute error? Why squared error is more popul | In theory you could use any kind of loss function. The absolute and the squared loss functions just happen to be the most popular and the most intuitive loss functions. According to this wikipedia ent | Is minimizing squared error equivalent to minimizing absolute error? Why squared error is more popular than the latter?
In theory you could use any kind of loss function. The absolute and the squared loss functions just happen to be the most popular and the most intuitive loss functions. According to this wikipedia ent... | Is minimizing squared error equivalent to minimizing absolute error? Why squared error is more popul
In theory you could use any kind of loss function. The absolute and the squared loss functions just happen to be the most popular and the most intuitive loss functions. According to this wikipedia ent |
4,810 | Is minimizing squared error equivalent to minimizing absolute error? Why squared error is more popular than the latter? | As another answer has explained, minimizing squared error is not the same as minimizing absolute error.
The reason minimizing squared error is preferred is because it prevents large errors better.
Say your empolyer's payroll department accidentally pays each of a total of ten employees \$50 less than required. That's a... | Is minimizing squared error equivalent to minimizing absolute error? Why squared error is more popul | As another answer has explained, minimizing squared error is not the same as minimizing absolute error.
The reason minimizing squared error is preferred is because it prevents large errors better.
Say | Is minimizing squared error equivalent to minimizing absolute error? Why squared error is more popular than the latter?
As another answer has explained, minimizing squared error is not the same as minimizing absolute error.
The reason minimizing squared error is preferred is because it prevents large errors better.
Say... | Is minimizing squared error equivalent to minimizing absolute error? Why squared error is more popul
As another answer has explained, minimizing squared error is not the same as minimizing absolute error.
The reason minimizing squared error is preferred is because it prevents large errors better.
Say |
4,811 | Is minimizing squared error equivalent to minimizing absolute error? Why squared error is more popular than the latter? | Short answers
nope
the mean has more interesting statistical properties than the median | Is minimizing squared error equivalent to minimizing absolute error? Why squared error is more popul | Short answers
nope
the mean has more interesting statistical properties than the median | Is minimizing squared error equivalent to minimizing absolute error? Why squared error is more popular than the latter?
Short answers
nope
the mean has more interesting statistical properties than the median | Is minimizing squared error equivalent to minimizing absolute error? Why squared error is more popul
Short answers
nope
the mean has more interesting statistical properties than the median |
4,812 | Why zero correlation does not necessarily imply independence | Correlation measures linear association between two given variables and it has no obligation to detect any other form of association else.
So those two variables might be associated in several other non-linear ways and correlation could not distinguish from independent case.
As a very didactic, artificial and non reali... | Why zero correlation does not necessarily imply independence | Correlation measures linear association between two given variables and it has no obligation to detect any other form of association else.
So those two variables might be associated in several other n | Why zero correlation does not necessarily imply independence
Correlation measures linear association between two given variables and it has no obligation to detect any other form of association else.
So those two variables might be associated in several other non-linear ways and correlation could not distinguish from i... | Why zero correlation does not necessarily imply independence
Correlation measures linear association between two given variables and it has no obligation to detect any other form of association else.
So those two variables might be associated in several other n |
4,813 | Why zero correlation does not necessarily imply independence | There is a generalized lack of rigor in the use of the word "correlation" for the simple reason that it can have widely differing assumptions and meanings. The simplest, loosest and most common usage is that there is some vague association, relationship or lack of independence between a static pair of random variables.... | Why zero correlation does not necessarily imply independence | There is a generalized lack of rigor in the use of the word "correlation" for the simple reason that it can have widely differing assumptions and meanings. The simplest, loosest and most common usage | Why zero correlation does not necessarily imply independence
There is a generalized lack of rigor in the use of the word "correlation" for the simple reason that it can have widely differing assumptions and meanings. The simplest, loosest and most common usage is that there is some vague association, relationship or la... | Why zero correlation does not necessarily imply independence
There is a generalized lack of rigor in the use of the word "correlation" for the simple reason that it can have widely differing assumptions and meanings. The simplest, loosest and most common usage |
4,814 | Why zero correlation does not necessarily imply independence | It depends on your exact definition of "correlation", but it isn't too hard to construct degenerate cases. "Independent" could mean something like "no predictive power, at all, ever" just as much as "linear correlation".
Linear correlation, for example, would not indicate dependence on $y= \sin(2000x)$ if the domain o... | Why zero correlation does not necessarily imply independence | It depends on your exact definition of "correlation", but it isn't too hard to construct degenerate cases. "Independent" could mean something like "no predictive power, at all, ever" just as much as " | Why zero correlation does not necessarily imply independence
It depends on your exact definition of "correlation", but it isn't too hard to construct degenerate cases. "Independent" could mean something like "no predictive power, at all, ever" just as much as "linear correlation".
Linear correlation, for example, woul... | Why zero correlation does not necessarily imply independence
It depends on your exact definition of "correlation", but it isn't too hard to construct degenerate cases. "Independent" could mean something like "no predictive power, at all, ever" just as much as " |
4,815 | Why zero correlation does not necessarily imply independence | An intuitive example would be a circle. I have two variables $X$ and $Y$. And they are satisfy the equation
$$X^2+Y^2=1$$
Now, $X$ and $Y$ are definitely not independent to each other, because given $X$ we can calculate $Y$ and vice versa. But their person correlation coefficient is $0$. This is because it only captur... | Why zero correlation does not necessarily imply independence | An intuitive example would be a circle. I have two variables $X$ and $Y$. And they are satisfy the equation
$$X^2+Y^2=1$$
Now, $X$ and $Y$ are definitely not independent to each other, because given | Why zero correlation does not necessarily imply independence
An intuitive example would be a circle. I have two variables $X$ and $Y$. And they are satisfy the equation
$$X^2+Y^2=1$$
Now, $X$ and $Y$ are definitely not independent to each other, because given $X$ we can calculate $Y$ and vice versa. But their person c... | Why zero correlation does not necessarily imply independence
An intuitive example would be a circle. I have two variables $X$ and $Y$. And they are satisfy the equation
$$X^2+Y^2=1$$
Now, $X$ and $Y$ are definitely not independent to each other, because given |
4,816 | Why zero correlation does not necessarily imply independence | Basically, dependence of Y on X means the distribution of values of Y depends on some way of the value of X. That dependence can be on the mean value of Y (the usual case presented in most of the answers) or whatever other characteristic of Y.
For example, let X be 0 or 1. If X = 0 then let Y be 0, if X= 1 let Y be -1,... | Why zero correlation does not necessarily imply independence | Basically, dependence of Y on X means the distribution of values of Y depends on some way of the value of X. That dependence can be on the mean value of Y (the usual case presented in most of the answ | Why zero correlation does not necessarily imply independence
Basically, dependence of Y on X means the distribution of values of Y depends on some way of the value of X. That dependence can be on the mean value of Y (the usual case presented in most of the answers) or whatever other characteristic of Y.
For example, le... | Why zero correlation does not necessarily imply independence
Basically, dependence of Y on X means the distribution of values of Y depends on some way of the value of X. That dependence can be on the mean value of Y (the usual case presented in most of the answ |
4,817 | Why zero correlation does not necessarily imply independence | Adding to @Marcelo Ventura and @Mike Hunter great answers, and the reference to a great discussion around this on Quora.
An important point (implicit) is made in here and in the quora thread. Although correlation is a linear measure, it does not exclusively mean it can only quantify the relationship between linearly ... | Why zero correlation does not necessarily imply independence | Adding to @Marcelo Ventura and @Mike Hunter great answers, and the reference to a great discussion around this on Quora.
An important point (implicit) is made in here and in the quora thread. Althou | Why zero correlation does not necessarily imply independence
Adding to @Marcelo Ventura and @Mike Hunter great answers, and the reference to a great discussion around this on Quora.
An important point (implicit) is made in here and in the quora thread. Although correlation is a linear measure, it does not exclusively... | Why zero correlation does not necessarily imply independence
Adding to @Marcelo Ventura and @Mike Hunter great answers, and the reference to a great discussion around this on Quora.
An important point (implicit) is made in here and in the quora thread. Althou |
4,818 | Why zero correlation does not necessarily imply independence | Zero correlation does not imply independence for multiple reasons. One of these is possible is that two variables could be dependent on a third causing correlation. | Why zero correlation does not necessarily imply independence | Zero correlation does not imply independence for multiple reasons. One of these is possible is that two variables could be dependent on a third causing correlation. | Why zero correlation does not necessarily imply independence
Zero correlation does not imply independence for multiple reasons. One of these is possible is that two variables could be dependent on a third causing correlation. | Why zero correlation does not necessarily imply independence
Zero correlation does not imply independence for multiple reasons. One of these is possible is that two variables could be dependent on a third causing correlation. |
4,819 | Excel as a statistics workbench | Use the right tool for the right job and exploit the strengths of the tools you are familiar with.
In Excel's case there are some salient issues:
Please don't use a spreadsheet to manage data, even if your data will fit into one. You're just asking for trouble, terrible trouble. There is virtually no protection again... | Excel as a statistics workbench | Use the right tool for the right job and exploit the strengths of the tools you are familiar with.
In Excel's case there are some salient issues:
Please don't use a spreadsheet to manage data, even i | Excel as a statistics workbench
Use the right tool for the right job and exploit the strengths of the tools you are familiar with.
In Excel's case there are some salient issues:
Please don't use a spreadsheet to manage data, even if your data will fit into one. You're just asking for trouble, terrible trouble. There ... | Excel as a statistics workbench
Use the right tool for the right job and exploit the strengths of the tools you are familiar with.
In Excel's case there are some salient issues:
Please don't use a spreadsheet to manage data, even i |
4,820 | Excel as a statistics workbench | An interesting paper about using Excel in a Bioinformatics setting is:
Mistaken Identifiers: Gene name errors
can be introduced inadvertently when
using Excel in bioinformatics, BMC
Bioinformatics, 2004 (link).
This short paper describes the problem of automatic type conversions in Excel (in particular date and... | Excel as a statistics workbench | An interesting paper about using Excel in a Bioinformatics setting is:
Mistaken Identifiers: Gene name errors
can be introduced inadvertently when
using Excel in bioinformatics, BMC
Bioinformat | Excel as a statistics workbench
An interesting paper about using Excel in a Bioinformatics setting is:
Mistaken Identifiers: Gene name errors
can be introduced inadvertently when
using Excel in bioinformatics, BMC
Bioinformatics, 2004 (link).
This short paper describes the problem of automatic type conversions ... | Excel as a statistics workbench
An interesting paper about using Excel in a Bioinformatics setting is:
Mistaken Identifiers: Gene name errors
can be introduced inadvertently when
using Excel in bioinformatics, BMC
Bioinformat |
4,821 | Excel as a statistics workbench | Well, the question whether the paper is correct or biased should be easy: you could just replicate some of their analyses and see whether you get the same answers.
McCullough has been taking different versions of MS Excel apart for some years now, and apparently MS haven't seen fit to fix errors he pointed out years ag... | Excel as a statistics workbench | Well, the question whether the paper is correct or biased should be easy: you could just replicate some of their analyses and see whether you get the same answers.
