idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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6,901 | What are the dangers of violating the homoscedasticity assumption for linear regression? | It is good to remember that having unbiased estimators does not mean that the model is "right". In many situations, the least squares criterion for regression coefficient estimation gives rise to a model that either has (1) regression coefficients that don't have the right meaning or (2) predictions that are tilted to... | What are the dangers of violating the homoscedasticity assumption for linear regression? | It is good to remember that having unbiased estimators does not mean that the model is "right". In many situations, the least squares criterion for regression coefficient estimation gives rise to a m | What are the dangers of violating the homoscedasticity assumption for linear regression?
It is good to remember that having unbiased estimators does not mean that the model is "right". In many situations, the least squares criterion for regression coefficient estimation gives rise to a model that either has (1) regres... | What are the dangers of violating the homoscedasticity assumption for linear regression?
It is good to remember that having unbiased estimators does not mean that the model is "right". In many situations, the least squares criterion for regression coefficient estimation gives rise to a m |
6,902 | What are the dangers of violating the homoscedasticity assumption for linear regression? | There is good information here in the other answers, particularly to your first question. I thought I would add some complimentary information regarding your last two questions.
The problems associated with heteroscedasticity are not limited to extrapolation. Since they primarily involve confidence intervals, p-val... | What are the dangers of violating the homoscedasticity assumption for linear regression? | There is good information here in the other answers, particularly to your first question. I thought I would add some complimentary information regarding your last two questions.
The problems associ | What are the dangers of violating the homoscedasticity assumption for linear regression?
There is good information here in the other answers, particularly to your first question. I thought I would add some complimentary information regarding your last two questions.
The problems associated with heteroscedasticity ar... | What are the dangers of violating the homoscedasticity assumption for linear regression?
There is good information here in the other answers, particularly to your first question. I thought I would add some complimentary information regarding your last two questions.
The problems associ |
6,903 | What's considered a good log loss? | The logloss is simply $L(p_i)=-\log(p_i)$ where $p$ is simply the probability attributed to the real class.
So $L(p)=0$ is good, we attributed the probability $1$ to the right class, while $L(p)=+\infty$ is bad, because we attributed the probability $0$ to the actual class.
So, answering your question, $L(p)=0.5$ means... | What's considered a good log loss? | The logloss is simply $L(p_i)=-\log(p_i)$ where $p$ is simply the probability attributed to the real class.
So $L(p)=0$ is good, we attributed the probability $1$ to the right class, while $L(p)=+\inf | What's considered a good log loss?
The logloss is simply $L(p_i)=-\log(p_i)$ where $p$ is simply the probability attributed to the real class.
So $L(p)=0$ is good, we attributed the probability $1$ to the right class, while $L(p)=+\infty$ is bad, because we attributed the probability $0$ to the actual class.
So, answer... | What's considered a good log loss?
The logloss is simply $L(p_i)=-\log(p_i)$ where $p$ is simply the probability attributed to the real class.
So $L(p)=0$ is good, we attributed the probability $1$ to the right class, while $L(p)=+\inf |
6,904 | What's considered a good log loss? | Like any metric, a good metric is the one better that the "dumb", by-chance guess, if you would have to guess with no information on the observations. This is called the intercept-only model in statistics.
This "dumb"-guess depends on 2 factors :
the number of classes
the balance of classes : their prevalence in the o... | What's considered a good log loss? | Like any metric, a good metric is the one better that the "dumb", by-chance guess, if you would have to guess with no information on the observations. This is called the intercept-only model in statis | What's considered a good log loss?
Like any metric, a good metric is the one better that the "dumb", by-chance guess, if you would have to guess with no information on the observations. This is called the intercept-only model in statistics.
This "dumb"-guess depends on 2 factors :
the number of classes
the balance of ... | What's considered a good log loss?
Like any metric, a good metric is the one better that the "dumb", by-chance guess, if you would have to guess with no information on the observations. This is called the intercept-only model in statis |
6,905 | What's considered a good log loss? | So this is actually more complicated than Firebugs response and it all depends on the inherent variation of the process you are trying to predict.
When I say variation what I mean is 'if an event was to repeat under the exact same conditions, known and unknown, what's the probability that the same outcome will occur a... | What's considered a good log loss? | So this is actually more complicated than Firebugs response and it all depends on the inherent variation of the process you are trying to predict.
When I say variation what I mean is 'if an event was | What's considered a good log loss?
So this is actually more complicated than Firebugs response and it all depends on the inherent variation of the process you are trying to predict.
When I say variation what I mean is 'if an event was to repeat under the exact same conditions, known and unknown, what's the probability... | What's considered a good log loss?
So this is actually more complicated than Firebugs response and it all depends on the inherent variation of the process you are trying to predict.
When I say variation what I mean is 'if an event was |
6,906 | What's considered a good log loss? | I'd say the standard statistics answer is to compare to the intercept only model. (this handles the unbalanced classes mentioned in other answers)
cf mcFadden's pseudo r^2.
https://stats.idre.ucla.edu/other/mult-pkg/faq/general/faq-what-are-pseudo-r-squareds/
Now the problem is what the maximum value is. fundamentally... | What's considered a good log loss? | I'd say the standard statistics answer is to compare to the intercept only model. (this handles the unbalanced classes mentioned in other answers)
cf mcFadden's pseudo r^2.
https://stats.idre.ucla.edu | What's considered a good log loss?
I'd say the standard statistics answer is to compare to the intercept only model. (this handles the unbalanced classes mentioned in other answers)
cf mcFadden's pseudo r^2.
https://stats.idre.ucla.edu/other/mult-pkg/faq/general/faq-what-are-pseudo-r-squareds/
Now the problem is what t... | What's considered a good log loss?
I'd say the standard statistics answer is to compare to the intercept only model. (this handles the unbalanced classes mentioned in other answers)
cf mcFadden's pseudo r^2.
https://stats.idre.ucla.edu |
6,907 | What's considered a good log loss? | As others have pointed out, the - log of the loss = (probability of correct classification). So, for example, losses of -log(.9), -log(.8), -log(.7), -log(.6), and -log(.5), or .11, .22, .36, .51, and .69 corresponding to probabilities of correct classification of 90%, 80%, 70%, 60%, 50%. Thinking evaluatively, a rando... | What's considered a good log loss? | As others have pointed out, the - log of the loss = (probability of correct classification). So, for example, losses of -log(.9), -log(.8), -log(.7), -log(.6), and -log(.5), or .11, .22, .36, .51, and | What's considered a good log loss?
As others have pointed out, the - log of the loss = (probability of correct classification). So, for example, losses of -log(.9), -log(.8), -log(.7), -log(.6), and -log(.5), or .11, .22, .36, .51, and .69 corresponding to probabilities of correct classification of 90%, 80%, 70%, 60%, ... | What's considered a good log loss?
As others have pointed out, the - log of the loss = (probability of correct classification). So, for example, losses of -log(.9), -log(.8), -log(.7), -log(.6), and -log(.5), or .11, .22, .36, .51, and |
6,908 | Is Tikhonov regularization the same as Ridge Regression? | Tikhonov regularizarization is a larger set than ridge regression. Here is my attempt to spell out exactly how they differ.
Suppose that for a known matrix $A$ and vector $b$, we wish to find a vector $\mathbf{x}$ such that
:
$A\mathbf{x}=\mathbf{b}$.
The standard approach is ordinary least squares linear regression... | Is Tikhonov regularization the same as Ridge Regression? | Tikhonov regularizarization is a larger set than ridge regression. Here is my attempt to spell out exactly how they differ.
Suppose that for a known matrix $A$ and vector $b$, we wish to find a vecto | Is Tikhonov regularization the same as Ridge Regression?
Tikhonov regularizarization is a larger set than ridge regression. Here is my attempt to spell out exactly how they differ.
Suppose that for a known matrix $A$ and vector $b$, we wish to find a vector $\mathbf{x}$ such that
:
$A\mathbf{x}=\mathbf{b}$.
The stan... | Is Tikhonov regularization the same as Ridge Regression?
Tikhonov regularizarization is a larger set than ridge regression. Here is my attempt to spell out exactly how they differ.
Suppose that for a known matrix $A$ and vector $b$, we wish to find a vecto |
6,909 | Is Tikhonov regularization the same as Ridge Regression? | Carl has given a thorough answer that nicely explains the mathematical differences between Tikhonov regularization vs. ridge regression. Inspired by the historical discussion here, I thought it might be useful to add a short example demonstrating how the more general Tikhonov framework can be useful.
First a brief note... | Is Tikhonov regularization the same as Ridge Regression? | Carl has given a thorough answer that nicely explains the mathematical differences between Tikhonov regularization vs. ridge regression. Inspired by the historical discussion here, I thought it might | Is Tikhonov regularization the same as Ridge Regression?
Carl has given a thorough answer that nicely explains the mathematical differences between Tikhonov regularization vs. ridge regression. Inspired by the historical discussion here, I thought it might be useful to add a short example demonstrating how the more gen... | Is Tikhonov regularization the same as Ridge Regression?
Carl has given a thorough answer that nicely explains the mathematical differences between Tikhonov regularization vs. ridge regression. Inspired by the historical discussion here, I thought it might |
6,910 | What is the difference between "mean value" and "average"? | Mean versus average
The mean most commonly refers to the arithmetic mean, but may refer to some other form of mean, such as harmonic or geometric (see the Wikipedia article). Thus, when used without qualification, I think most people would assume that "mean" refers to the arithmetic mean.
Average has many meanings, so... | What is the difference between "mean value" and "average"? | Mean versus average
The mean most commonly refers to the arithmetic mean, but may refer to some other form of mean, such as harmonic or geometric (see the Wikipedia article). Thus, when used without | What is the difference between "mean value" and "average"?
Mean versus average
The mean most commonly refers to the arithmetic mean, but may refer to some other form of mean, such as harmonic or geometric (see the Wikipedia article). Thus, when used without qualification, I think most people would assume that "mean" r... | What is the difference between "mean value" and "average"?
Mean versus average
The mean most commonly refers to the arithmetic mean, but may refer to some other form of mean, such as harmonic or geometric (see the Wikipedia article). Thus, when used without |
6,911 | What is the difference between "mean value" and "average"? | There are several "averages." Just think of this trick question: "What is the probability that the next person you meet has more than the average number of arms?"
The "mean" or "arithmetic mean" or "arithmetic average" is one average that you learned in the past. But the median (the value with half the observations g... | What is the difference between "mean value" and "average"? | There are several "averages." Just think of this trick question: "What is the probability that the next person you meet has more than the average number of arms?"