McCullough has been taking different | Excel as a statistics workbench
Well, the question whether the paper is correct or biased should be easy: you could just replicate some of their analyses and see whether you get the same answers.
McCullough has been taking different versions of MS Excel apart for some years now, and apparently MS haven't seen fit to fi... | Excel as a statistics workbench
Well, the question whether the paper is correct or biased should be easy: you could just replicate some of their analyses and see whether you get the same answers.
McCullough has been taking different |
4,822 | Excel as a statistics workbench | Another good reference source for why you might not want to use excel is:
Spreadsheet addiction
If you find yourself in a situation where you really need to use excel (some accademic departments insist), then I would suggest using the Rexcel plugin. This lets you interface using Excel, but uses the R program as the co... | Excel as a statistics workbench | Another good reference source for why you might not want to use excel is:
Spreadsheet addiction
If you find yourself in a situation where you really need to use excel (some accademic departments insis | Excel as a statistics workbench
Another good reference source for why you might not want to use excel is:
Spreadsheet addiction
If you find yourself in a situation where you really need to use excel (some accademic departments insist), then I would suggest using the Rexcel plugin. This lets you interface using Excel, ... | Excel as a statistics workbench
Another good reference source for why you might not want to use excel is:
Spreadsheet addiction
If you find yourself in a situation where you really need to use excel (some accademic departments insis |
4,823 | Excel as a statistics workbench | The papers and other participants point out to technical weaknesses. Whuber does a good job of outlining at least some of its strengths. I personally do extensive statistical work in Excel (hypothesis testing, linear and multiple regressions) and love it. I use Excel 2003 with a capacity of 256 columns and 65,000 ro... | Excel as a statistics workbench | The papers and other participants point out to technical weaknesses. Whuber does a good job of outlining at least some of its strengths. I personally do extensive statistical work in Excel (hypothes | Excel as a statistics workbench
The papers and other participants point out to technical weaknesses. Whuber does a good job of outlining at least some of its strengths. I personally do extensive statistical work in Excel (hypothesis testing, linear and multiple regressions) and love it. I use Excel 2003 with a capac... | Excel as a statistics workbench
The papers and other participants point out to technical weaknesses. Whuber does a good job of outlining at least some of its strengths. I personally do extensive statistical work in Excel (hypothes |
4,824 | Excel as a statistics workbench | Incidently, a question around the use of Google spreadsheets raised contrasting (hence, interesting) opinions about that, Do some of you use Google Docs spreadsheet to conduct and share your statistical work with others?
I have in mind an older paper which didn't seem so pessimist, but it is only marginally cited in th... | Excel as a statistics workbench | Incidently, a question around the use of Google spreadsheets raised contrasting (hence, interesting) opinions about that, Do some of you use Google Docs spreadsheet to conduct and share your statistic | Excel as a statistics workbench
Incidently, a question around the use of Google spreadsheets raised contrasting (hence, interesting) opinions about that, Do some of you use Google Docs spreadsheet to conduct and share your statistical work with others?
I have in mind an older paper which didn't seem so pessimist, but i... | Excel as a statistics workbench
Incidently, a question around the use of Google spreadsheets raised contrasting (hence, interesting) opinions about that, Do some of you use Google Docs spreadsheet to conduct and share your statistic |
4,825 | Excel as a statistics workbench | Excel is no good for statistics, but it can be wonderful for exploratory data analysis. Take a look at this video for some particularly interesting techniques. Excel's ability to conditionally color your data and add in-cell bar charts can give great insight into the structure of your raw data. | Excel as a statistics workbench | Excel is no good for statistics, but it can be wonderful for exploratory data analysis. Take a look at this video for some particularly interesting techniques. Excel's ability to conditionally color | Excel as a statistics workbench
Excel is no good for statistics, but it can be wonderful for exploratory data analysis. Take a look at this video for some particularly interesting techniques. Excel's ability to conditionally color your data and add in-cell bar charts can give great insight into the structure of your ... | Excel as a statistics workbench
Excel is no good for statistics, but it can be wonderful for exploratory data analysis. Take a look at this video for some particularly interesting techniques. Excel's ability to conditionally color |
4,826 | Excel as a statistics workbench | Excel can be great both for exploratory data analysis and linear regression analysis with the right plugins. There are a number of commercial products, although most of them leave something to be desired in terms of the quality of the output they produce (they don't take full advantage of Excel's charting options or t... | Excel as a statistics workbench | Excel can be great both for exploratory data analysis and linear regression analysis with the right plugins. There are a number of commercial products, although most of them leave something to be des | Excel as a statistics workbench
Excel can be great both for exploratory data analysis and linear regression analysis with the right plugins. There are a number of commercial products, although most of them leave something to be desired in terms of the quality of the output they produce (they don't take full advantage ... | Excel as a statistics workbench
Excel can be great both for exploratory data analysis and linear regression analysis with the right plugins. There are a number of commercial products, although most of them leave something to be des |
4,827 | Best method for short time-series | It is very common for extremely simple forecasting methods like "forecast the historical average" to outperform more complex methods. This is even more likely for short time series. Yes, in principle you can fit an ARIMA or even more complex model to 20 or fewer observations, but you will be rather likely to overfit an... | Best method for short time-series | It is very common for extremely simple forecasting methods like "forecast the historical average" to outperform more complex methods. This is even more likely for short time series. Yes, in principle | Best method for short time-series
It is very common for extremely simple forecasting methods like "forecast the historical average" to outperform more complex methods. This is even more likely for short time series. Yes, in principle you can fit an ARIMA or even more complex model to 20 or fewer observations, but you w... | Best method for short time-series
It is very common for extremely simple forecasting methods like "forecast the historical average" to outperform more complex methods. This is even more likely for short time series. Yes, in principle |
4,828 | Best method for short time-series | I am again using a question as an opportunity to learn more about time series - one of the (many) topics of my interest. After a brief research, it seems to me that there exist several approaches to the problem of modeling short time series.
The first approach is to use standard/linear time series models (AR, MA, ARMA,... | Best method for short time-series | I am again using a question as an opportunity to learn more about time series - one of the (many) topics of my interest. After a brief research, it seems to me that there exist several approaches to t | Best method for short time-series
I am again using a question as an opportunity to learn more about time series - one of the (many) topics of my interest. After a brief research, it seems to me that there exist several approaches to the problem of modeling short time series.
The first approach is to use standard/linear... | Best method for short time-series
I am again using a question as an opportunity to learn more about time series - one of the (many) topics of my interest. After a brief research, it seems to me that there exist several approaches to t |
4,829 | Best method for short time-series | No, There is no best univariate extrapolation method for a short time series with $T \leq 20$ series. Extrapolation methods need lots and lots of data.
Following qualitative methods work well in practice for very short or no data:
Composite forecasts
Surveys
Delphi method
Scenario building
Forecast by analogy
Executiv... | Best method for short time-series | No, There is no best univariate extrapolation method for a short time series with $T \leq 20$ series. Extrapolation methods need lots and lots of data.
Following qualitative methods work well in pract | Best method for short time-series
No, There is no best univariate extrapolation method for a short time series with $T \leq 20$ series. Extrapolation methods need lots and lots of data.
Following qualitative methods work well in practice for very short or no data:
Composite forecasts
Surveys
Delphi method
Scenario bui... | Best method for short time-series
No, There is no best univariate extrapolation method for a short time series with $T \leq 20$ series. Extrapolation methods need lots and lots of data.
Following qualitative methods work well in pract |
4,830 | Best method for short time-series | The assumption that the number of observations is critical came from an off-handed comment by G.E.P. Box regarding the minimum sample size to identify a model. A more nuanced answer as far as I am concerned is that the problem/quality of model identification is not solely based upon the sample size but the ratio of si... | Best method for short time-series | The assumption that the number of observations is critical came from an off-handed comment by G.E.P. Box regarding the minimum sample size to identify a model. A more nuanced answer as far as I am co | Best method for short time-series
The assumption that the number of observations is critical came from an off-handed comment by G.E.P. Box regarding the minimum sample size to identify a model. A more nuanced answer as far as I am concerned is that the problem/quality of model identification is not solely based upon t... | Best method for short time-series
The assumption that the number of observations is critical came from an off-handed comment by G.E.P. Box regarding the minimum sample size to identify a model. A more nuanced answer as far as I am co |
4,831 | Best method for short time-series | With very limited data, I would be more inclined to fit the data using Bayesian techniques.
Stationarity can be a bit tricky when dealing with Bayesian time series models. One choice is to enforce constraints on parameters. Or, you could not. This is fine if you just want to look at the distribution of the parameters. ... | Best method for short time-series | With very limited data, I would be more inclined to fit the data using Bayesian techniques.
Stationarity can be a bit tricky when dealing with Bayesian time series models. One choice is to enforce con | Best method for short time-series
With very limited data, I would be more inclined to fit the data using Bayesian techniques.
Stationarity can be a bit tricky when dealing with Bayesian time series models. One choice is to enforce constraints on parameters. Or, you could not. This is fine if you just want to look at th... | Best method for short time-series
With very limited data, I would be more inclined to fit the data using Bayesian techniques.
Stationarity can be a bit tricky when dealing with Bayesian time series models. One choice is to enforce con |
4,832 | Best method for short time-series | The problem as you wisely pointed out is the "overfitting" caused by fixed list-based procedures. A smart way is to try and keep the equation simple when you have a negligible amount of data. I have found after many moons that if you simply use an AR(1) model and leave the rate of adaption ( the ar coefficient) to the ... | Best method for short time-series | The problem as you wisely pointed out is the "overfitting" caused by fixed list-based procedures. A smart way is to try and keep the equation simple when you have a negligible amount of data. I have f | Best method for short time-series
The problem as you wisely pointed out is the "overfitting" caused by fixed list-based procedures. A smart way is to try and keep the equation simple when you have a negligible amount of data. I have found after many moons that if you simply use an AR(1) model and leave the rate of adap... | Best method for short time-series
The problem as you wisely pointed out is the "overfitting" caused by fixed list-based procedures. A smart way is to try and keep the equation simple when you have a negligible amount of data. I have f |
4,833 | What is difference-in-differences? | What is a difference in differences estimator
Difference in differences (DiD) is a tool to estimate treatment effects comparing the pre- and post-treatment differences in the outcome of a treatment and a control group. In general, we are interested in estimating the effect of a treatment $D_i$ (e.g. union status, medic... | What is difference-in-differences? | What is a difference in differences estimator
Difference in differences (DiD) is a tool to estimate treatment effects comparing the pre- and post-treatment differences in the outcome of a treatment an | What is difference-in-differences?
What is a difference in differences estimator
Difference in differences (DiD) is a tool to estimate treatment effects comparing the pre- and post-treatment differences in the outcome of a treatment and a control group. In general, we are interested in estimating the effect of a treatm... | What is difference-in-differences?