The "mean" or "arithmetic mean" or " | What is the difference between "mean value" and "average"?
There are several "averages." Just think of this trick question: "What is the probability that the next person you meet has more than the average number of arms?"
The "mean" or "arithmetic mean" or "arithmetic average" is one average that you learned in the pa... | What is the difference between "mean value" and "average"?
There are several "averages." Just think of this trick question: "What is the probability that the next person you meet has more than the average number of arms?"
The "mean" or "arithmetic mean" or " |
6,912 | What is the difference between "mean value" and "average"? | Mean and average are generally used interchangeably (although I've seen them used as referring to population versus empirical).
They, like median and mode, are measures of central tendency, but in many cases, the other two are different. | What is the difference between "mean value" and "average"? | Mean and average are generally used interchangeably (although I've seen them used as referring to population versus empirical).
They, like median and mode, are measures of central tendency, but in man | What is the difference between "mean value" and "average"?
Mean and average are generally used interchangeably (although I've seen them used as referring to population versus empirical).
They, like median and mode, are measures of central tendency, but in many cases, the other two are different. | What is the difference between "mean value" and "average"?
Mean and average are generally used interchangeably (although I've seen them used as referring to population versus empirical).
They, like median and mode, are measures of central tendency, but in man |
6,913 | What is the difference between "mean value" and "average"? | The mean you described (the arithmetic mean) is what people typically intend when they say "mean" and, yes, that is the same as average. The only ambiguity that can occur is when someone is using a different type of mean, such as the geometric mean or the harmonic mean, but I think it is implicit from your question tha... | What is the difference between "mean value" and "average"? | The mean you described (the arithmetic mean) is what people typically intend when they say "mean" and, yes, that is the same as average. The only ambiguity that can occur is when someone is using a di | What is the difference between "mean value" and "average"?
The mean you described (the arithmetic mean) is what people typically intend when they say "mean" and, yes, that is the same as average. The only ambiguity that can occur is when someone is using a different type of mean, such as the geometric mean or the harmo... | What is the difference between "mean value" and "average"?
The mean you described (the arithmetic mean) is what people typically intend when they say "mean" and, yes, that is the same as average. The only ambiguity that can occur is when someone is using a di |
6,914 | What is the difference between "mean value" and "average"? | I see "average" and "mean" used mostly as synonyms. One author who draws a clear distinction is Donald Wheeler, in "Advanced Topics in Statistical Quality Control." He declares that the "average" is a statistic determined by some arithmetic procedure, whereas "mean" is a parameter, specifying location of a distribution... | What is the difference between "mean value" and "average"? | I see "average" and "mean" used mostly as synonyms. One author who draws a clear distinction is Donald Wheeler, in "Advanced Topics in Statistical Quality Control." He declares that the "average" is a | What is the difference between "mean value" and "average"?
I see "average" and "mean" used mostly as synonyms. One author who draws a clear distinction is Donald Wheeler, in "Advanced Topics in Statistical Quality Control." He declares that the "average" is a statistic determined by some arithmetic procedure, whereas "... | What is the difference between "mean value" and "average"?
I see "average" and "mean" used mostly as synonyms. One author who draws a clear distinction is Donald Wheeler, in "Advanced Topics in Statistical Quality Control." He declares that the "average" is a |
6,915 | Data has two trends; how to extract independent trendlines? | To solve your problem, a good approach is to define a probabilistic model that matches the assumptions about your dataset. In your case, you probably want a mixture of linear regression models. You can create a "mixture of regressors" model similar to a gaussian mixture model by associating different data points with d... | Data has two trends; how to extract independent trendlines? | To solve your problem, a good approach is to define a probabilistic model that matches the assumptions about your dataset. In your case, you probably want a mixture of linear regression models. You ca | Data has two trends; how to extract independent trendlines?
To solve your problem, a good approach is to define a probabilistic model that matches the assumptions about your dataset. In your case, you probably want a mixture of linear regression models. You can create a "mixture of regressors" model similar to a gaussi... | Data has two trends; how to extract independent trendlines?
To solve your problem, a good approach is to define a probabilistic model that matches the assumptions about your dataset. In your case, you probably want a mixture of linear regression models. You ca |
6,916 | Data has two trends; how to extract independent trendlines? | Elsewhere in this thread, user1149913 provides great advice (define a probabilistic model) and code for a powerful approach (EM estimation). Two issues remain to be addressed:
How to cope with departures from the probabilistic model (which are very evident in the 2011-2012 data and somewhat evident in the undulations... | Data has two trends; how to extract independent trendlines? | Elsewhere in this thread, user1149913 provides great advice (define a probabilistic model) and code for a powerful approach (EM estimation). Two issues remain to be addressed:
How to cope with depar | Data has two trends; how to extract independent trendlines?
Elsewhere in this thread, user1149913 provides great advice (define a probabilistic model) and code for a powerful approach (EM estimation). Two issues remain to be addressed:
How to cope with departures from the probabilistic model (which are very evident i... | Data has two trends; how to extract independent trendlines?
Elsewhere in this thread, user1149913 provides great advice (define a probabilistic model) and code for a powerful approach (EM estimation). Two issues remain to be addressed:
How to cope with depar |
6,917 | Data has two trends; how to extract independent trendlines? | I found this question linked on another question. I actually did academic research on this kind of problem. Please check my answer "Least square root" fitting? A fitting method with multiple minima for more details.
whuber's Hough transform based approach is a very good solution for simple scenarios as the one you gave... | Data has two trends; how to extract independent trendlines? | I found this question linked on another question. I actually did academic research on this kind of problem. Please check my answer "Least square root" fitting? A fitting method with multiple minima fo | Data has two trends; how to extract independent trendlines?
I found this question linked on another question. I actually did academic research on this kind of problem. Please check my answer "Least square root" fitting? A fitting method with multiple minima for more details.
whuber's Hough transform based approach is a... | Data has two trends; how to extract independent trendlines?
I found this question linked on another question. I actually did academic research on this kind of problem. Please check my answer "Least square root" fitting? A fitting method with multiple minima fo |
6,918 | Data has two trends; how to extract independent trendlines? | user1149913 has an excellent answer (+1), but it looks to me that your data collection fell apart in late 2011, so you'd have to cut that part of your data off, and then still run things a few times with different random starting coefficients to see what you get.
One straightforward way to do things would be to separat... | Data has two trends; how to extract independent trendlines? | user1149913 has an excellent answer (+1), but it looks to me that your data collection fell apart in late 2011, so you'd have to cut that part of your data off, and then still run things a few times w | Data has two trends; how to extract independent trendlines?
user1149913 has an excellent answer (+1), but it looks to me that your data collection fell apart in late 2011, so you'd have to cut that part of your data off, and then still run things a few times with different random starting coefficients to see what you g... | Data has two trends; how to extract independent trendlines?
user1149913 has an excellent answer (+1), but it looks to me that your data collection fell apart in late 2011, so you'd have to cut that part of your data off, and then still run things a few times w |
6,919 | What is the difference between the vertical bar and semi-colon notations? | I believe the origin of this is the likelihood paradigm (though I have not checked the actual historical correctness of the below, it is a reasonable way of understanding how it came to be).
Let's say in a regression setting, you would have a distribution:
$$
p(Y | x, \beta)
$$
Which means: the distribution of $Y$ if y... | What is the difference between the vertical bar and semi-colon notations? | I believe the origin of this is the likelihood paradigm (though I have not checked the actual historical correctness of the below, it is a reasonable way of understanding how it came to be).
Let's say | What is the difference between the vertical bar and semi-colon notations?
I believe the origin of this is the likelihood paradigm (though I have not checked the actual historical correctness of the below, it is a reasonable way of understanding how it came to be).
Let's say in a regression setting, you would have a dis... | What is the difference between the vertical bar and semi-colon notations?
I believe the origin of this is the likelihood paradigm (though I have not checked the actual historical correctness of the below, it is a reasonable way of understanding how it came to be).
Let's say |
6,920 | What is the difference between the vertical bar and semi-colon notations? | $f(x;\theta)$ is the density of the random variable $X$ at the point $x$, with $\theta$ being the parameter of the distribution. $f(x,\theta)$ is the joint density of $X$ and $\Theta$ at the point $(x,\theta)$ and only makes sense if $\Theta$ is a random variable. $f(x|\theta)$ is the conditional distribution of $X$ gi... | What is the difference between the vertical bar and semi-colon notations? | $f(x;\theta)$ is the density of the random variable $X$ at the point $x$, with $\theta$ being the parameter of the distribution. $f(x,\theta)$ is the joint density of $X$ and $\Theta$ at the point $(x | What is the difference between the vertical bar and semi-colon notations?
$f(x;\theta)$ is the density of the random variable $X$ at the point $x$, with $\theta$ being the parameter of the distribution. $f(x,\theta)$ is the joint density of $X$ and $\Theta$ at the point $(x,\theta)$ and only makes sense if $\Theta$ is ... | What is the difference between the vertical bar and semi-colon notations?
$f(x;\theta)$ is the density of the random variable $X$ at the point $x$, with $\theta$ being the parameter of the distribution. $f(x,\theta)$ is the joint density of $X$ and $\Theta$ at the point $(x |
6,921 | What is the difference between the vertical bar and semi-colon notations? | $f(x;\theta)$ is the same as $f(x|\theta)$, simply meaning that $\theta$ is a fixed parameter and the function $f$ is a function of $x$. $f(x,\Theta)$, OTOH, is an element of a family (or set) of functions, where the elements are indexed by $\Theta$. A subtle distinction, perhaps, but an important one, esp. when it com... | What is the difference between the vertical bar and semi-colon notations? | $f(x;\theta)$ is the same as $f(x|\theta)$, simply meaning that $\theta$ is a fixed parameter and the function $f$ is a function of $x$. $f(x,\Theta)$, OTOH, is an element of a family (or set) of func | What is the difference between the vertical bar and semi-colon notations?
$f(x;\theta)$ is the same as $f(x|\theta)$, simply meaning that $\theta$ is a fixed parameter and the function $f$ is a function of $x$. $f(x,\Theta)$, OTOH, is an element of a family (or set) of functions, where the elements are indexed by $\The... | What is the difference between the vertical bar and semi-colon notations?
$f(x;\theta)$ is the same as $f(x|\theta)$, simply meaning that $\theta$ is a fixed parameter and the function $f$ is a function of $x$. $f(x,\Theta)$, OTOH, is an element of a family (or set) of func |
6,922 | What is the difference between the vertical bar and semi-colon notations? | Although it hasn't always been this way, these days $P(z; d, w)$ is generally used when $d,w$ are not random variables (which isn't to say that they're known, necessarily). $P(z | d, w)$ indicates conditioning on values of $d,w$. Conditioning is an operation on random variables and as such using this notation when $d, ... | What is the difference between the vertical bar and semi-colon notations? | Although it hasn't always been this way, these days $P(z; d, w)$ is generally used when $d,w$ are not random variables (which isn't to say that they're known, necessarily). $P(z | d, w)$ indicates con | What is the difference between the vertical bar and semi-colon notations?
Although it hasn't always been this way, these days $P(z; d, w)$ is generally used when $d,w$ are not random variables (which isn't to say that they're known, necessarily). $P(z | d, w)$ indicates conditioning on values of $d,w$. Conditioning is ... | What is the difference between the vertical bar and semi-colon notations?
Although it hasn't always been this way, these days $P(z; d, w)$ is generally used when $d,w$ are not random variables (which isn't to say that they're known, necessarily). $P(z | d, w)$ indicates con |
6,923 | Can cross validation be used for causal inference? | I think it's useful to review what we know about cross-validation. Statistical results around CV fall into two classes: efficiency and consistency.
Efficiency is what we're usually concerned with when building predictive models. The idea is that we use CV to determine a model with asymtptotic guarantees concerning ... | Can cross validation be used for causal inference? | I think it's useful to review what we know about cross-validation. Statistical results around CV fall into two classes: efficiency and consistency.
Efficiency is what we're usually concerned with w | Can cross validation be used for causal inference?
I think it's useful to review what we know about cross-validation. Statistical results around CV fall into two classes: efficiency and consistency.
Efficiency is what we're usually concerned with when building predictive models. The idea is that we use CV to determ... | Can cross validation be used for causal inference?
I think it's useful to review what we know about cross-validation. Statistical results around CV fall into two classes: efficiency and consistency.
Efficiency is what we're usually concerned with w |
6,924 | Can cross validation be used for causal inference? | This is a really interesting question and I don't offer any specific citations. However, in general, I'd say, NO, in and of itself, cross-validation does not offer any insight into causality. In absence of a designed experiment, the issue of causality is always uncertain. As you suggest, cross-validation can and wil... | Can cross validation be used for causal inference? | This is a really interesting question and I don't offer any specific citations. However, in general, I'd say, NO, in and of itself, cross-validation does not offer any insight into causality. In abs | Can cross validation be used for causal inference?
This is a really interesting question and I don't offer any specific citations. However, in general, I'd say, NO, in and of itself, cross-validation does not offer any insight into causality. In absence of a designed experiment, the issue of causality is always uncer... | Can cross validation be used for causal inference?
This is a really interesting question and I don't offer any specific citations. However, in general, I'd say, NO, in and of itself, cross-validation does not offer any insight into causality. In abs |
6,925 | Can cross validation be used for causal inference? | It seems to me that your question more generally addresses different flavour of validation for a predictive model: Cross-validation has somewhat more to do with internal validity, or at least the initial modelling stage, whereas drawing causal links on a wider population is more related to external validity. By that (a... | Can cross validation be used for causal inference? | It seems to me that your question more generally addresses different flavour of validation for a predictive model: Cross-validation has somewhat more to do with internal validity, or at least the init | Can cross validation be used for causal inference?
It seems to me that your question more generally addresses different flavour of validation for a predictive model: Cross-validation has somewhat more to do with internal validity, or at least the initial modelling stage, whereas drawing causal links on a wider populati... | Can cross validation be used for causal inference?
It seems to me that your question more generally addresses different flavour of validation for a predictive model: Cross-validation has somewhat more to do with internal validity, or at least the init |
6,926 | Can cross validation be used for causal inference? | This is a good question, but the answer is definitely no: cross-validation will not improve causal inference. If you have a mapping between symptoms and diseases, cross-validation will help to insure that your model matches their joint distribution better than if you had simply fit your model to the entire raw data set... | Can cross validation be used for causal inference? | This is a good question, but the answer is definitely no: cross-validation will not improve causal inference. If you have a mapping between symptoms and diseases, cross-validation will help to insure | Can cross validation be used for causal inference?
This is a good question, but the answer is definitely no: cross-validation will not improve causal inference. If you have a mapping between symptoms and diseases, cross-validation will help to insure that your model matches their joint distribution better than if you h... | Can cross validation be used for causal inference?
This is a good question, but the answer is definitely no: cross-validation will not improve causal inference. If you have a mapping between symptoms and diseases, cross-validation will help to insure |
6,927 | Can cross validation be used for causal inference? | To respond to the follow-up @Andy posted as an answer here...
Although I could not say which estimate is correct and which is false, doesn't the inconsistency in the Assault Conviction and the Gun conviction estimates between the two models cast doubt that either has a true causal effect on sentence length?
I think ... | Can cross validation be used for causal inference? | To respond to the follow-up @Andy posted as an answer here...
Although I could not say which estimate is correct and which is false, doesn't the inconsistency in the Assault Conviction and the Gun co | Can cross validation be used for causal inference?
To respond to the follow-up @Andy posted as an answer here...
Although I could not say which estimate is correct and which is false, doesn't the inconsistency in the Assault Conviction and the Gun conviction estimates between the two models cast doubt that either has ... | Can cross validation be used for causal inference?
To respond to the follow-up @Andy posted as an answer here...
Although I could not say which estimate is correct and which is false, doesn't the inconsistency in the Assault Conviction and the Gun co |
6,928 | Can cross validation be used for causal inference? | I thank everyone for their answers, but the question has grown to something I did not intend it to, being mainly an essay on the general notion of causal inference with no right answer.
I initially intended the question to probe the audience for examples of the use of cross validation for causal inference. I had assum... | Can cross validation be used for causal inference? | I thank everyone for their answers, but the question has grown to something I did not intend it to, being mainly an essay on the general notion of causal inference with no right answer.
I initially i | Can cross validation be used for causal inference?
I thank everyone for their answers, but the question has grown to something I did not intend it to, being mainly an essay on the general notion of causal inference with no right answer.
I initially intended the question to probe the audience for examples of the use of... | Can cross validation be used for causal inference?
I thank everyone for their answers, but the question has grown to something I did not intend it to, being mainly an essay on the general notion of causal inference with no right answer.
I initially i |
6,929 | Can cross validation be used for causal inference? | I guess this is an intuitive way to think about the relation between CV and causal inference: (please correct if I am wrong)
I always think about CV as a way to evaluate the performance of a model in predictions. However, in causal inference we are more concerned with something equivalent to Occam's Razor (parsimony), ... | Can cross validation be used for causal inference? | I guess this is an intuitive way to think about the relation between CV and causal inference: (please correct if I am wrong)
I always think about CV as a way to evaluate the performance of a model in | Can cross validation be used for causal inference?
I guess this is an intuitive way to think about the relation between CV and causal inference: (please correct if I am wrong)
I always think about CV as a way to evaluate the performance of a model in predictions. However, in causal inference we are more concerned with ... | Can cross validation be used for causal inference?
I guess this is an intuitive way to think about the relation between CV and causal inference: (please correct if I am wrong)
I always think about CV as a way to evaluate the performance of a model in |
6,930 | Is there any supervised-learning problem that (deep) neural networks obviously couldn't outperform any other methods? | Here is one theoretical and two practical reasons why someone might rationally prefer a non-DNN approach.
The No Free Lunch Theorem from Wolpert and Macready says
We have dubbed the associated results NFL theorems because they demonstrate that if an algorithm performs well on a certain class of problems then it nec... | Is there any supervised-learning problem that (deep) neural networks obviously couldn't outperform a | Here is one theoretical and two practical reasons why someone might rationally prefer a non-DNN approach.
The No Free Lunch Theorem from Wolpert and Macready says
We have dubbed the associated res | Is there any supervised-learning problem that (deep) neural networks obviously couldn't outperform any other methods?
Here is one theoretical and two practical reasons why someone might rationally prefer a non-DNN approach.
The No Free Lunch Theorem from Wolpert and Macready says
We have dubbed the associated resul... | Is there any supervised-learning problem that (deep) neural networks obviously couldn't outperform a
Here is one theoretical and two practical reasons why someone might rationally prefer a non-DNN approach.
The No Free Lunch Theorem from Wolpert and Macready says
We have dubbed the associated res |
6,931 | Is there any supervised-learning problem that (deep) neural networks obviously couldn't outperform any other methods? | Somewhere on this playlist of lectures by Geoff Hinton (from his Coursera course on neural networks), there's a segment where he talks about two classes of problems:
Problems where noise is the key feature,
Problems where signal is the key feature.
I remember the explanation that while neural nets thrive in this latt... | Is there any supervised-learning problem that (deep) neural networks obviously couldn't outperform a | Somewhere on this playlist of lectures by Geoff Hinton (from his Coursera course on neural networks), there's a segment where he talks about two classes of problems:
Problems where noise is the key f | Is there any supervised-learning problem that (deep) neural networks obviously couldn't outperform any other methods?
Somewhere on this playlist of lectures by Geoff Hinton (from his Coursera course on neural networks), there's a segment where he talks about two classes of problems:
Problems where noise is the key fea... | Is there any supervised-learning problem that (deep) neural networks obviously couldn't outperform a
Somewhere on this playlist of lectures by Geoff Hinton (from his Coursera course on neural networks), there's a segment where he talks about two classes of problems:
Problems where noise is the key f |
6,932 | Is there any supervised-learning problem that (deep) neural networks obviously couldn't outperform any other methods? | Two linearly perfected correlated variables. Can deep-network with 1 million hidden layers and 2 trillion neutrons beat a simple linear regression?
EDITED
In my experience, sample collection is more expensive than computation. I mean, we can just hire some Amazon instances, run deep learning training and then come back... | Is there any supervised-learning problem that (deep) neural networks obviously couldn't outperform a | Two linearly perfected correlated variables. Can deep-network with 1 million hidden layers and 2 trillion neutrons beat a simple linear regression?
EDITED
In my experience, sample collection is more e | Is there any supervised-learning problem that (deep) neural networks obviously couldn't outperform any other methods?
Two linearly perfected correlated variables. Can deep-network with 1 million hidden layers and 2 trillion neutrons beat a simple linear regression?