What is a difference in differences estimator
Difference in differences (DiD) is a tool to estimate treatment effects comparing the pre- and post-treatment differences in the outcome of a treatment an |
4,834 | What is difference-in-differences? | Wikipedia has a decent entry on this subject, but why not just use linear regression allowing for interactions between your independent variables of interest? This seems more interpretable to me. Then you might read up on analysis of simple slopes (in the Cohen et al book free on Google Books) if your variables of inte... | What is difference-in-differences? | Wikipedia has a decent entry on this subject, but why not just use linear regression allowing for interactions between your independent variables of interest? This seems more interpretable to me. Then | What is difference-in-differences?
Wikipedia has a decent entry on this subject, but why not just use linear regression allowing for interactions between your independent variables of interest? This seems more interpretable to me. Then you might read up on analysis of simple slopes (in the Cohen et al book free on Goog... | What is difference-in-differences?
Wikipedia has a decent entry on this subject, but why not just use linear regression allowing for interactions between your independent variables of interest? This seems more interpretable to me. Then |
4,835 | What is difference-in-differences? | It is a technique widely used in econometrics to examine the influence of any exogenous event in a time series. You pick two separate groups of data relating to before and after the event studied.
A good reference to learn more is the book Introduction to Econometrics by Wooldridge. | What is difference-in-differences? | It is a technique widely used in econometrics to examine the influence of any exogenous event in a time series. You pick two separate groups of data relating to before and after the event studied.
A | What is difference-in-differences?
It is a technique widely used in econometrics to examine the influence of any exogenous event in a time series. You pick two separate groups of data relating to before and after the event studied.
A good reference to learn more is the book Introduction to Econometrics by Wooldridge. | What is difference-in-differences?
It is a technique widely used in econometrics to examine the influence of any exogenous event in a time series. You pick two separate groups of data relating to before and after the event studied.
A |
4,836 | What is difference-in-differences? | Careful:
Two additional points are worth noting. First, 80 of the original 92 DD papers have a potential problem with grouped error terms as the unit of observation is more detailed than the level of variation (a point discussed by Donald and Lang [2001]). Only 36 of these papers address this problem, either by cluste... | What is difference-in-differences? | Careful:
Two additional points are worth noting. First, 80 of the original 92 DD papers have a potential problem with grouped error terms as the unit of observation is more detailed than the level of | What is difference-in-differences?
Careful:
Two additional points are worth noting. First, 80 of the original 92 DD papers have a potential problem with grouped error terms as the unit of observation is more detailed than the level of variation (a point discussed by Donald and Lang [2001]). Only 36 of these papers add... | What is difference-in-differences?
Careful:
Two additional points are worth noting. First, 80 of the original 92 DD papers have a potential problem with grouped error terms as the unit of observation is more detailed than the level of |
4,837 | Bayesian equivalent of two sample t-test? | This is a good question, that seems to pop up a lot: link 1, link 2. The paper Bayesian Estimation Superseeds the T-Test that Cam.Davidson.Pilon pointed out is an excellent resource on this subject. It is also very recent, published in 2012, which I think in part is due to the current interest in the area.
I will try t... | Bayesian equivalent of two sample t-test? | This is a good question, that seems to pop up a lot: link 1, link 2. The paper Bayesian Estimation Superseeds the T-Test that Cam.Davidson.Pilon pointed out is an excellent resource on this subject. I | Bayesian equivalent of two sample t-test?
This is a good question, that seems to pop up a lot: link 1, link 2. The paper Bayesian Estimation Superseeds the T-Test that Cam.Davidson.Pilon pointed out is an excellent resource on this subject. It is also very recent, published in 2012, which I think in part is due to the ... | Bayesian equivalent of two sample t-test?
This is a good question, that seems to pop up a lot: link 1, link 2. The paper Bayesian Estimation Superseeds the T-Test that Cam.Davidson.Pilon pointed out is an excellent resource on this subject. I |
4,838 | Bayesian equivalent of two sample t-test? | The excellent answer by user1068430 implemented in Python
import numpy as np
from pylab import plt
def dnorm(x, mu, sig):
return 1/(sig * np.sqrt(2 * np.pi)) * np.exp(-(x - mu)**2 / (2 * sig**2))
def dexp(x, l):
return l * np.exp(- l*x)
def like(parameters):
[mu1, sig1, mu2, sig2] = parameters
return... | Bayesian equivalent of two sample t-test? | The excellent answer by user1068430 implemented in Python
import numpy as np
from pylab import plt
def dnorm(x, mu, sig):
return 1/(sig * np.sqrt(2 * np.pi)) * np.exp(-(x - mu)**2 / (2 * sig**2)) | Bayesian equivalent of two sample t-test?
The excellent answer by user1068430 implemented in Python
import numpy as np
from pylab import plt
def dnorm(x, mu, sig):
return 1/(sig * np.sqrt(2 * np.pi)) * np.exp(-(x - mu)**2 / (2 * sig**2))
def dexp(x, l):
return l * np.exp(- l*x)
def like(parameters):
[mu1... | Bayesian equivalent of two sample t-test?
The excellent answer by user1068430 implemented in Python
import numpy as np
from pylab import plt
def dnorm(x, mu, sig):
return 1/(sig * np.sqrt(2 * np.pi)) * np.exp(-(x - mu)**2 / (2 * sig**2)) |
4,839 | Bayesian equivalent of two sample t-test? | With a Bayesian analysis you have more things to specify (that is actually a good thing, since it gives much more flexibility and ability to model what you believe the truth to be). Are you assuming normals for the likelihoods? Will the 2 groups have the same variance?
One straight forward approach is to model the 2 ... | Bayesian equivalent of two sample t-test? | With a Bayesian analysis you have more things to specify (that is actually a good thing, since it gives much more flexibility and ability to model what you believe the truth to be). Are you assuming | Bayesian equivalent of two sample t-test?
With a Bayesian analysis you have more things to specify (that is actually a good thing, since it gives much more flexibility and ability to model what you believe the truth to be). Are you assuming normals for the likelihoods? Will the 2 groups have the same variance?
One st... | Bayesian equivalent of two sample t-test?
With a Bayesian analysis you have more things to specify (that is actually a good thing, since it gives much more flexibility and ability to model what you believe the truth to be). Are you assuming |
4,840 | Bayesian equivalent of two sample t-test? | a mathematical explanation of what are some Bayesian methods I can use to test the difference between the mean of two samples.
There are several approaches to "testing" this. I'll mention a couple:
If you want an explicit decision you could look at decision theory.
A pretty simple thing that's sometimes done is to f... | Bayesian equivalent of two sample t-test? | a mathematical explanation of what are some Bayesian methods I can use to test the difference between the mean of two samples.
There are several approaches to "testing" this. I'll mention a couple:
| Bayesian equivalent of two sample t-test?
a mathematical explanation of what are some Bayesian methods I can use to test the difference between the mean of two samples.
There are several approaches to "testing" this. I'll mention a couple:
If you want an explicit decision you could look at decision theory.
A pretty ... | Bayesian equivalent of two sample t-test?
a mathematical explanation of what are some Bayesian methods I can use to test the difference between the mean of two samples.
There are several approaches to "testing" this. I'll mention a couple:
|
4,841 | Bayesian equivalent of two sample t-test? | First you should consider whether you would like to do this at all.
A good start would be to read this even more recent (2022) paper by Costello and Watts to learn about the various theoretical pitfalls associated with hypothesis testing in a Bayesian framework.
One of the most serious problems they see with the usual ... | Bayesian equivalent of two sample t-test? | First you should consider whether you would like to do this at all.
A good start would be to read this even more recent (2022) paper by Costello and Watts to learn about the various theoretical pitfal | Bayesian equivalent of two sample t-test?
First you should consider whether you would like to do this at all.
A good start would be to read this even more recent (2022) paper by Costello and Watts to learn about the various theoretical pitfalls associated with hypothesis testing in a Bayesian framework.
One of the most... | Bayesian equivalent of two sample t-test?
First you should consider whether you would like to do this at all.
A good start would be to read this even more recent (2022) paper by Costello and Watts to learn about the various theoretical pitfal |
4,842 | Why is Entropy maximised when the probability distribution is uniform? | Heuristically, the probability density function on $\{x_1, x_2,..,.x_n\}$ with maximum entropy turns out to be the one that corresponds to the least amount of knowledge of $\{x_1, x_2,..,.x_n\}$, in other words the Uniform distribution.
Now, for a more formal proof consider the following:
A probability density function... | Why is Entropy maximised when the probability distribution is uniform? | Heuristically, the probability density function on $\{x_1, x_2,..,.x_n\}$ with maximum entropy turns out to be the one that corresponds to the least amount of knowledge of $\{x_1, x_2,..,.x_n\}$, in o | Why is Entropy maximised when the probability distribution is uniform?
Heuristically, the probability density function on $\{x_1, x_2,..,.x_n\}$ with maximum entropy turns out to be the one that corresponds to the least amount of knowledge of $\{x_1, x_2,..,.x_n\}$, in other words the Uniform distribution.
Now, for a m... | Why is Entropy maximised when the probability distribution is uniform?
Heuristically, the probability density function on $\{x_1, x_2,..,.x_n\}$ with maximum entropy turns out to be the one that corresponds to the least amount of knowledge of $\{x_1, x_2,..,.x_n\}$, in o |
4,843 | Why is Entropy maximised when the probability distribution is uniform? | Entropy in physics and information theory are not unrelated. They're more different than the name suggests, yet there's clearly a link between. The purpose of entropy metric is to measure the amount of information. See my answer with graphs here to show how entropy changes from uniform distribution to a humped one.
The... | Why is Entropy maximised when the probability distribution is uniform? | Entropy in physics and information theory are not unrelated. They're more different than the name suggests, yet there's clearly a link between. The purpose of entropy metric is to measure the amount o | Why is Entropy maximised when the probability distribution is uniform?
Entropy in physics and information theory are not unrelated. They're more different than the name suggests, yet there's clearly a link between. The purpose of entropy metric is to measure the amount of information. See my answer with graphs here to ... | Why is Entropy maximised when the probability distribution is uniform?
Entropy in physics and information theory are not unrelated. They're more different than the name suggests, yet there's clearly a link between. The purpose of entropy metric is to measure the amount o |
4,844 | Why is Entropy maximised when the probability distribution is uniform? | The mathematical argument is based on Jensen inequality for concave functions. That is, if $f(x)$ is a concave function on $[a,b]$ and $y_1, \ldots y_n$ are points in $[a,b]$, then:
$n \cdot f(\frac{y_1 + \ldots y_n}{n}) \geq f(y_1) + \ldots + f(y_n)$
Apply this for the concave function $f(x) = -x \log(x)$ and Jensen ... | Why is Entropy maximised when the probability distribution is uniform? | The mathematical argument is based on Jensen inequality for concave functions. That is, if $f(x)$ is a concave function on $[a,b]$ and $y_1, \ldots y_n$ are points in $[a,b]$, then:
$n \cdot f(\frac{ | Why is Entropy maximised when the probability distribution is uniform?
The mathematical argument is based on Jensen inequality for concave functions. That is, if $f(x)$ is a concave function on $[a,b]$ and $y_1, \ldots y_n$ are points in $[a,b]$, then:
$n \cdot f(\frac{y_1 + \ldots y_n}{n}) \geq f(y_1) + \ldots + f(y_... | Why is Entropy maximised when the probability distribution is uniform?
The mathematical argument is based on Jensen inequality for concave functions. That is, if $f(x)$ is a concave function on $[a,b]$ and $y_1, \ldots y_n$ are points in $[a,b]$, then:
$n \cdot f(\frac{ |
4,845 | Why is Entropy maximised when the probability distribution is uniform? | On a side note, is there any connnection between the entropy that occurs information theory and the entropy calculations in chemistry (thermodynamics) ?
Yes, there is! You can see the work of Jaynes and many others following his work (such as here and here, for instance).
But the main idea is that statistical mechanic... | Why is Entropy maximised when the probability distribution is uniform? | On a side note, is there any connnection between the entropy that occurs information theory and the entropy calculations in chemistry (thermodynamics) ?
Yes, there is! You can see the work of Jaynes | Why is Entropy maximised when the probability distribution is uniform?
On a side note, is there any connnection between the entropy that occurs information theory and the entropy calculations in chemistry (thermodynamics) ?
Yes, there is! You can see the work of Jaynes and many others following his work (such as here ... | Why is Entropy maximised when the probability distribution is uniform?
On a side note, is there any connnection between the entropy that occurs information theory and the entropy calculations in chemistry (thermodynamics) ?
Yes, there is! You can see the work of Jaynes |
4,846 | Why is Entropy maximised when the probability distribution is uniform? | Main idea: take partial derivative of each $p_i$, set them all to zero, solve the system of linear equations.
Take a finite number of $p_i$ where $i=1,...,n$ for an example.
Denote $q = 1-\sum_{i=0}^{n-1} p_i$.
\begin{align}
H &= -\sum_{i=0}^{n-1} p_i \log p_i - (1-q)\log q\\
H*\ln 2 &= -\sum_{i=0}^{n-1} p_i \ln p_i - ... | Why is Entropy maximised when the probability distribution is uniform? | Main idea: take partial derivative of each $p_i$, set them all to zero, solve the system of linear equations.
Take a finite number of $p_i$ where $i=1,...,n$ for an example.
Denote $q = 1-\sum_{i=0}^{ | Why is Entropy maximised when the probability distribution is uniform?
Main idea: take partial derivative of each $p_i$, set them all to zero, solve the system of linear equations.
Take a finite number of $p_i$ where $i=1,...,n$ for an example.
Denote $q = 1-\sum_{i=0}^{n-1} p_i$.
\begin{align}
H &= -\sum_{i=0}^{n-1} p... | Why is Entropy maximised when the probability distribution is uniform?
Main idea: take partial derivative of each $p_i$, set them all to zero, solve the system of linear equations.
Take a finite number of $p_i$ where $i=1,...,n$ for an example.
Denote $q = 1-\sum_{i=0}^{ |
4,847 | Why is Entropy maximised when the probability distribution is uniform? | There are already several good answers. Another argument uses the fact that H is a symmetric, strictly concave function. More precisely, consider the unit simplex $\Delta_n=\{(p_1,\dots,p_n): p_i\ge 0,\sum_i p_i=1\}$.Then $H$ may be considered a function $H: \Delta_n\to \mathbb{R}$, and it is easy to show that it is st... | Why is Entropy maximised when the probability distribution is uniform? | There are already several good answers. Another argument uses the fact that H is a symmetric, strictly concave function. More precisely, consider the unit simplex $\Delta_n=\{(p_1,\dots,p_n): p_i\ge 0 | Why is Entropy maximised when the probability distribution is uniform?
There are already several good answers. Another argument uses the fact that H is a symmetric, strictly concave function. More precisely, consider the unit simplex $\Delta_n=\{(p_1,\dots,p_n): p_i\ge 0,\sum_i p_i=1\}$.Then $H$ may be considered a fun... | Why is Entropy maximised when the probability distribution is uniform?
There are already several good answers. Another argument uses the fact that H is a symmetric, strictly concave function. More precisely, consider the unit simplex $\Delta_n=\{(p_1,\dots,p_n): p_i\ge 0 |
4,848 | Why is Entropy maximised when the probability distribution is uniform? | Calculus of Variations
To handle varying functions, we will make use of the Calculus of Variations. The variation $\delta f(x)$ refers to a rate of change of $f(x)$ with respect to "time". That is, $\delta$ works like a partial derivative with respect to "time". For example,
$$
\begin{align}
\delta(\log(f(x))f(x))
&=\l... | Why is Entropy maximised when the probability distribution is uniform? | Calculus of Variations
To handle varying functions, we will make use of the Calculus of Variations. The variation $\delta f(x)$ refers to a rate of change of $f(x)$ with respect to "time". That is, $\ | Why is Entropy maximised when the probability distribution is uniform?
Calculus of Variations
To handle varying functions, we will make use of the Calculus of Variations. The variation $\delta f(x)$ refers to a rate of change of $f(x)$ with respect to "time". That is, $\delta$ works like a partial derivative with respe... | Why is Entropy maximised when the probability distribution is uniform?
Calculus of Variations
To handle varying functions, we will make use of the Calculus of Variations. The variation $\delta f(x)$ refers to a rate of change of $f(x)$ with respect to "time". That is, $\ |
4,849 | Why is Entropy maximised when the probability distribution is uniform? | An intuitive explanation:
If we put more probability mass into one event of a random variable, we will have to take away some from other events. The one will have less information content and more weight, the others more information content and less weight. Therefore the entropy being the expected information content w... | Why is Entropy maximised when the probability distribution is uniform? | An intuitive explanation:
If we put more probability mass into one event of a random variable, we will have to take away some from other events. The one will have less information content and more wei | Why is Entropy maximised when the probability distribution is uniform?
An intuitive explanation:
If we put more probability mass into one event of a random variable, we will have to take away some from other events. The one will have less information content and more weight, the others more information content and less... | Why is Entropy maximised when the probability distribution is uniform?
An intuitive explanation:
If we put more probability mass into one event of a random variable, we will have to take away some from other events. The one will have less information content and more wei |
4,850 | Obtaining predicted values (Y=1 or 0) from a logistic regression model fit | Once you have the predicted probabilities, it is up to you what threshold you would like to use. You may choose the threshold to optimize sensitivity, specificity or whatever measure it most important in the context of the application (some additional info would be helpful here for a more specific answer). You may want... | Obtaining predicted values (Y=1 or 0) from a logistic regression model fit | Once you have the predicted probabilities, it is up to you what threshold you would like to use. You may choose the threshold to optimize sensitivity, specificity or whatever measure it most important | Obtaining predicted values (Y=1 or 0) from a logistic regression model fit
Once you have the predicted probabilities, it is up to you what threshold you would like to use. You may choose the threshold to optimize sensitivity, specificity or whatever measure it most important in the context of the application (some addi... | Obtaining predicted values (Y=1 or 0) from a logistic regression model fit
Once you have the predicted probabilities, it is up to you what threshold you would like to use. You may choose the threshold to optimize sensitivity, specificity or whatever measure it most important |
4,851 | Understanding "almost all local minimum have very similar function value to the global optimum" | A recent paper The Loss Surfaces of Multilayer Networks offers some possible explanations for this. From their abstract (bold is mine):
"We conjecture that both simulated annealing and SGD converge
to the band of low critical points, and that all critical points found there are local minima of high quality measured... | Understanding "almost all local minimum have very similar function value to the global optimum" | A recent paper The Loss Surfaces of Multilayer Networks offers some possible explanations for this. From their abstract (bold is mine):
"We conjecture that both simulated annealing and SGD converge
t | Understanding "almost all local minimum have very similar function value to the global optimum"
A recent paper The Loss Surfaces of Multilayer Networks offers some possible explanations for this. From their abstract (bold is mine):
"We conjecture that both simulated annealing and SGD converge
to the band of low critic... | Understanding "almost all local minimum have very similar function value to the global optimum"
A recent paper The Loss Surfaces of Multilayer Networks offers some possible explanations for this. From their abstract (bold is mine):
"We conjecture that both simulated annealing and SGD converge
t |
4,852 | Does the sign of scores or of loadings in PCA or FA have a meaning? May I reverse the sign? | PCA is a simple mathematical transformation. If you change the signs of the component(s), you do not change the variance that is contained in the first component. Moreover, when you change the signs, the weights (prcomp( ... )$rotation) also change the sign, so the interpretation stays exactly the same:
set.seed( 999 ... | Does the sign of scores or of loadings in PCA or FA have a meaning? May I reverse the sign? | PCA is a simple mathematical transformation. If you change the signs of the component(s), you do not change the variance that is contained in the first component. Moreover, when you change the signs, | Does the sign of scores or of loadings in PCA or FA have a meaning? May I reverse the sign?
PCA is a simple mathematical transformation. If you change the signs of the component(s), you do not change the variance that is contained in the first component. Moreover, when you change the signs, the weights (prcomp( ... )$... | Does the sign of scores or of loadings in PCA or FA have a meaning? May I reverse the sign?
PCA is a simple mathematical transformation. If you change the signs of the component(s), you do not change the variance that is contained in the first component. Moreover, when you change the signs, |
4,853 | Does the sign of scores or of loadings in PCA or FA have a meaning? May I reverse the sign? | This question gets asked a lot on this forum, so I would like to supplement @January's excellent answer with a bit more general considerations.
In both principal component analysis (PCA) and factor analysis (FA), we use the original variables $x_1, x_2, ... x_d$ to estimate several latent components (or latent variable... | Does the sign of scores or of loadings in PCA or FA have a meaning? May I reverse the sign? | This question gets asked a lot on this forum, so I would like to supplement @January's excellent answer with a bit more general considerations.
In both principal component analysis (PCA) and factor an | Does the sign of scores or of loadings in PCA or FA have a meaning? May I reverse the sign?
This question gets asked a lot on this forum, so I would like to supplement @January's excellent answer with a bit more general considerations.
In both principal component analysis (PCA) and factor analysis (FA), we use the orig... | Does the sign of scores or of loadings in PCA or FA have a meaning? May I reverse the sign?
This question gets asked a lot on this forum, so I would like to supplement @January's excellent answer with a bit more general considerations.
In both principal component analysis (PCA) and factor an |
4,854 | Does the sign of scores or of loadings in PCA or FA have a meaning? May I reverse the sign? | This was well answered above. Just to provide some further mathematical relevance, the directions that the principal components act correspond to the eigenvectors of the system. If you are getting a positive or negative PC it just means that you are projecting on an eigenvector that is pointing in one direction or $180... | Does the sign of scores or of loadings in PCA or FA have a meaning? May I reverse the sign? | This was well answered above. Just to provide some further mathematical relevance, the directions that the principal components act correspond to the eigenvectors of the system. If you are getting a p | Does the sign of scores or of loadings in PCA or FA have a meaning? May I reverse the sign?