EDITED
In my experience, sample collection is more exp... | Is there any supervised-learning problem that (deep) neural networks obviously couldn't outperform a
Two linearly perfected correlated variables. Can deep-network with 1 million hidden layers and 2 trillion neutrons beat a simple linear regression?
EDITED
In my experience, sample collection is more e |
6,933 | Is there any supervised-learning problem that (deep) neural networks obviously couldn't outperform any other methods? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
To be honest, it is not possible for a deep-learning m... | Is there any supervised-learning problem that (deep) neural networks obviously couldn't outperform a | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| Is there any supervised-learning problem that (deep) neural networks obviously couldn't outperform any other methods?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
... | Is there any supervised-learning problem that (deep) neural networks obviously couldn't outperform a
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
|
6,934 | Determine different clusters of 1d data from database | In one dimensional data, don't use cluster analysis.
Cluster analysis is usually a multivariate technique. Or let me better put it the other way around: for one-dimensional data -- which is completely ordered -- there are much better techniques. Using k-means and similar techniques here is a total waste, unless you put... | Determine different clusters of 1d data from database | In one dimensional data, don't use cluster analysis.
Cluster analysis is usually a multivariate technique. Or let me better put it the other way around: for one-dimensional data -- which is completely | Determine different clusters of 1d data from database
In one dimensional data, don't use cluster analysis.
Cluster analysis is usually a multivariate technique. Or let me better put it the other way around: for one-dimensional data -- which is completely ordered -- there are much better techniques. Using k-means and si... | Determine different clusters of 1d data from database
In one dimensional data, don't use cluster analysis.
Cluster analysis is usually a multivariate technique. Or let me better put it the other way around: for one-dimensional data -- which is completely |
6,935 | Determine different clusters of 1d data from database | One-dimensional clustering can be done optimally and efficiently, which may be able to give you insight on the structure of your data.
In the one-dimensional case, there are methods that are optimal and efficient (O(kn)), and as a bonus there are even regularized clustering algorithms that will let you automatically se... | Determine different clusters of 1d data from database | One-dimensional clustering can be done optimally and efficiently, which may be able to give you insight on the structure of your data.
In the one-dimensional case, there are methods that are optimal a | Determine different clusters of 1d data from database
One-dimensional clustering can be done optimally and efficiently, which may be able to give you insight on the structure of your data.
In the one-dimensional case, there are methods that are optimal and efficient (O(kn)), and as a bonus there are even regularized cl... | Determine different clusters of 1d data from database
One-dimensional clustering can be done optimally and efficiently, which may be able to give you insight on the structure of your data.
In the one-dimensional case, there are methods that are optimal a |
6,936 | Determine different clusters of 1d data from database | Is your question whether you should cluster or what method you should use to cluster?
Regarding whether you should cluster, it depends if you want to automatically partition your data (for example if you want to repeat this partitioning several times). If you are doing this only once, you can just look at the histogram... | Determine different clusters of 1d data from database | Is your question whether you should cluster or what method you should use to cluster?
Regarding whether you should cluster, it depends if you want to automatically partition your data (for example if | Determine different clusters of 1d data from database
Is your question whether you should cluster or what method you should use to cluster?
Regarding whether you should cluster, it depends if you want to automatically partition your data (for example if you want to repeat this partitioning several times). If you are do... | Determine different clusters of 1d data from database
Is your question whether you should cluster or what method you should use to cluster?
Regarding whether you should cluster, it depends if you want to automatically partition your data (for example if |
6,937 | Determine different clusters of 1d data from database | You can try:
KMeans, GMM or other methods by specifying n_clusters= no. of peaks in kernel density plot.
KMeans, GMM or other methods by determining the optimum no. of clusters based on some metrics. More info: [here] https://en.wikipedia.org/wiki/Determining_the_number_of_clusters_in_a_data_set | Determine different clusters of 1d data from database | You can try:
KMeans, GMM or other methods by specifying n_clusters= no. of peaks in kernel density plot.
KMeans, GMM or other methods by determining the optimum no. of clusters based on some metrics. | Determine different clusters of 1d data from database
You can try:
KMeans, GMM or other methods by specifying n_clusters= no. of peaks in kernel density plot.
KMeans, GMM or other methods by determining the optimum no. of clusters based on some metrics. More info: [here] https://en.wikipedia.org/wiki/Determining_the_n... | Determine different clusters of 1d data from database
You can try:
KMeans, GMM or other methods by specifying n_clusters= no. of peaks in kernel density plot.
KMeans, GMM or other methods by determining the optimum no. of clusters based on some metrics. |
6,938 | Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces? | I'm not sure there is one accepted definition for a multivariate median. The one I'm familiar with is Oja's median point, which minimizes the sum of volumes of simplices formed over subsets of points. (See the link for a technical definition.)
Update: The site referenced for the Oja definition above also has a nice p... | Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces? | I'm not sure there is one accepted definition for a multivariate median. The one I'm familiar with is Oja's median point, which minimizes the sum of volumes of simplices formed over subsets of points | Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces?
I'm not sure there is one accepted definition for a multivariate median. The one I'm familiar with is Oja's median point, which minimizes the sum of volumes of simplices formed over subsets of points. (See the link for ... | Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces?
I'm not sure there is one accepted definition for a multivariate median. The one I'm familiar with is Oja's median point, which minimizes the sum of volumes of simplices formed over subsets of points |
6,939 | Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces? | As @Ars said there are no accepted definition (and this is a good point). There are general alternatives families of ways to generalize quantiles on $\mathbb{R}^d$, I think the most significant are:
Generalize quantile process Let $P_n(A)$ be the empirical measure (=the proportion of observations in $A$). Then, with $... | Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces? | As @Ars said there are no accepted definition (and this is a good point). There are general alternatives families of ways to generalize quantiles on $\mathbb{R}^d$, I think the most significant are:
| Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces?
As @Ars said there are no accepted definition (and this is a good point). There are general alternatives families of ways to generalize quantiles on $\mathbb{R}^d$, I think the most significant are:
Generalize quantile p... | Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces?
As @Ars said there are no accepted definition (and this is a good point). There are general alternatives families of ways to generalize quantiles on $\mathbb{R}^d$, I think the most significant are:
|
6,940 | Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces? | There are distinct ways to generalize the concept of median to higher dimensions. One not yet mentioned, but which was proposed long ago, is to construct a convex hull, peel it away, and iterate for as long as you can: what's left in the last hull is a set of points that are all candidates to be "medians."
"Head-bangi... | Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces? | There are distinct ways to generalize the concept of median to higher dimensions. One not yet mentioned, but which was proposed long ago, is to construct a convex hull, peel it away, and iterate for | Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces?
There are distinct ways to generalize the concept of median to higher dimensions. One not yet mentioned, but which was proposed long ago, is to construct a convex hull, peel it away, and iterate for as long as you can: w... | Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces?
There are distinct ways to generalize the concept of median to higher dimensions. One not yet mentioned, but which was proposed long ago, is to construct a convex hull, peel it away, and iterate for |
6,941 | Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces? | Geometric median is the point with the smallest average euclidian distance from the samples | Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces? | Geometric median is the point with the smallest average euclidian distance from the samples | Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces?
Geometric median is the point with the smallest average euclidian distance from the samples | Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces?
Geometric median is the point with the smallest average euclidian distance from the samples |
6,942 | Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces? | The Tukey halfspace median can be extended to >2 dimensions using DEEPLOC, an algorithm due to Struyf and Rousseeuw; see here for details.
The algorithm is used to approximate the point of greatest depth efficiently; naive methods which attempt to determine this exactly usually run afoul of (the computational version o... | Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces? | The Tukey halfspace median can be extended to >2 dimensions using DEEPLOC, an algorithm due to Struyf and Rousseeuw; see here for details.
The algorithm is used to approximate the point of greatest de | Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces?
The Tukey halfspace median can be extended to >2 dimensions using DEEPLOC, an algorithm due to Struyf and Rousseeuw; see here for details.
The algorithm is used to approximate the point of greatest depth efficiently; naiv... | Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces?
The Tukey halfspace median can be extended to >2 dimensions using DEEPLOC, an algorithm due to Struyf and Rousseeuw; see here for details.
The algorithm is used to approximate the point of greatest de |
6,943 | Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces? | A definition that comes close to it, for unimodal distributions, is the tukey halfspace median
http://cgm.cs.mcgill.ca/~athens/Geometric-Estimators/halfspace.html
http://www.isical.ac.in/~statmath/html/publication/Tukey_tech_rep.pdf
https://www.isical.ac.in/~statmath/report/11310-15.pdf | Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces? | A definition that comes close to it, for unimodal distributions, is the tukey halfspace median
http://cgm.cs.mcgill.ca/~athens/Geometric-Estimators/halfspace.html
http://www.isical.ac.in/~statmath/h | Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces?
A definition that comes close to it, for unimodal distributions, is the tukey halfspace median
http://cgm.cs.mcgill.ca/~athens/Geometric-Estimators/halfspace.html
http://www.isical.ac.in/~statmath/html/publication/Tukey... | Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces?
A definition that comes close to it, for unimodal distributions, is the tukey halfspace median
http://cgm.cs.mcgill.ca/~athens/Geometric-Estimators/halfspace.html
http://www.isical.ac.in/~statmath/h |
6,944 | Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces? | I do not know if any such definition exists but I will try and extend the standard definition of the median to $R^2$. I will use the following notation:
$X$, $Y$: the random variables associated with the two dimensions.
$m_x$, $m_y$: the corresponding medians.
$f(x,y)$: the joint pdf for our random variables
To extend ... | Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces? | I do not know if any such definition exists but I will try and extend the standard definition of the median to $R^2$. I will use the following notation:
$X$, $Y$: the random variables associated with | Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces?
I do not know if any such definition exists but I will try and extend the standard definition of the median to $R^2$. I will use the following notation:
$X$, $Y$: the random variables associated with the two dimensions.
$... | Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces?
I do not know if any such definition exists but I will try and extend the standard definition of the median to $R^2$. I will use the following notation:
$X$, $Y$: the random variables associated with |
6,945 | How to interpret root mean squared error (RMSE) vs standard deviation? | Let's say that our responses are $y_1, \dots, y_n$ and our predicted values are $\hat y_1, \dots, \hat y_n$.