This was well answered above. Just to provide some further mathematical relevance, the directions that the principal components act correspond to the eigenvectors of the system. If you are getting a positive or negative PC it ju... | Does the sign of scores or of loadings in PCA or FA have a meaning? May I reverse the sign?
This was well answered above. Just to provide some further mathematical relevance, the directions that the principal components act correspond to the eigenvectors of the system. If you are getting a p |
4,855 | Does the sign of scores or of loadings in PCA or FA have a meaning? May I reverse the sign? | It is easy to see that the sign of scores does not matter when using PCA for classification or clustering. But it seems to matter for regression. Consider a case where you have just one principal component or one common factor underlying several variables. Then lm(y ~ PC1) will give you different predictions of y compa... | Does the sign of scores or of loadings in PCA or FA have a meaning? May I reverse the sign? | It is easy to see that the sign of scores does not matter when using PCA for classification or clustering. But it seems to matter for regression. Consider a case where you have just one principal comp | Does the sign of scores or of loadings in PCA or FA have a meaning? May I reverse the sign?
It is easy to see that the sign of scores does not matter when using PCA for classification or clustering. But it seems to matter for regression. Consider a case where you have just one principal component or one common factor u... | Does the sign of scores or of loadings in PCA or FA have a meaning? May I reverse the sign?
It is easy to see that the sign of scores does not matter when using PCA for classification or clustering. But it seems to matter for regression. Consider a case where you have just one principal comp |
4,856 | What is pre training a neural network? | The usual way of training a network:
You want to train a neural network to perform a task (e.g. classification) on a data set (e.g. a set of images). You start training by initializing the weights randomly. As soon as you start training, the weights are changed in order to perform the task with less mistakes (i.e. opti... | What is pre training a neural network? | The usual way of training a network:
You want to train a neural network to perform a task (e.g. classification) on a data set (e.g. a set of images). You start training by initializing the weights ran | What is pre training a neural network?
The usual way of training a network:
You want to train a neural network to perform a task (e.g. classification) on a data set (e.g. a set of images). You start training by initializing the weights randomly. As soon as you start training, the weights are changed in order to perform... | What is pre training a neural network?
The usual way of training a network:
You want to train a neural network to perform a task (e.g. classification) on a data set (e.g. a set of images). You start training by initializing the weights ran |
4,857 | What is pre training a neural network? | Pretraining / fine-tuning works as follows:
You have machine learning model $m$.
Pre-training: You have a dataset $A$ on which you train $m$.
You have a dataset $B$. Before you start training the model, you initialize some of the parameters of $m$ with the model which is trained on $A$.
Fine-tuning: You train $m$ on $... | What is pre training a neural network? | Pretraining / fine-tuning works as follows:
You have machine learning model $m$.
Pre-training: You have a dataset $A$ on which you train $m$.
You have a dataset $B$. Before you start training the mod | What is pre training a neural network?
Pretraining / fine-tuning works as follows:
You have machine learning model $m$.
Pre-training: You have a dataset $A$ on which you train $m$.
You have a dataset $B$. Before you start training the model, you initialize some of the parameters of $m$ with the model which is trained ... | What is pre training a neural network?
Pretraining / fine-tuning works as follows:
You have machine learning model $m$.
Pre-training: You have a dataset $A$ on which you train $m$.
You have a dataset $B$. Before you start training the mod |
4,858 | What is pre training a neural network? | The two answers above explains well. Just want to add one subtle thing regarding the pre-training for Deep Belief Nets (DBN). The pre-training for DBN is unsupervised learning (i.e. w/o labeled data) and the training afterwards is supervised learning (i.e. w/. labeled data). | What is pre training a neural network? | The two answers above explains well. Just want to add one subtle thing regarding the pre-training for Deep Belief Nets (DBN). The pre-training for DBN is unsupervised learning (i.e. w/o labeled data) | What is pre training a neural network?
The two answers above explains well. Just want to add one subtle thing regarding the pre-training for Deep Belief Nets (DBN). The pre-training for DBN is unsupervised learning (i.e. w/o labeled data) and the training afterwards is supervised learning (i.e. w/. labeled data). | What is pre training a neural network?
The two answers above explains well. Just want to add one subtle thing regarding the pre-training for Deep Belief Nets (DBN). The pre-training for DBN is unsupervised learning (i.e. w/o labeled data) |
4,859 | How to choose between ROC AUC and F1 score? | Calculation formula：
Precision TP/(TP+FP)
Recall: TP/(TP+FN)
F1-score： 2/(1/P+1/R)
ROC/AUC： TPR=TP/(TP+FN), FPR=FP/(FP+TN)
ROC / AUC is the same criteria and the PR (Precision-Recall) curve (F1-score, Precision, Recall) is also the same criteria.
Real data will tend to have an imbalance between positive and negative... | How to choose between ROC AUC and F1 score? | Calculation formula：
Precision TP/(TP+FP)
Recall: TP/(TP+FN)
F1-score： 2/(1/P+1/R)
ROC/AUC： TPR=TP/(TP+FN), FPR=FP/(FP+TN)
ROC / AUC is the same criteria and the PR (Precision-Recall) curve (F1-sco | How to choose between ROC AUC and F1 score?
Calculation formula：
Precision TP/(TP+FP)
Recall: TP/(TP+FN)
F1-score： 2/(1/P+1/R)
ROC/AUC： TPR=TP/(TP+FN), FPR=FP/(FP+TN)
ROC / AUC is the same criteria and the PR (Precision-Recall) curve (F1-score, Precision, Recall) is also the same criteria.
Real data will tend to hav... | How to choose between ROC AUC and F1 score?
Calculation formula：
Precision TP/(TP+FP)
Recall: TP/(TP+FN)
F1-score： 2/(1/P+1/R)
ROC/AUC： TPR=TP/(TP+FN), FPR=FP/(FP+TN)
ROC / AUC is the same criteria and the PR (Precision-Recall) curve (F1-sco |
4,860 | How to choose between ROC AUC and F1 score? | None of the measures listed here are proper accuracy scoring rules, i.e., rules that are optimized by a correct model. Consider the Brier score and log-likelihood-based measures such as pseudo $R^2$. The $c$-index (AUROC; concordance probability) is not proper but is good for describing a single model. It is not sen... | How to choose between ROC AUC and F1 score? | None of the measures listed here are proper accuracy scoring rules, i.e., rules that are optimized by a correct model. Consider the Brier score and log-likelihood-based measures such as pseudo $R^2$. | How to choose between ROC AUC and F1 score?
None of the measures listed here are proper accuracy scoring rules, i.e., rules that are optimized by a correct model. Consider the Brier score and log-likelihood-based measures such as pseudo $R^2$. The $c$-index (AUROC; concordance probability) is not proper but is good f... | How to choose between ROC AUC and F1 score?
None of the measures listed here are proper accuracy scoring rules, i.e., rules that are optimized by a correct model. Consider the Brier score and log-likelihood-based measures such as pseudo $R^2$. |
4,861 | How to choose between ROC AUC and F1 score? | Above answers are both good.
But what I want to point out is AUC (Area under ROC) is problematic especially the data is imbalanced (so called highly skewed: $Skew=\frac{negative\;examples}{positive\;examples}$ is large). This kind of situations is very common in action detection, fraud detection, bankruptcy prediction... | How to choose between ROC AUC and F1 score? | Above answers are both good.
But what I want to point out is AUC (Area under ROC) is problematic especially the data is imbalanced (so called highly skewed: $Skew=\frac{negative\;examples}{positive\; | How to choose between ROC AUC and F1 score?
Above answers are both good.
But what I want to point out is AUC (Area under ROC) is problematic especially the data is imbalanced (so called highly skewed: $Skew=\frac{negative\;examples}{positive\;examples}$ is large). This kind of situations is very common in action detec... | How to choose between ROC AUC and F1 score?
Above answers are both good.
But what I want to point out is AUC (Area under ROC) is problematic especially the data is imbalanced (so called highly skewed: $Skew=\frac{negative\;examples}{positive\; |
4,862 | How to choose between ROC AUC and F1 score? | To put in very simple words when you have a data imbalance i.e., the difference between the number of examples you have for positive and negative classes is large, you should always use F1-score. Otherwise you can use ROC/AUC curves. | How to choose between ROC AUC and F1 score? | To put in very simple words when you have a data imbalance i.e., the difference between the number of examples you have for positive and negative classes is large, you should always use F1-score. Othe | How to choose between ROC AUC and F1 score?
To put in very simple words when you have a data imbalance i.e., the difference between the number of examples you have for positive and negative classes is large, you should always use F1-score. Otherwise you can use ROC/AUC curves. | How to choose between ROC AUC and F1 score?
To put in very simple words when you have a data imbalance i.e., the difference between the number of examples you have for positive and negative classes is large, you should always use F1-score. Othe |
4,863 | How to choose between ROC AUC and F1 score? | Despite the less interpretable graph that AUC integrates, the number itself tells you the probability that a randomly chosen positive would be ranked higher than a randomly chosen negative. This is a nice summary of the degree to which positive examples are scored higher than negative examples. If the negatives are ran... | How to choose between ROC AUC and F1 score? | Despite the less interpretable graph that AUC integrates, the number itself tells you the probability that a randomly chosen positive would be ranked higher than a randomly chosen negative. This is a | How to choose between ROC AUC and F1 score?
Despite the less interpretable graph that AUC integrates, the number itself tells you the probability that a randomly chosen positive would be ranked higher than a randomly chosen negative. This is a nice summary of the degree to which positive examples are scored higher than... | How to choose between ROC AUC and F1 score?
Despite the less interpretable graph that AUC integrates, the number itself tells you the probability that a randomly chosen positive would be ranked higher than a randomly chosen negative. This is a |
4,864 | How to choose between ROC AUC and F1 score? | If the objective of classification is scoring by probability, it is better to use AUC which averages over all possible thresholds. However, if the objective of classification just needs to classify between two possible classes and doesn't require how likely each class is predicted by the model, it is more appropriate t... | How to choose between ROC AUC and F1 score? | If the objective of classification is scoring by probability, it is better to use AUC which averages over all possible thresholds. However, if the objective of classification just needs to classify be | How to choose between ROC AUC and F1 score?
If the objective of classification is scoring by probability, it is better to use AUC which averages over all possible thresholds. However, if the objective of classification just needs to classify between two possible classes and doesn't require how likely each class is pred... | How to choose between ROC AUC and F1 score?
If the objective of classification is scoring by probability, it is better to use AUC which averages over all possible thresholds. However, if the objective of classification just needs to classify be |
4,865 | How to choose between ROC AUC and F1 score? | For some multi class classification problems, analyzing and visualizing ROC/AUC is not straightforward. You may look into this question, How to plot ROC curves in multiclass classification?. Under such situation, using F1 score could be a better metric.
And F1 score is a common choice for information retrieval problem... | How to choose between ROC AUC and F1 score? | For some multi class classification problems, analyzing and visualizing ROC/AUC is not straightforward. You may look into this question, How to plot ROC curves in multiclass classification?. Under suc | How to choose between ROC AUC and F1 score?
For some multi class classification problems, analyzing and visualizing ROC/AUC is not straightforward. You may look into this question, How to plot ROC curves in multiclass classification?. Under such situation, using F1 score could be a better metric.
And F1 score is a com... | How to choose between ROC AUC and F1 score?
For some multi class classification problems, analyzing and visualizing ROC/AUC is not straightforward. You may look into this question, How to plot ROC curves in multiclass classification?. Under suc |
4,866 | How to choose between ROC AUC and F1 score? | Lets start with some formula to see how each measure is calculated (see Wikipedia for a complete list)：
Precision: $\frac{TP}{TP+FP}$
Recall: $\frac{TP}{TP+FN}$
F1-score： $\frac{2}{\frac{1}{Precision}+\frac{1}{Recall}}=2\times\frac{Precision \times Recall}{Precision + Recall}$
AUC curve is built using the following me... | How to choose between ROC AUC and F1 score? | Lets start with some formula to see how each measure is calculated (see Wikipedia for a complete list)：
Precision: $\frac{TP}{TP+FP}$
Recall: $\frac{TP}{TP+FN}$
F1-score： $\frac{2}{\frac{1}{Precision | How to choose between ROC AUC and F1 score?
Lets start with some formula to see how each measure is calculated (see Wikipedia for a complete list)：
Precision: $\frac{TP}{TP+FP}$
Recall: $\frac{TP}{TP+FN}$
F1-score： $\frac{2}{\frac{1}{Precision}+\frac{1}{Recall}}=2\times\frac{Precision \times Recall}{Precision + Recall... | How to choose between ROC AUC and F1 score?
Lets start with some formula to see how each measure is calculated (see Wikipedia for a complete list)：
Precision: $\frac{TP}{TP+FP}$
Recall: $\frac{TP}{TP+FN}$
F1-score： $\frac{2}{\frac{1}{Precision |
4,867 | How to determine the optimal threshold for a classifier and generate ROC curve? | Use the SVM classifier to classify a set of annotated examples, and "one point" on the ROC space based on one prediction of the examples can be identified. Suppose the number of examples is 200, first count the number of examples of the four cases.
\begin{array} {|r|r|r|}
\hline
& \text{labeled true} & \text{labeled... | How to determine the optimal threshold for a classifier and generate ROC curve? | Use the SVM classifier to classify a set of annotated examples, and "one point" on the ROC space based on one prediction of the examples can be identified. Suppose the number of examples is 200, first | How to determine the optimal threshold for a classifier and generate ROC curve?
Use the SVM classifier to classify a set of annotated examples, and "one point" on the ROC space based on one prediction of the examples can be identified. Suppose the number of examples is 200, first count the number of examples of the fou... | How to determine the optimal threshold for a classifier and generate ROC curve?
Use the SVM classifier to classify a set of annotated examples, and "one point" on the ROC space based on one prediction of the examples can be identified. Suppose the number of examples is 200, first |
4,868 | How to determine the optimal threshold for a classifier and generate ROC curve? | The choice of a threshold depends on the importance of TPR and FPR classification problem. For example, if your classifier will decide which criminal suspects will receive a death sentence, false positives are very bad (innocents will be killed!). Thus you would choose a threshold that yields a low FPR while keeping a ... | How to determine the optimal threshold for a classifier and generate ROC curve? | The choice of a threshold depends on the importance of TPR and FPR classification problem. For example, if your classifier will decide which criminal suspects will receive a death sentence, false posi | How to determine the optimal threshold for a classifier and generate ROC curve?
The choice of a threshold depends on the importance of TPR and FPR classification problem. For example, if your classifier will decide which criminal suspects will receive a death sentence, false positives are very bad (innocents will be ki... | How to determine the optimal threshold for a classifier and generate ROC curve?
The choice of a threshold depends on the importance of TPR and FPR classification problem. For example, if your classifier will decide which criminal suspects will receive a death sentence, false posi |
4,869 | How to determine the optimal threshold for a classifier and generate ROC curve? | Choose the point closest to the top left corner of your ROC space. Now the threshold used to generate this point should be the optimal one. | How to determine the optimal threshold for a classifier and generate ROC curve? | Choose the point closest to the top left corner of your ROC space. Now the threshold used to generate this point should be the optimal one. | How to determine the optimal threshold for a classifier and generate ROC curve?
Choose the point closest to the top left corner of your ROC space. Now the threshold used to generate this point should be the optimal one. | How to determine the optimal threshold for a classifier and generate ROC curve?
Choose the point closest to the top left corner of your ROC space. Now the threshold used to generate this point should be the optimal one. |
4,870 | How to determine the optimal threshold for a classifier and generate ROC curve? | ####################################
The optimal cut off would be where tpr is high and fpr is low
tpr - (1-fpr) is zero or near to zero is the optimal cut off point
####################################
def plot_roc_curve(fpr, tpr):
plt.plot(fpr, tpr, color='orange', label='ROC')
plt.plot([0, 1], [0, 1], color=... | How to determine the optimal threshold for a classifier and generate ROC curve? | ####################################
The optimal cut off would be where tpr is high and fpr is low
tpr - (1-fpr) is zero or near to zero is the optimal cut off point
################################## | How to determine the optimal threshold for a classifier and generate ROC curve?
####################################
The optimal cut off would be where tpr is high and fpr is low
tpr - (1-fpr) is zero or near to zero is the optimal cut off point
####################################
def plot_roc_curve(fpr, tpr):
plt... | How to determine the optimal threshold for a classifier and generate ROC curve?
####################################
The optimal cut off would be where tpr is high and fpr is low
tpr - (1-fpr) is zero or near to zero is the optimal cut off point
################################## |
4,871 | How to determine the optimal threshold for a classifier and generate ROC curve? | A really easy way to pick a threshold is to take the median predicted values of the positive cases for a test set. This becomes your threshold.
The threshold comes relatively close to the same threshold you would get by using the roc curve where true positive rate(tpr) and 1 - false positive rate(fpr) overlap. This tp... | How to determine the optimal threshold for a classifier and generate ROC curve? | A really easy way to pick a threshold is to take the median predicted values of the positive cases for a test set. This becomes your threshold.
The threshold comes relatively close to the same thresho | How to determine the optimal threshold for a classifier and generate ROC curve?
A really easy way to pick a threshold is to take the median predicted values of the positive cases for a test set. This becomes your threshold.
The threshold comes relatively close to the same threshold you would get by using the roc curve ... | How to determine the optimal threshold for a classifier and generate ROC curve?
A really easy way to pick a threshold is to take the median predicted values of the positive cases for a test set. This becomes your threshold.
The threshold comes relatively close to the same thresho |
4,872 | How to determine the optimal threshold for a classifier and generate ROC curve? | Following Will's comment.
This article (www0.cs.ucl.ac.uk/staff/W.Langdon/roc) has some good points under the heading "Choosing the Operating Point". picking the point closest to the top left corner of a ROC curve equates to choosing the operating point such that TPR = TNR, i.e. false positives are equally bad as fals... | How to determine the optimal threshold for a classifier and generate ROC curve? | Following Will's comment.
This article (www0.cs.ucl.ac.uk/staff/W.Langdon/roc) has some good points under the heading "Choosing the Operating Point". picking the point closest to the top left corner | How to determine the optimal threshold for a classifier and generate ROC curve?
Following Will's comment.
This article (www0.cs.ucl.ac.uk/staff/W.Langdon/roc) has some good points under the heading "Choosing the Operating Point". picking the point closest to the top left corner of a ROC curve equates to choosing the o... | How to determine the optimal threshold for a classifier and generate ROC curve?
Following Will's comment.
This article (www0.cs.ucl.ac.uk/staff/W.Langdon/roc) has some good points under the heading "Choosing the Operating Point". picking the point closest to the top left corner |
4,873 | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than always use a Welch approximation of the df? | I would like to oppose the other two answers based on a paper (in German) by Kubinger, Rasch and Moder (2009).
They argue, based on "extensive" simulations from distributions either meeting or not meeting the assumptions imposed by a t-test, (normality and homogenity of variance) that the welch-tests performs equally w... | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than al | I would like to oppose the other two answers based on a paper (in German) by Kubinger, Rasch and Moder (2009).
They argue, based on "extensive" simulations from distributions either meeting or not mee | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than always use a Welch approximation of the df?
I would like to oppose the other two answers based on a paper (in German) by Kubinger, Rasch and Moder (2009).
They argue, based on "extensive" simulations from distributions eit... | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than al
I would like to oppose the other two answers based on a paper (in German) by Kubinger, Rasch and Moder (2009).
They argue, based on "extensive" simulations from distributions either meeting or not mee |
4,874 | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than always use a Welch approximation of the df? | Of course, one could ditch both tests, and start using a Bayesian t-test (Savage-Dickey ratio test), which can account for equal and unequal variances, and best of all, it allows for a quantification of evidence in favor of the null hypothesis (which means, no more of old "failure to reject" talk)
This test is very sim... | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than al | Of course, one could ditch both tests, and start using a Bayesian t-test (Savage-Dickey ratio test), which can account for equal and unequal variances, and best of all, it allows for a quantification | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than always use a Welch approximation of the df?
Of course, one could ditch both tests, and start using a Bayesian t-test (Savage-Dickey ratio test), which can account for equal and unequal variances, and best of all, it allows... | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than al
Of course, one could ditch both tests, and start using a Bayesian t-test (Savage-Dickey ratio test), which can account for equal and unequal variances, and best of all, it allows for a quantification |
4,875 | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than always use a Welch approximation of the df? | Because exact results are preferable to approximations, and avoid odd edge cases where the approximation may lead to a different result than the exact method.
The Welch method isn't a quicker way to do any old t-test, it's a tractable approximation to an otherwise very hard problem: how to construct a t-test under un... | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than al | Because exact results are preferable to approximations, and avoid odd edge cases where the approximation may lead to a different result than the exact method.
The Welch method isn't a quicker way to | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than always use a Welch approximation of the df?
Because exact results are preferable to approximations, and avoid odd edge cases where the approximation may lead to a different result than the exact method.
The Welch method ... | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than al
Because exact results are preferable to approximations, and avoid odd edge cases where the approximation may lead to a different result than the exact method.
The Welch method isn't a quicker way to |
4,876 | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than always use a Welch approximation of the df? | Two reasons I can think of:
Regular Student's T is pretty robust to heteroscedasticity if the sample sizes are equal.
If you believe strongly a priori that the data is homoscedastic, then you lose nothing and might gain a small amount of power by using Studen'ts T instead of Welch's T.
One reason that I would not g... | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than al | Two reasons I can think of:
Regular Student's T is pretty robust to heteroscedasticity if the sample sizes are equal.
If you believe strongly a priori that the data is homoscedastic, then you lose | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than always use a Welch approximation of the df?
Two reasons I can think of:
Regular Student's T is pretty robust to heteroscedasticity if the sample sizes are equal.
If you believe strongly a priori that the data is homosce... | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than al
Two reasons I can think of:
Regular Student's T is pretty robust to heteroscedasticity if the sample sizes are equal.