The sample variance (using $n$ rather than $n-1$ for simplicity) is $\frac{1}{n} \sum_{i=1}^n (y_i - \bar y)^2$ while the MSE is $\frac{1}{n} \sum_{i=1}^n (y_i - \hat y_i)^2$. Thus the sample variance gives how ... | How to interpret root mean squared error (RMSE) vs standard deviation? | Let's say that our responses are $y_1, \dots, y_n$ and our predicted values are $\hat y_1, \dots, \hat y_n$.
The sample variance (using $n$ rather than $n-1$ for simplicity) is $\frac{1}{n} \sum_{i=1} | How to interpret root mean squared error (RMSE) vs standard deviation?
Let's say that our responses are $y_1, \dots, y_n$ and our predicted values are $\hat y_1, \dots, \hat y_n$.
The sample variance (using $n$ rather than $n-1$ for simplicity) is $\frac{1}{n} \sum_{i=1}^n (y_i - \bar y)^2$ while the MSE is $\frac{1}{n... | How to interpret root mean squared error (RMSE) vs standard deviation?
Let's say that our responses are $y_1, \dots, y_n$ and our predicted values are $\hat y_1, \dots, \hat y_n$.
The sample variance (using $n$ rather than $n-1$ for simplicity) is $\frac{1}{n} \sum_{i=1} |
6,946 | How to interpret root mean squared error (RMSE) vs standard deviation? | In the absence of better information, the mean value of the target variable can be considered a simple estimate for values of the target variable, whether in trying to model the existing data or trying to predict future values. This simple estimate of the target variable (that is, predicted values all equal the mean of... | How to interpret root mean squared error (RMSE) vs standard deviation? | In the absence of better information, the mean value of the target variable can be considered a simple estimate for values of the target variable, whether in trying to model the existing data or tryin | How to interpret root mean squared error (RMSE) vs standard deviation?
In the absence of better information, the mean value of the target variable can be considered a simple estimate for values of the target variable, whether in trying to model the existing data or trying to predict future values. This simple estimate ... | How to interpret root mean squared error (RMSE) vs standard deviation?
In the absence of better information, the mean value of the target variable can be considered a simple estimate for values of the target variable, whether in trying to model the existing data or tryin |
6,947 | How to interpret root mean squared error (RMSE) vs standard deviation? | In case you are talking about the mean squared error of prediction, here it can be:
$$
\frac{\sum_i(y_i-\hat{y}_i)^2}{n-p},
$$
depending on how many (p) parameters are estimated for the prediction, i.e., loss of the degree of freedom (DF).
The sample variance can be:
$$
\frac{\sum_i(y_i - \bar{y}) ^2}{n-1},
$$
where ... | How to interpret root mean squared error (RMSE) vs standard deviation? | In case you are talking about the mean squared error of prediction, here it can be:
$$
\frac{\sum_i(y_i-\hat{y}_i)^2}{n-p},
$$
depending on how many (p) parameters are estimated for the prediction, | How to interpret root mean squared error (RMSE) vs standard deviation?
In case you are talking about the mean squared error of prediction, here it can be:
$$
\frac{\sum_i(y_i-\hat{y}_i)^2}{n-p},
$$
depending on how many (p) parameters are estimated for the prediction, i.e., loss of the degree of freedom (DF).
The sam... | How to interpret root mean squared error (RMSE) vs standard deviation?
In case you are talking about the mean squared error of prediction, here it can be:
$$
\frac{\sum_i(y_i-\hat{y}_i)^2}{n-p},
$$
depending on how many (p) parameters are estimated for the prediction, |
6,948 | Why doesn't regularization solve Deep Neural Nets hunger for data? | The simple way to explain it is that regularization helps to not fit to the noise, it doesn't do much in terms of determining the shape of the signal. If you think of deep learning as a giant glorious function approximator, then you realize that it needs a lot of data to define the shape of the complex signal.
If ther... | Why doesn't regularization solve Deep Neural Nets hunger for data? | The simple way to explain it is that regularization helps to not fit to the noise, it doesn't do much in terms of determining the shape of the signal. If you think of deep learning as a giant glorious | Why doesn't regularization solve Deep Neural Nets hunger for data?
The simple way to explain it is that regularization helps to not fit to the noise, it doesn't do much in terms of determining the shape of the signal. If you think of deep learning as a giant glorious function approximator, then you realize that it need... | Why doesn't regularization solve Deep Neural Nets hunger for data?
The simple way to explain it is that regularization helps to not fit to the noise, it doesn't do much in terms of determining the shape of the signal. If you think of deep learning as a giant glorious |
6,949 | Why doesn't regularization solve Deep Neural Nets hunger for data? | At this point in time, its not well-understood when and why certain regularization methods succeed and fail. In fact, its not understood at all why deep learning works in the first place.
Considering the fact that a sufficiently deep neural net can memorize most well-behaved training data perfectly, there are considera... | Why doesn't regularization solve Deep Neural Nets hunger for data? | At this point in time, its not well-understood when and why certain regularization methods succeed and fail. In fact, its not understood at all why deep learning works in the first place.
Considering | Why doesn't regularization solve Deep Neural Nets hunger for data?
At this point in time, its not well-understood when and why certain regularization methods succeed and fail. In fact, its not understood at all why deep learning works in the first place.
Considering the fact that a sufficiently deep neural net can memo... | Why doesn't regularization solve Deep Neural Nets hunger for data?
At this point in time, its not well-understood when and why certain regularization methods succeed and fail. In fact, its not understood at all why deep learning works in the first place.
Considering |
6,950 | Why doesn't regularization solve Deep Neural Nets hunger for data? | One class of theorems that show why this problem is fundamental are the No Free Lunch Theorems. For every problem with limited samples where a certain regularization helps, there is another problem where that same regularization will make things worse. As Austin points out, we generally find that L1/L2 regularization a... | Why doesn't regularization solve Deep Neural Nets hunger for data? | One class of theorems that show why this problem is fundamental are the No Free Lunch Theorems. For every problem with limited samples where a certain regularization helps, there is another problem wh | Why doesn't regularization solve Deep Neural Nets hunger for data?
One class of theorems that show why this problem is fundamental are the No Free Lunch Theorems. For every problem with limited samples where a certain regularization helps, there is another problem where that same regularization will make things worse. ... | Why doesn't regularization solve Deep Neural Nets hunger for data?
One class of theorems that show why this problem is fundamental are the No Free Lunch Theorems. For every problem with limited samples where a certain regularization helps, there is another problem wh |
6,951 | Why doesn't regularization solve Deep Neural Nets hunger for data? | I would say that at a high level, the inductive bias of DNNs (deep neural networks) is powerful but slightly too loose or not opinionated enough. By that I mean that DNNs capture a lot of surface statistics about what is going on, but fail to get to the deeper causal/compositional high level structure. (You could view ... | Why doesn't regularization solve Deep Neural Nets hunger for data? | I would say that at a high level, the inductive bias of DNNs (deep neural networks) is powerful but slightly too loose or not opinionated enough. By that I mean that DNNs capture a lot of surface stat | Why doesn't regularization solve Deep Neural Nets hunger for data?
I would say that at a high level, the inductive bias of DNNs (deep neural networks) is powerful but slightly too loose or not opinionated enough. By that I mean that DNNs capture a lot of surface statistics about what is going on, but fail to get to the... | Why doesn't regularization solve Deep Neural Nets hunger for data?
I would say that at a high level, the inductive bias of DNNs (deep neural networks) is powerful but slightly too loose or not opinionated enough. By that I mean that DNNs capture a lot of surface stat |
6,952 | Why doesn't regularization solve Deep Neural Nets hunger for data? | To clarify my thinking: Say we are using a large Deep NNet to try to model our data, but the data set is small and could actually be modeled by a linear model. Then why don't the network weights converge in such a way that one neuron simulates the linear regression and all the others converge to zeros? Why doesn't regu... | Why doesn't regularization solve Deep Neural Nets hunger for data? | To clarify my thinking: Say we are using a large Deep NNet to try to model our data, but the data set is small and could actually be modeled by a linear model. Then why don't the network weights conve | Why doesn't regularization solve Deep Neural Nets hunger for data?
To clarify my thinking: Say we are using a large Deep NNet to try to model our data, but the data set is small and could actually be modeled by a linear model. Then why don't the network weights converge in such a way that one neuron simulates the linea... | Why doesn't regularization solve Deep Neural Nets hunger for data?
To clarify my thinking: Say we are using a large Deep NNet to try to model our data, but the data set is small and could actually be modeled by a linear model. Then why don't the network weights conve |
6,953 | Why doesn't regularization solve Deep Neural Nets hunger for data? | First of all there are plenty of regularization methods both in use and in active research for deep learning. So your premise isn't entirely certain.
As for methods in use, weight decay is a direct implementation of an L2 penalty on the weights via gradient descent. Take the gradient of the squared norm of your weight... | Why doesn't regularization solve Deep Neural Nets hunger for data? | First of all there are plenty of regularization methods both in use and in active research for deep learning. So your premise isn't entirely certain.
As for methods in use, weight decay is a direct i | Why doesn't regularization solve Deep Neural Nets hunger for data?
First of all there are plenty of regularization methods both in use and in active research for deep learning. So your premise isn't entirely certain.
As for methods in use, weight decay is a direct implementation of an L2 penalty on the weights via gra... | Why doesn't regularization solve Deep Neural Nets hunger for data?
First of all there are plenty of regularization methods both in use and in active research for deep learning. So your premise isn't entirely certain.
As for methods in use, weight decay is a direct i |
6,954 | Why doesn't regularization solve Deep Neural Nets hunger for data? | Regularization is a method for including prior information into a model. This will seem straightforward from the Bayesian perspective but is easy to see outside from the perspective as well. For example, the $L_2$ penalty + standarization of covariates in Ridge Regression is essentially using the prior information that... | Why doesn't regularization solve Deep Neural Nets hunger for data? | Regularization is a method for including prior information into a model. This will seem straightforward from the Bayesian perspective but is easy to see outside from the perspective as well. For examp | Why doesn't regularization solve Deep Neural Nets hunger for data?
Regularization is a method for including prior information into a model. This will seem straightforward from the Bayesian perspective but is easy to see outside from the perspective as well. For example, the $L_2$ penalty + standarization of covariates ... | Why doesn't regularization solve Deep Neural Nets hunger for data?
Regularization is a method for including prior information into a model. This will seem straightforward from the Bayesian perspective but is easy to see outside from the perspective as well. For examp |
6,955 | Intuitive explanation of Kolmogorov Smirnov Test | The Kolmogorov-Smirnov test assesses the hypothesis that a random sample (of numerical data) came from a continuous distribution that was completely specified without referring to the data.
Here is the graph of the cumulative distribution function (CDF) of such a distribution.
A sample can be fully described by its em... | Intuitive explanation of Kolmogorov Smirnov Test | The Kolmogorov-Smirnov test assesses the hypothesis that a random sample (of numerical data) came from a continuous distribution that was completely specified without referring to the data.
Here is th | Intuitive explanation of Kolmogorov Smirnov Test
The Kolmogorov-Smirnov test assesses the hypothesis that a random sample (of numerical data) came from a continuous distribution that was completely specified without referring to the data.
Here is the graph of the cumulative distribution function (CDF) of such a distrib... | Intuitive explanation of Kolmogorov Smirnov Test
The Kolmogorov-Smirnov test assesses the hypothesis that a random sample (of numerical data) came from a continuous distribution that was completely specified without referring to the data.
Here is th |
6,956 | Intuitive explanation of Kolmogorov Smirnov Test | The one-sample Kolmogorov-Smirnov test finds the largest vertical distance between a completely specified continuous hypothesized cdf and the empirical cdf.
The two-sample Kolmogorov-Smirnov test finds the largest vertical distance between the empirical cdfs for two samples.
Unusually large distances indicate that the ... | Intuitive explanation of Kolmogorov Smirnov Test | The one-sample Kolmogorov-Smirnov test finds the largest vertical distance between a completely specified continuous hypothesized cdf and the empirical cdf.
The two-sample Kolmogorov-Smirnov test find | Intuitive explanation of Kolmogorov Smirnov Test
The one-sample Kolmogorov-Smirnov test finds the largest vertical distance between a completely specified continuous hypothesized cdf and the empirical cdf.
The two-sample Kolmogorov-Smirnov test finds the largest vertical distance between the empirical cdfs for two samp... | Intuitive explanation of Kolmogorov Smirnov Test
The one-sample Kolmogorov-Smirnov test finds the largest vertical distance between a completely specified continuous hypothesized cdf and the empirical cdf.
The two-sample Kolmogorov-Smirnov test find |
6,957 | Intuitive explanation of Kolmogorov Smirnov Test | You are looking for the maximum deviation of empirical CDF (built from observations) from the theoretical values. By definition it can't be larger than 1.
Here's a plot for a uniform distribution CDF (black) and two stylized candidate CDFs (red):
You see that your candidate CDF can't be over the theoretical by more th... | Intuitive explanation of Kolmogorov Smirnov Test | You are looking for the maximum deviation of empirical CDF (built from observations) from the theoretical values. By definition it can't be larger than 1.
Here's a plot for a uniform distribution CDF | Intuitive explanation of Kolmogorov Smirnov Test
You are looking for the maximum deviation of empirical CDF (built from observations) from the theoretical values. By definition it can't be larger than 1.
Here's a plot for a uniform distribution CDF (black) and two stylized candidate CDFs (red):
You see that your candi... | Intuitive explanation of Kolmogorov Smirnov Test
You are looking for the maximum deviation of empirical CDF (built from observations) from the theoretical values. By definition it can't be larger than 1.
Here's a plot for a uniform distribution CDF |
6,958 | Intuitive explanation of Kolmogorov Smirnov Test | I find it helpful to think of the two CDFs, whether population of empirical, as dancing around each other but staying close. Dance partners can spin around each other but will stay two armslengths of each other, right? When two people are further apart than that, they probably aren't dancing with each other.
ONE-SAMPLE... | Intuitive explanation of Kolmogorov Smirnov Test | I find it helpful to think of the two CDFs, whether population of empirical, as dancing around each other but staying close. Dance partners can spin around each other but will stay two armslengths of | Intuitive explanation of Kolmogorov Smirnov Test
I find it helpful to think of the two CDFs, whether population of empirical, as dancing around each other but staying close. Dance partners can spin around each other but will stay two armslengths of each other, right? When two people are further apart than that, they pr... | Intuitive explanation of Kolmogorov Smirnov Test
I find it helpful to think of the two CDFs, whether population of empirical, as dancing around each other but staying close. Dance partners can spin around each other but will stay two armslengths of |
6,959 | How to do logistic regression in R when outcome is fractional (a ratio of two counts)? | The glm function in R allows 3 ways to specify the formula for a logistic regression model.
The most common is that each row of the data frame represents a single observation and the response variable is either 0 or 1 (or a factor with 2 levels, or other varibale with only 2 unique values).
Another option is to use a... | How to do logistic regression in R when outcome is fractional (a ratio of two counts)? | The glm function in R allows 3 ways to specify the formula for a logistic regression model.
The most common is that each row of the data frame represents a single observation and the response variab | How to do logistic regression in R when outcome is fractional (a ratio of two counts)?
The glm function in R allows 3 ways to specify the formula for a logistic regression model.
The most common is that each row of the data frame represents a single observation and the response variable is either 0 or 1 (or a factor ... | How to do logistic regression in R when outcome is fractional (a ratio of two counts)?
The glm function in R allows 3 ways to specify the formula for a logistic regression model.
The most common is that each row of the data frame represents a single observation and the response variab |
6,960 | How to do logistic regression in R when outcome is fractional (a ratio of two counts)? | As a start, if you have a dependent variable that is a proportion, you can use Beta Regression. This doesn't extend (with my limited knowledge) to multiple proportions.
For Beta Regression overview and an R implementation check out betareg. | How to do logistic regression in R when outcome is fractional (a ratio of two counts)? | As a start, if you have a dependent variable that is a proportion, you can use Beta Regression. This doesn't extend (with my limited knowledge) to multiple proportions.
For Beta Regression overview an | How to do logistic regression in R when outcome is fractional (a ratio of two counts)?
As a start, if you have a dependent variable that is a proportion, you can use Beta Regression. This doesn't extend (with my limited knowledge) to multiple proportions.
For Beta Regression overview and an R implementation check out b... | How to do logistic regression in R when outcome is fractional (a ratio of two counts)?
As a start, if you have a dependent variable that is a proportion, you can use Beta Regression. This doesn't extend (with my limited knowledge) to multiple proportions.
For Beta Regression overview an |
6,961 | How to do logistic regression in R when outcome is fractional (a ratio of two counts)? | I'v been using nnet::multinom (package nnet is part of MASS) for a similar purpose, it accepts continuous input in [0, 1].
If you need a reference: C. Beleites et.al.:
Raman spectroscopic grading of astrocytoma tissues: using soft reference information.
Anal Bioanal Chem, 2011, Vol. 400(9), pp. 2801-2816 | How to do logistic regression in R when outcome is fractional (a ratio of two counts)? | I'v been using nnet::multinom (package nnet is part of MASS) for a similar purpose, it accepts continuous input in [0, 1].
If you need a reference: C. Beleites et.al.:
Raman spectroscopic grading of a | How to do logistic regression in R when outcome is fractional (a ratio of two counts)?
I'v been using nnet::multinom (package nnet is part of MASS) for a similar purpose, it accepts continuous input in [0, 1].
If you need a reference: C. Beleites et.al.:
Raman spectroscopic grading of astrocytoma tissues: using soft re... | How to do logistic regression in R when outcome is fractional (a ratio of two counts)?
I'v been using nnet::multinom (package nnet is part of MASS) for a similar purpose, it accepts continuous input in [0, 1].
If you need a reference: C. Beleites et.al.:
Raman spectroscopic grading of a |
6,962 | What is a standard deviation? | Standard deviation is a number that represents the "spread" or "dispersion" of a set of data. There are other measures for spread, such as range and variance.
Here are some example sets of data, and their standard deviations:
[1,1,1] standard deviation = 0 (there's no spread)
[-1,1,3] standard deviation = 1... | What is a standard deviation? | Standard deviation is a number that represents the "spread" or "dispersion" of a set of data. There are other measures for spread, such as range and variance.
Here are some example sets of data, and | What is a standard deviation?
Standard deviation is a number that represents the "spread" or "dispersion" of a set of data. There are other measures for spread, such as range and variance.
Here are some example sets of data, and their standard deviations:
[1,1,1] standard deviation = 0 (there's no spread)
[-1,... | What is a standard deviation?
Standard deviation is a number that represents the "spread" or "dispersion" of a set of data. There are other measures for spread, such as range and variance.
Here are some example sets of data, and |
6,963 | What is a standard deviation? | A quote from Wikipedia.
It shows how much variation there is from the "average" (mean, or expected/budgeted value). A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data is spread out over a large range of values. | What is a standard deviation? | A quote from Wikipedia.
It shows how much variation there is from the "average" (mean, or expected/budgeted value). A low standard deviation indicates that the data points tend to be very close to th | What is a standard deviation?
A quote from Wikipedia.
It shows how much variation there is from the "average" (mean, or expected/budgeted value). A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data is spread out over a large... | What is a standard deviation?
A quote from Wikipedia.
It shows how much variation there is from the "average" (mean, or expected/budgeted value). A low standard deviation indicates that the data points tend to be very close to th |
6,964 | What is a standard deviation? | When describing a variable we typically summarise it using two measures: a measure of centre and a measure of spread. Common measures of centre include the mean, median and mode. Common measure of spread include the variance and interquartile range.
The variance (represented by the Greek lowercase sigma raised to the p... | What is a standard deviation? | When describing a variable we typically summarise it using two measures: a measure of centre and a measure of spread. Common measures of centre include the mean, median and mode. Common measure of spr | What is a standard deviation?
When describing a variable we typically summarise it using two measures: a measure of centre and a measure of spread. Common measures of centre include the mean, median and mode. Common measure of spread include the variance and interquartile range.
The variance (represented by the Greek l... | What is a standard deviation?
When describing a variable we typically summarise it using two measures: a measure of centre and a measure of spread. Common measures of centre include the mean, median and mode. Common measure of spr |
6,965 | What is a standard deviation? | Here's how I would answer this question using a diagram.
Let's say we weigh 30 cats and calculate the mean weight. Then we produce a scatter plot, with weight on the y axis and cat identity on the x axis. The mean weight can be drawn in as a horizontal line. We can then draw in vertical lines which connect each da... | What is a standard deviation? | Here's how I would answer this question using a diagram.
Let's say we weigh 30 cats and calculate the mean weight. Then we produce a scatter plot, with weight on the y axis and cat identity on the | What is a standard deviation?
Here's how I would answer this question using a diagram.
Let's say we weigh 30 cats and calculate the mean weight. Then we produce a scatter plot, with weight on the y axis and cat identity on the x axis. The mean weight can be drawn in as a horizontal line. We can then draw in vertic... | What is a standard deviation?