If you believe strongly a priori that the data is homoscedastic, then you lose |
4,877 | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than always use a Welch approximation of the df? | The fact that something more complex reduces to something less complex when some assumption is checked is not enough to throw the simpler method away. | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than al | The fact that something more complex reduces to something less complex when some assumption is checked is not enough to throw the simpler method away. | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than always use a Welch approximation of the df?
The fact that something more complex reduces to something less complex when some assumption is checked is not enough to throw the simpler method away. | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than al
The fact that something more complex reduces to something less complex when some assumption is checked is not enough to throw the simpler method away. |
4,878 | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than always use a Welch approximation of the df? | I would take the opposite view here. Why bother with the Welch test when the standard unpaired student t test gives you nearly identical results. I studied this issue a while back and I explored a range of scenarios in an attempt to break down the t test and favor the Welch test. To do so I used sample sizes up to 5... | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than al | I would take the opposite view here. Why bother with the Welch test when the standard unpaired student t test gives you nearly identical results. I studied this issue a while back and I explored a r | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than always use a Welch approximation of the df?
I would take the opposite view here. Why bother with the Welch test when the standard unpaired student t test gives you nearly identical results. I studied this issue a while b... | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than al
I would take the opposite view here. Why bother with the Welch test when the standard unpaired student t test gives you nearly identical results. I studied this issue a while back and I explored a r |
4,879 | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than always use a Welch approximation of the df? | With the assumption of equal variance, one can derive the non asymptotic distribution of t statistics. But when the assumption is violated, two variance terms cannot be cancelled, and we cannot simplify the distribution of statistics to a fixed one. Thus test can't be done.
Welch t test is an approximation which is rob... | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than al | With the assumption of equal variance, one can derive the non asymptotic distribution of t statistics. But when the assumption is violated, two variance terms cannot be cancelled, and we cannot simpli | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than always use a Welch approximation of the df?
With the assumption of equal variance, one can derive the non asymptotic distribution of t statistics. But when the assumption is violated, two variance terms cannot be cancelled... | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than al
With the assumption of equal variance, one can derive the non asymptotic distribution of t statistics. But when the assumption is violated, two variance terms cannot be cancelled, and we cannot simpli |
4,880 | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than always use a Welch approximation of the df? | It's true that the frequentist properties of the Welch corrected test are better than the ordinary Student's T, at least for errors. I agree that that alone is a pretty good argument for the Welch test. However, I'm usually reluctant to recommend the Welch correction because it's use is often deceptive. Which is, admit... | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than al | It's true that the frequentist properties of the Welch corrected test are better than the ordinary Student's T, at least for errors. I agree that that alone is a pretty good argument for the Welch tes | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than always use a Welch approximation of the df?
It's true that the frequentist properties of the Welch corrected test are better than the ordinary Student's T, at least for errors. I agree that that alone is a pretty good argu... | When conducting a t-test why would one prefer to assume (or test for) equal variances rather than al
It's true that the frequentist properties of the Welch corrected test are better than the ordinary Student's T, at least for errors. I agree that that alone is a pretty good argument for the Welch tes |
4,881 | Are all models useless? Is any exact model possible -- or useful? | The cited article seems to be based on fears that statisticians "will not be an intrinsic part of the scientific team, and the scientists will naturally have their doubts about the methods used" and that "collaborators will view us as technicians they can steer to get their scientific results published." My comments on... | Are all models useless? Is any exact model possible -- or useful? | The cited article seems to be based on fears that statisticians "will not be an intrinsic part of the scientific team, and the scientists will naturally have their doubts about the methods used" and t | Are all models useless? Is any exact model possible -- or useful?
The cited article seems to be based on fears that statisticians "will not be an intrinsic part of the scientific team, and the scientists will naturally have their doubts about the methods used" and that "collaborators will view us as technicians they ca... | Are all models useless? Is any exact model possible -- or useful?
The cited article seems to be based on fears that statisticians "will not be an intrinsic part of the scientific team, and the scientists will naturally have their doubts about the methods used" and t |
4,882 | Are all models useless? Is any exact model possible -- or useful? | Maybe I missed the point, but I think you have to step back a little bit.
I think his point is the abuse of easy-accessible tools with no further knowledge. This is also true for a simple t-test: just feed the algorithm with your data, getting a p<0.05 and thinking, that your thesis is true. Completely wrong. You, of c... | Are all models useless? Is any exact model possible -- or useful? | Maybe I missed the point, but I think you have to step back a little bit.
I think his point is the abuse of easy-accessible tools with no further knowledge. This is also true for a simple t-test: just | Are all models useless? Is any exact model possible -- or useful?
Maybe I missed the point, but I think you have to step back a little bit.
I think his point is the abuse of easy-accessible tools with no further knowledge. This is also true for a simple t-test: just feed the algorithm with your data, getting a p<0.05 a... | Are all models useless? Is any exact model possible -- or useful?
Maybe I missed the point, but I think you have to step back a little bit.
I think his point is the abuse of easy-accessible tools with no further knowledge. This is also true for a simple t-test: just |
4,883 | Are all models useless? Is any exact model possible -- or useful? | In econ, much is said of understanding the 'data generating process.' I'm not sure what exactly is meant by an 'exact' model, but in econ it might be the same as a 'correctly specified' model.
Certainly, you want to know as much about the process that generated the data as you can before attempting a model, right? I... | Are all models useless? Is any exact model possible -- or useful? | In econ, much is said of understanding the 'data generating process.' I'm not sure what exactly is meant by an 'exact' model, but in econ it might be the same as a 'correctly specified' model.
Certa | Are all models useless? Is any exact model possible -- or useful?
In econ, much is said of understanding the 'data generating process.' I'm not sure what exactly is meant by an 'exact' model, but in econ it might be the same as a 'correctly specified' model.
Certainly, you want to know as much about the process that ... | Are all models useless? Is any exact model possible -- or useful?
In econ, much is said of understanding the 'data generating process.' I'm not sure what exactly is meant by an 'exact' model, but in econ it might be the same as a 'correctly specified' model.
Certa |
4,884 | Are all models useless? Is any exact model possible -- or useful? | Said article appears to me to be a honest but political article, a sincere polemic. As such, it contains a lot of passionate passages that are scientific non-sense, but that nevertheless may be effective in stirring up useful conversations and deliberations on important matters.
There are many good answers here so le... | Are all models useless? Is any exact model possible -- or useful? | Said article appears to me to be a honest but political article, a sincere polemic. As such, it contains a lot of passionate passages that are scientific non-sense, but that nevertheless may be effect | Are all models useless? Is any exact model possible -- or useful?
Said article appears to me to be a honest but political article, a sincere polemic. As such, it contains a lot of passionate passages that are scientific non-sense, but that nevertheless may be effective in stirring up useful conversations and deliberati... | Are all models useless? Is any exact model possible -- or useful?
Said article appears to me to be a honest but political article, a sincere polemic. As such, it contains a lot of passionate passages that are scientific non-sense, but that nevertheless may be effect |
4,885 | Are all models useless? Is any exact model possible -- or useful? | This post was brought to my attention just a few days ago. Thank you for your interest.
Question 1: What useful statistical inferences can be made using a model that makes no assumptions at all?
Before I answer this question we should agree on a definition of the word model:
A common definition of a statistical model i... | Are all models useless? Is any exact model possible -- or useful? | This post was brought to my attention just a few days ago. Thank you for your interest.
Question 1: What useful statistical inferences can be made using a model that makes no assumptions at all?
Befor | Are all models useless? Is any exact model possible -- or useful?
This post was brought to my attention just a few days ago. Thank you for your interest.
Question 1: What useful statistical inferences can be made using a model that makes no assumptions at all?
Before I answer this question we should agree on a definiti... | Are all models useless? Is any exact model possible -- or useful?
This post was brought to my attention just a few days ago. Thank you for your interest.
Question 1: What useful statistical inferences can be made using a model that makes no assumptions at all?
Befor |
4,886 | Are all models useless? Is any exact model possible -- or useful? | To address point 3, the answer, obviously, is no. Just about every human enterprise is based on a simplified model at some point: cooking, building, interpersonal relationships all involve humans acting on some kind of data + assumptions. No one has ever constructed a model that they did not intend to make use of. To a... | Are all models useless? Is any exact model possible -- or useful? | To address point 3, the answer, obviously, is no. Just about every human enterprise is based on a simplified model at some point: cooking, building, interpersonal relationships all involve humans acti | Are all models useless? Is any exact model possible -- or useful?
To address point 3, the answer, obviously, is no. Just about every human enterprise is based on a simplified model at some point: cooking, building, interpersonal relationships all involve humans acting on some kind of data + assumptions. No one has ever... | Are all models useless? Is any exact model possible -- or useful?
To address point 3, the answer, obviously, is no. Just about every human enterprise is based on a simplified model at some point: cooking, building, interpersonal relationships all involve humans acti |
4,887 | Are all models useless? Is any exact model possible -- or useful? | 1) What useful statistical inferences can be made using a model that makes no assumptions at all?
A model is by definition a generalization of what you are observing that can be captured by certain causal factors that in turn can explain and estimate the event you are observing. Given that all those generalization alg... | Are all models useless? Is any exact model possible -- or useful? | 1) What useful statistical inferences can be made using a model that makes no assumptions at all?
A model is by definition a generalization of what you are observing that can be captured by certain ca | Are all models useless? Is any exact model possible -- or useful?
1) What useful statistical inferences can be made using a model that makes no assumptions at all?
A model is by definition a generalization of what you are observing that can be captured by certain causal factors that in turn can explain and estimate the... | Are all models useless? Is any exact model possible -- or useful?
1) What useful statistical inferences can be made using a model that makes no assumptions at all?
A model is by definition a generalization of what you are observing that can be captured by certain ca |
4,888 | Are all models useless? Is any exact model possible -- or useful? | (I don't see the phrase "exact model" in the article (though quoted above))
1) What useful statistical inferences can be made using a model that makes no assumptions at all?
You have to start somewhere.
If that's all you have (nothing), it can be a starting point.
2) Does there exist a case study, with important, real... | Are all models useless? Is any exact model possible -- or useful? | (I don't see the phrase "exact model" in the article (though quoted above))
1) What useful statistical inferences can be made using a model that makes no assumptions at all?
You have to start somewher | Are all models useless? Is any exact model possible -- or useful?
(I don't see the phrase "exact model" in the article (though quoted above))
1) What useful statistical inferences can be made using a model that makes no assumptions at all?
You have to start somewhere.
If that's all you have (nothing), it can be a start... | Are all models useless? Is any exact model possible -- or useful?
(I don't see the phrase "exact model" in the article (though quoted above))
1) What useful statistical inferences can be made using a model that makes no assumptions at all?
You have to start somewher |
4,889 | Are all models useless? Is any exact model possible -- or useful? | I'm going to approach this from the alternate direction of philosophy, in light of the really useful principles of Uncertainty Management discussed in George F. Klir's books on fuzzy sets. I can't give van der Laan exactness, but I can provide a somewhat exhaustive case for why his goal is logically impossible; that is... | Are all models useless? Is any exact model possible -- or useful? | I'm going to approach this from the alternate direction of philosophy, in light of the really useful principles of Uncertainty Management discussed in George F. Klir's books on fuzzy sets. I can't giv | Are all models useless? Is any exact model possible -- or useful?