Here's how I would answer this question using a diagram.
Let's say we weigh 30 cats and calculate the mean weight. Then we produce a scatter plot, with weight on the y axis and cat identity on the |
6,966 | What is a standard deviation? | I like to think of it as follows: the standard deviation is the average distance from the average. This is more conceptually useful than mathematically useful, but its a nice way to explain it to the uninitiated. | What is a standard deviation? | I like to think of it as follows: the standard deviation is the average distance from the average. This is more conceptually useful than mathematically useful, but its a nice way to explain it to the | What is a standard deviation?
I like to think of it as follows: the standard deviation is the average distance from the average. This is more conceptually useful than mathematically useful, but its a nice way to explain it to the uninitiated. | What is a standard deviation?
I like to think of it as follows: the standard deviation is the average distance from the average. This is more conceptually useful than mathematically useful, but its a nice way to explain it to the |
6,967 | What is a standard deviation? | A standard deviation is the square root of the second central moment of a distribution. A central moment is the expected difference from the expected value of the distribution. A first central moment would usually be 0, so we define a second central moment as the expected value of the squared distance of a random varia... | What is a standard deviation? | A standard deviation is the square root of the second central moment of a distribution. A central moment is the expected difference from the expected value of the distribution. A first central moment | What is a standard deviation?
A standard deviation is the square root of the second central moment of a distribution. A central moment is the expected difference from the expected value of the distribution. A first central moment would usually be 0, so we define a second central moment as the expected value of the squa... | What is a standard deviation?
A standard deviation is the square root of the second central moment of a distribution. A central moment is the expected difference from the expected value of the distribution. A first central moment |
6,968 | What is a standard deviation? | If the information required is the distribution of data about the mean, standard deviation comes in handy.
The sum of the difference of each value from the mean is zero (obviously, since the value are evenly spread around the mean), hence we square each difference so as to convert negative values to positive, sum them ... | What is a standard deviation? | If the information required is the distribution of data about the mean, standard deviation comes in handy.
The sum of the difference of each value from the mean is zero (obviously, since the value are | What is a standard deviation?
If the information required is the distribution of data about the mean, standard deviation comes in handy.
The sum of the difference of each value from the mean is zero (obviously, since the value are evenly spread around the mean), hence we square each difference so as to convert negative... | What is a standard deviation?
If the information required is the distribution of data about the mean, standard deviation comes in handy.
The sum of the difference of each value from the mean is zero (obviously, since the value are |
6,969 | What is a standard deviation? | The best way I have understood standard deviation is to think of a hair dresser! (You need to collect data from a hair dresser and averge her hair cutting speed for this example to work.)
It takes an average of 30 minutes for the hair dresser to cut a persons hair.
Suppose you do the calculation (most software package... | What is a standard deviation? | The best way I have understood standard deviation is to think of a hair dresser! (You need to collect data from a hair dresser and averge her hair cutting speed for this example to work.)
It takes an | What is a standard deviation?
The best way I have understood standard deviation is to think of a hair dresser! (You need to collect data from a hair dresser and averge her hair cutting speed for this example to work.)
It takes an average of 30 minutes for the hair dresser to cut a persons hair.
Suppose you do the calc... | What is a standard deviation?
The best way I have understood standard deviation is to think of a hair dresser! (You need to collect data from a hair dresser and averge her hair cutting speed for this example to work.)
It takes an |
6,970 | Linearity of PCA | When we say that PCA is a linear method, we refer to the dimensionality reducing mapping $f:\mathbf x\mapsto \mathbf z$ from high-dimensional space $\mathbb R^p$ to a lower-dimensional space $\mathbb R^k$. In PCA, this mapping is given by multiplication of $\mathbf x$ by the matrix of PCA eigenvectors and so is manifes... | Linearity of PCA | When we say that PCA is a linear method, we refer to the dimensionality reducing mapping $f:\mathbf x\mapsto \mathbf z$ from high-dimensional space $\mathbb R^p$ to a lower-dimensional space $\mathbb | Linearity of PCA
When we say that PCA is a linear method, we refer to the dimensionality reducing mapping $f:\mathbf x\mapsto \mathbf z$ from high-dimensional space $\mathbb R^p$ to a lower-dimensional space $\mathbb R^k$. In PCA, this mapping is given by multiplication of $\mathbf x$ by the matrix of PCA eigenvectors ... | Linearity of PCA
When we say that PCA is a linear method, we refer to the dimensionality reducing mapping $f:\mathbf x\mapsto \mathbf z$ from high-dimensional space $\mathbb R^p$ to a lower-dimensional space $\mathbb |
6,971 | Linearity of PCA | "Linear" can mean many things, and is not exclusively employed in a formal manner.
PCA is not often defined as a function in the formal sense, and therefore it is not expected to fulfill the requirements of a linear function when described as such. It is more often described, as you said, as a procedure, and sometimes ... | Linearity of PCA | "Linear" can mean many things, and is not exclusively employed in a formal manner.
PCA is not often defined as a function in the formal sense, and therefore it is not expected to fulfill the requireme | Linearity of PCA
"Linear" can mean many things, and is not exclusively employed in a formal manner.
PCA is not often defined as a function in the formal sense, and therefore it is not expected to fulfill the requirements of a linear function when described as such. It is more often described, as you said, as a procedur... | Linearity of PCA
"Linear" can mean many things, and is not exclusively employed in a formal manner.
PCA is not often defined as a function in the formal sense, and therefore it is not expected to fulfill the requireme |
6,972 | Linearity of PCA | PCA provides/is a linear transformation.
If you take the map associated with a particular analysis, say $\mathbf{M} \equiv PCA(X_1 + X_2)$ then $\mathbf{M}(X_1+X_2) = \mathbf{M}(X_1) + \mathbf{M}(X_2)$.
The culprit is that $PCA(X_1 + X_2)$, $PCA(X_1)$ and $PCA(X_2)$ are not the same linear transformations.
As a com... | Linearity of PCA | PCA provides/is a linear transformation.
If you take the map associated with a particular analysis, say $\mathbf{M} \equiv PCA(X_1 + X_2)$ then $\mathbf{M}(X_1+X_2) = \mathbf{M}(X_1) + \mathbf{M}(X_ | Linearity of PCA
PCA provides/is a linear transformation.
If you take the map associated with a particular analysis, say $\mathbf{M} \equiv PCA(X_1 + X_2)$ then $\mathbf{M}(X_1+X_2) = \mathbf{M}(X_1) + \mathbf{M}(X_2)$.
The culprit is that $PCA(X_1 + X_2)$, $PCA(X_1)$ and $PCA(X_2)$ are not the same linear transforma... | Linearity of PCA
PCA provides/is a linear transformation.
If you take the map associated with a particular analysis, say $\mathbf{M} \equiv PCA(X_1 + X_2)$ then $\mathbf{M}(X_1+X_2) = \mathbf{M}(X_1) + \mathbf{M}(X_ |
6,973 | how to represent geography or zip code in machine learning model or recommender system? | One of my favorite uses of zip code data is to look up demographic variables based on zipcode that may not be available at the individual level otherwise...
For instance, with http://www.city-data.com/ you can look up income distribution, age ranges, etc., which might tell you something about your data. These continu... | how to represent geography or zip code in machine learning model or recommender system? | One of my favorite uses of zip code data is to look up demographic variables based on zipcode that may not be available at the individual level otherwise...
For instance, with http://www.city-data.co | how to represent geography or zip code in machine learning model or recommender system?
One of my favorite uses of zip code data is to look up demographic variables based on zipcode that may not be available at the individual level otherwise...
For instance, with http://www.city-data.com/ you can look up income distri... | how to represent geography or zip code in machine learning model or recommender system?
One of my favorite uses of zip code data is to look up demographic variables based on zipcode that may not be available at the individual level otherwise...
For instance, with http://www.city-data.co |
6,974 | how to represent geography or zip code in machine learning model or recommender system? | There's 2 good options that I've seen:
Convert each zipcode to a dummy variable. If you have a lot of
data, this can be a quick and easy solution, but you won't be able
to make predictions for new zip codes. If you're worried about the number of features, you can add some regularization to your model to drop some of... | how to represent geography or zip code in machine learning model or recommender system? | There's 2 good options that I've seen:
Convert each zipcode to a dummy variable. If you have a lot of
data, this can be a quick and easy solution, but you won't be able
to make predictions for new z | how to represent geography or zip code in machine learning model or recommender system?
There's 2 good options that I've seen:
Convert each zipcode to a dummy variable. If you have a lot of
data, this can be a quick and easy solution, but you won't be able
to make predictions for new zip codes. If you're worried abo... | how to represent geography or zip code in machine learning model or recommender system?
There's 2 good options that I've seen:
Convert each zipcode to a dummy variable. If you have a lot of
data, this can be a quick and easy solution, but you won't be able
to make predictions for new z |
6,975 | how to represent geography or zip code in machine learning model or recommender system? | If you are calculating distance between records, as in clustering or K-NN, distances between zipcodes in their raw form might be informative. 02138 is much closer to 02139, geographically, than it is to 45809. | how to represent geography or zip code in machine learning model or recommender system? | If you are calculating distance between records, as in clustering or K-NN, distances between zipcodes in their raw form might be informative. 02138 is much closer to 02139, geographically, than it is | how to represent geography or zip code in machine learning model or recommender system?
If you are calculating distance between records, as in clustering or K-NN, distances between zipcodes in their raw form might be informative. 02138 is much closer to 02139, geographically, than it is to 45809. | how to represent geography or zip code in machine learning model or recommender system?
If you are calculating distance between records, as in clustering or K-NN, distances between zipcodes in their raw form might be informative. 02138 is much closer to 02139, geographically, than it is |
6,976 | how to represent geography or zip code in machine learning model or recommender system? | I would make a choropleth map of your model's residuals at the zip code level.
The result is called a spatial residual map and it may help you choose a new explanatory variable to include in your model. This approach is called exploratory spatial data analysis (ESDA) .
One potential workflow:
for each zip code get the... | how to represent geography or zip code in machine learning model or recommender system? | I would make a choropleth map of your model's residuals at the zip code level.
The result is called a spatial residual map and it may help you choose a new explanatory variable to include in your mode | how to represent geography or zip code in machine learning model or recommender system?
I would make a choropleth map of your model's residuals at the zip code level.