I'm going to approach this from the alternate direction of philosophy, in light of the really useful principles of Uncertainty Management discussed in George F. Klir's books on fuzzy sets. I can't give van der Laan exactness, but I can provide a somewhat... | Are all models useless? Is any exact model possible -- or useful?
I'm going to approach this from the alternate direction of philosophy, in light of the really useful principles of Uncertainty Management discussed in George F. Klir's books on fuzzy sets. I can't giv |
4,890 | Why is a Bayesian not allowed to look at the residuals? | Of course Bayesians can look at the residuals! And of course there are bad models in Bayesian analysis. Maybe a few Bayesians in the 70's supported views like that (and I doubt that), but you will hardly find any Bayesian supporting this view these days.
I didn't read the text, but Bayesians use things like Bayes facto... | Why is a Bayesian not allowed to look at the residuals? | Of course Bayesians can look at the residuals! And of course there are bad models in Bayesian analysis. Maybe a few Bayesians in the 70's supported views like that (and I doubt that), but you will har | Why is a Bayesian not allowed to look at the residuals?
Of course Bayesians can look at the residuals! And of course there are bad models in Bayesian analysis. Maybe a few Bayesians in the 70's supported views like that (and I doubt that), but you will hardly find any Bayesian supporting this view these days.
I didn't ... | Why is a Bayesian not allowed to look at the residuals?
Of course Bayesians can look at the residuals! And of course there are bad models in Bayesian analysis. Maybe a few Bayesians in the 70's supported views like that (and I doubt that), but you will har |
4,891 | Why is a Bayesian not allowed to look at the residuals? | They can look but not touch. After all, the residuals are the part of the data that don't carry any information about model parameters, and their prior expresses all uncertainty about those—they can't change their prior based on what they see in the data.
For example, suppose you're fitting a Gaussian model, but notice... | Why is a Bayesian not allowed to look at the residuals? | They can look but not touch. After all, the residuals are the part of the data that don't carry any information about model parameters, and their prior expresses all uncertainty about those—they can't | Why is a Bayesian not allowed to look at the residuals?
They can look but not touch. After all, the residuals are the part of the data that don't carry any information about model parameters, and their prior expresses all uncertainty about those—they can't change their prior based on what they see in the data.
For exam... | Why is a Bayesian not allowed to look at the residuals?
They can look but not touch. After all, the residuals are the part of the data that don't carry any information about model parameters, and their prior expresses all uncertainty about those—they can't |
4,892 | How to do logistic regression subset selection? | Stepwise and "all subsets" methods are generally bad. See Stopping Stepwise: Why Stepwise Methods are Bad and what you Should Use by David Cassell and myself (we used SAS, but the lesson applies) or Frank Harrell Regression Modeling Strategies. If you need an automatic method, I recommend LASSO or LAR. A LASSO packa... | How to do logistic regression subset selection? | Stepwise and "all subsets" methods are generally bad. See Stopping Stepwise: Why Stepwise Methods are Bad and what you Should Use by David Cassell and myself (we used SAS, but the lesson applies) or | How to do logistic regression subset selection?
Stepwise and "all subsets" methods are generally bad. See Stopping Stepwise: Why Stepwise Methods are Bad and what you Should Use by David Cassell and myself (we used SAS, but the lesson applies) or Frank Harrell Regression Modeling Strategies. If you need an automatic ... | How to do logistic regression subset selection?
Stepwise and "all subsets" methods are generally bad. See Stopping Stepwise: Why Stepwise Methods are Bad and what you Should Use by David Cassell and myself (we used SAS, but the lesson applies) or |
4,893 | How to do logistic regression subset selection? | First of all $R^2$ is not an appropriate goodness-of-fit measure for logistic regression, take an information criterion $AIC$ or $BIC$, for example, as a good alternative.
Logistic regression is estimated by maximum likelihood method, so leaps is not used directly here. An extension of leaps to glm() functions is the b... | How to do logistic regression subset selection? | First of all $R^2$ is not an appropriate goodness-of-fit measure for logistic regression, take an information criterion $AIC$ or $BIC$, for example, as a good alternative.
Logistic regression is estim | How to do logistic regression subset selection?
First of all $R^2$ is not an appropriate goodness-of-fit measure for logistic regression, take an information criterion $AIC$ or $BIC$, for example, as a good alternative.
Logistic regression is estimated by maximum likelihood method, so leaps is not used directly here. A... | How to do logistic regression subset selection?
First of all $R^2$ is not an appropriate goodness-of-fit measure for logistic regression, take an information criterion $AIC$ or $BIC$, for example, as a good alternative.
Logistic regression is estim |
4,894 | How to do logistic regression subset selection? | One idea would be to use a random forest and then use the variable importance measures it outputs to choose your best 8 variables. Another idea would be to use the "boruta" package to repeat this process a few hundred times to find the 8 variables that are consistently most important to the model. | How to do logistic regression subset selection? | One idea would be to use a random forest and then use the variable importance measures it outputs to choose your best 8 variables. Another idea would be to use the "boruta" package to repeat this pro | How to do logistic regression subset selection?
One idea would be to use a random forest and then use the variable importance measures it outputs to choose your best 8 variables. Another idea would be to use the "boruta" package to repeat this process a few hundred times to find the 8 variables that are consistently m... | How to do logistic regression subset selection?
One idea would be to use a random forest and then use the variable importance measures it outputs to choose your best 8 variables. Another idea would be to use the "boruta" package to repeat this pro |
4,895 | How to do logistic regression subset selection? | stats::step function or the more general MASS::stepAIC function supports lm, glm (including logistic regression) and aov family models. | How to do logistic regression subset selection? | stats::step function or the more general MASS::stepAIC function supports lm, glm (including logistic regression) and aov family models. | How to do logistic regression subset selection?
stats::step function or the more general MASS::stepAIC function supports lm, glm (including logistic regression) and aov family models. | How to do logistic regression subset selection?
stats::step function or the more general MASS::stepAIC function supports lm, glm (including logistic regression) and aov family models. |
4,896 | Why is softmax output not a good uncertainty measure for Deep Learning models? | This question can be answered more precisely than the current answers. Fixing the deviation between the predicted probabilities (the output of the softmax layer of a neural network) and their true probabilities (which represent a notion of confidence), is known as calibration or reliability curves.
The issue with many ... | Why is softmax output not a good uncertainty measure for Deep Learning models? | This question can be answered more precisely than the current answers. Fixing the deviation between the predicted probabilities (the output of the softmax layer of a neural network) and their true pro | Why is softmax output not a good uncertainty measure for Deep Learning models?
This question can be answered more precisely than the current answers. Fixing the deviation between the predicted probabilities (the output of the softmax layer of a neural network) and their true probabilities (which represent a notion of c... | Why is softmax output not a good uncertainty measure for Deep Learning models?
This question can be answered more precisely than the current answers. Fixing the deviation between the predicted probabilities (the output of the softmax layer of a neural network) and their true pro |
4,897 | Why is softmax output not a good uncertainty measure for Deep Learning models? | The relationship between softmax confidence and uncertainty is more
complicated than a lot of work makes it sound.
Firstly, there are two separate issues that often get conflated.
Callibration - Does 90% softmax confidence mean it is correct 90% of the time? This is evaluated over the training distribution. We are int... | Why is softmax output not a good uncertainty measure for Deep Learning models? | The relationship between softmax confidence and uncertainty is more
complicated than a lot of work makes it sound.
Firstly, there are two separate issues that often get conflated.
Callibration - Does | Why is softmax output not a good uncertainty measure for Deep Learning models?
The relationship between softmax confidence and uncertainty is more
complicated than a lot of work makes it sound.
Firstly, there are two separate issues that often get conflated.
Callibration - Does 90% softmax confidence mean it is correc... | Why is softmax output not a good uncertainty measure for Deep Learning models?
The relationship between softmax confidence and uncertainty is more
complicated than a lot of work makes it sound.
Firstly, there are two separate issues that often get conflated.
Callibration - Does |
4,898 | Why is softmax output not a good uncertainty measure for Deep Learning models? | Softmax distributes the 'probability' 0-1 between the available classes.
It does not express incertitude, it is not a PDF function.
If you want to express the incertitude you should be looking into
bayesian neural networks.
Have a look at this paper: Uncertainty in Deep Learning
Some rather recent probability framewo... | Why is softmax output not a good uncertainty measure for Deep Learning models? | Softmax distributes the 'probability' 0-1 between the available classes.
It does not express incertitude, it is not a PDF function.
If you want to express the incertitude you should be looking into
b | Why is softmax output not a good uncertainty measure for Deep Learning models?
Softmax distributes the 'probability' 0-1 between the available classes.
It does not express incertitude, it is not a PDF function.
If you want to express the incertitude you should be looking into
bayesian neural networks.
Have a look at ... | Why is softmax output not a good uncertainty measure for Deep Learning models?
Softmax distributes the 'probability' 0-1 between the available classes.
It does not express incertitude, it is not a PDF function.
If you want to express the incertitude you should be looking into
b |
4,899 | Why is softmax output not a good uncertainty measure for Deep Learning models? | In the paper Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning, Yarin Gal and Zoubin Ghahramani argue the following
In classification, predictive probabilities obtained at the end of the pipeline
(the softmax output) are often erroneously interpreted as model confidence. A model ca... | Why is softmax output not a good uncertainty measure for Deep Learning models? | In the paper Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning, Yarin Gal and Zoubin Ghahramani argue the following
In classification, predictive probabilities obta | Why is softmax output not a good uncertainty measure for Deep Learning models?
In the paper Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning, Yarin Gal and Zoubin Ghahramani argue the following
In classification, predictive probabilities obtained at the end of the pipeline
(the so... | Why is softmax output not a good uncertainty measure for Deep Learning models?
In the paper Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning, Yarin Gal and Zoubin Ghahramani argue the following
In classification, predictive probabilities obta |
4,900 | Why is softmax output not a good uncertainty measure for Deep Learning models? | What is called softmax in ML has the same equation as multinomial logistic equation. The latter can be used to calculate the probabilities. In practice it is widely used in estimation of default probabilities in competing risks framework for mortgages, e.g. see Eq. 4 in this paper.
Hence, I would say that your intuitio... | Why is softmax output not a good uncertainty measure for Deep Learning models? | What is called softmax in ML has the same equation as multinomial logistic equation. The latter can be used to calculate the probabilities. In practice it is widely used in estimation of default proba | Why is softmax output not a good uncertainty measure for Deep Learning models?
What is called softmax in ML has the same equation as multinomial logistic equation. The latter can be used to calculate the probabilities. In practice it is widely used in estimation of default probabilities in competing risks framework for... | Why is softmax output not a good uncertainty measure for Deep Learning models?
What is called softmax in ML has the same equation as multinomial logistic equation. The latter can be used to calculate the probabilities. In practice it is widely used in estimation of default proba |
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