The result is called a spatial residual map and it may help you choose a new explanatory variable to include in your model. This approach is called explo... | how to represent geography or zip code in machine learning model or recommender system?
I would make a choropleth map of your model's residuals at the zip code level.
The result is called a spatial residual map and it may help you choose a new explanatory variable to include in your mode |
6,977 | how to represent geography or zip code in machine learning model or recommender system? | I dealt with something similar when training a classifier that used native language as a feature (how do you measure similarity between English and Spanish?) There are lots of methods out there for determining similarity among non-categorical data.
It depends on your data, but if you find that geographic distance from ... | how to represent geography or zip code in machine learning model or recommender system? | I dealt with something similar when training a classifier that used native language as a feature (how do you measure similarity between English and Spanish?) There are lots of methods out there for de | how to represent geography or zip code in machine learning model or recommender system?
I dealt with something similar when training a classifier that used native language as a feature (how do you measure similarity between English and Spanish?) There are lots of methods out there for determining similarity among non-c... | how to represent geography or zip code in machine learning model or recommender system?
I dealt with something similar when training a classifier that used native language as a feature (how do you measure similarity between English and Spanish?) There are lots of methods out there for de |
6,978 | how to represent geography or zip code in machine learning model or recommender system? | You could transform your zip code into a nominal variable (string/factor). However, as far as I remember, zip code might contain other information like county, region, etc. What I would do is to understand how zip code encodes information and decode that into multiple features.
Anyway letting zip code as a numeric vari... | how to represent geography or zip code in machine learning model or recommender system? | You could transform your zip code into a nominal variable (string/factor). However, as far as I remember, zip code might contain other information like county, region, etc. What I would do is to under | how to represent geography or zip code in machine learning model or recommender system?
You could transform your zip code into a nominal variable (string/factor). However, as far as I remember, zip code might contain other information like county, region, etc. What I would do is to understand how zip code encodes infor... | how to represent geography or zip code in machine learning model or recommender system?
You could transform your zip code into a nominal variable (string/factor). However, as far as I remember, zip code might contain other information like county, region, etc. What I would do is to under |
6,979 | how to represent geography or zip code in machine learning model or recommender system? | Any demographic data contain lots of categories, and there are different methods to convert categorical data into numeric. However, normal encoding method like one hot encoding might cause high cardinality issue or might get some issue related to memory.
In my opinion the best way to handle zip codes is to use "HashEnc... | how to represent geography or zip code in machine learning model or recommender system? | Any demographic data contain lots of categories, and there are different methods to convert categorical data into numeric. However, normal encoding method like one hot encoding might cause high cardin | how to represent geography or zip code in machine learning model or recommender system?
Any demographic data contain lots of categories, and there are different methods to convert categorical data into numeric. However, normal encoding method like one hot encoding might cause high cardinality issue or might get some is... | how to represent geography or zip code in machine learning model or recommender system?
Any demographic data contain lots of categories, and there are different methods to convert categorical data into numeric. However, normal encoding method like one hot encoding might cause high cardin |
6,980 | how to represent geography or zip code in machine learning model or recommender system? | You can featurize the Zipcodes using the above techniques, but let me suggest an alternative.
Suppose we have binary class labels. And in data we have "n" zip codes. Now we take the probability of occurence of each pincode in data, provided some class label(either 1 or zero).
So, lets say for a zipcode "j" ------>>>>
... | how to represent geography or zip code in machine learning model or recommender system? | You can featurize the Zipcodes using the above techniques, but let me suggest an alternative.
Suppose we have binary class labels. And in data we have "n" zip codes. Now we take the probability of occ | how to represent geography or zip code in machine learning model or recommender system?
You can featurize the Zipcodes using the above techniques, but let me suggest an alternative.
Suppose we have binary class labels. And in data we have "n" zip codes. Now we take the probability of occurence of each pincode in data, ... | how to represent geography or zip code in machine learning model or recommender system?
You can featurize the Zipcodes using the above techniques, but let me suggest an alternative.
Suppose we have binary class labels. And in data we have "n" zip codes. Now we take the probability of occ |
6,981 | Is it possible to prove a null hypothesis? | If you are talking about the real world & not formal logic, the answer is of course. "Proof" of anything by empirical means depends on the strength of the inference one can make, which in turn is determined by validity of the testing process as evaluated in light of everything one knows about how the world works (i.e.... | Is it possible to prove a null hypothesis? | If you are talking about the real world & not formal logic, the answer is of course. "Proof" of anything by empirical means depends on the strength of the inference one can make, which in turn is dete | Is it possible to prove a null hypothesis?
If you are talking about the real world & not formal logic, the answer is of course. "Proof" of anything by empirical means depends on the strength of the inference one can make, which in turn is determined by validity of the testing process as evaluated in light of everything... | Is it possible to prove a null hypothesis?
If you are talking about the real world & not formal logic, the answer is of course. "Proof" of anything by empirical means depends on the strength of the inference one can make, which in turn is dete |
6,982 | Is it possible to prove a null hypothesis? | Answer from the mathematical side : it is possible if and only if "hypotheses are mutually singular".
If by "prove" you mean have a rule that can "accept" (should I say that:) ) $H_0$ with a probability to make a mistake that is zero, then you are searching what could be called "ideal test" and this exists:
If you are... | Is it possible to prove a null hypothesis? | Answer from the mathematical side : it is possible if and only if "hypotheses are mutually singular".
If by "prove" you mean have a rule that can "accept" (should I say that:) ) $H_0$ with a probabil | Is it possible to prove a null hypothesis?
Answer from the mathematical side : it is possible if and only if "hypotheses are mutually singular".
If by "prove" you mean have a rule that can "accept" (should I say that:) ) $H_0$ with a probability to make a mistake that is zero, then you are searching what could be call... | Is it possible to prove a null hypothesis?
Answer from the mathematical side : it is possible if and only if "hypotheses are mutually singular".
If by "prove" you mean have a rule that can "accept" (should I say that:) ) $H_0$ with a probabil |
6,983 | Is it possible to prove a null hypothesis? | Yes there is a definitive answer. That answer is: No, there isn't a way to prove a null hypothesis. The best you can do, as far as I know, is throw confidence intervals around your estimate and demonstrate that the effect is so small that it might as well be essentially non-existent. | Is it possible to prove a null hypothesis? | Yes there is a definitive answer. That answer is: No, there isn't a way to prove a null hypothesis. The best you can do, as far as I know, is throw confidence intervals around your estimate and demo | Is it possible to prove a null hypothesis?
Yes there is a definitive answer. That answer is: No, there isn't a way to prove a null hypothesis. The best you can do, as far as I know, is throw confidence intervals around your estimate and demonstrate that the effect is so small that it might as well be essentially non-... | Is it possible to prove a null hypothesis?
Yes there is a definitive answer. That answer is: No, there isn't a way to prove a null hypothesis. The best you can do, as far as I know, is throw confidence intervals around your estimate and demo |
6,984 | Is it possible to prove a null hypothesis? | For me, the decision theoretical framework presents the easiest way to understand the "null hypothesis". It basically says that there must be at least two alternatives: the Null hypothesis, and at least one alternative. Then the "decision problem" is to accept one of the alternatives, and reject the others (although ... | Is it possible to prove a null hypothesis? | For me, the decision theoretical framework presents the easiest way to understand the "null hypothesis". It basically says that there must be at least two alternatives: the Null hypothesis, and at le | Is it possible to prove a null hypothesis?
For me, the decision theoretical framework presents the easiest way to understand the "null hypothesis". It basically says that there must be at least two alternatives: the Null hypothesis, and at least one alternative. Then the "decision problem" is to accept one of the alt... | Is it possible to prove a null hypothesis?
For me, the decision theoretical framework presents the easiest way to understand the "null hypothesis". It basically says that there must be at least two alternatives: the Null hypothesis, and at le |
6,985 | Is it possible to prove a null hypothesis? | Yes, it is possible to prove the null--in exactly the same sense that it is possible to prove any alternative to the null. In a Bayesian analysis, it is perfectly possible for the odds in favor of the null versus any of the proposed alternatives to it to become arbitrarily large. Moreover, it is false to assert, as som... | Is it possible to prove a null hypothesis? | Yes, it is possible to prove the null--in exactly the same sense that it is possible to prove any alternative to the null. In a Bayesian analysis, it is perfectly possible for the odds in favor of the | Is it possible to prove a null hypothesis?
Yes, it is possible to prove the null--in exactly the same sense that it is possible to prove any alternative to the null. In a Bayesian analysis, it is perfectly possible for the odds in favor of the null versus any of the proposed alternatives to it to become arbitrarily lar... | Is it possible to prove a null hypothesis?
Yes, it is possible to prove the null--in exactly the same sense that it is possible to prove any alternative to the null. In a Bayesian analysis, it is perfectly possible for the odds in favor of the |
6,986 | Is it possible to prove a null hypothesis? | Technically, no, a null hypothesis cannot be proven. For any fixed, finite sample size, there will always be some small but nonzero effect size for which your statistical test has virtually no power. More practically, though, you can prove that you're within some small epsilon of the null hypothesis, such that deviat... | Is it possible to prove a null hypothesis? | Technically, no, a null hypothesis cannot be proven. For any fixed, finite sample size, there will always be some small but nonzero effect size for which your statistical test has virtually no power. | Is it possible to prove a null hypothesis?
Technically, no, a null hypothesis cannot be proven. For any fixed, finite sample size, there will always be some small but nonzero effect size for which your statistical test has virtually no power. More practically, though, you can prove that you're within some small epsil... | Is it possible to prove a null hypothesis?
Technically, no, a null hypothesis cannot be proven. For any fixed, finite sample size, there will always be some small but nonzero effect size for which your statistical test has virtually no power. |
6,987 | Is it possible to prove a null hypothesis? | There is a case where a proof is possible. Suppose you have a school and your null hypothesis is that the numbers of boys and of girls is equal. As the sample size increases, the uncertainty in the ratio of boys to girls tends to reduce, eventually reaching certainty (which is what I assume you mean by proof) when th... | Is it possible to prove a null hypothesis? | There is a case where a proof is possible. Suppose you have a school and your null hypothesis is that the numbers of boys and of girls is equal. As the sample size increases, the uncertainty in the | Is it possible to prove a null hypothesis?
There is a case where a proof is possible. Suppose you have a school and your null hypothesis is that the numbers of boys and of girls is equal. As the sample size increases, the uncertainty in the ratio of boys to girls tends to reduce, eventually reaching certainty (which ... | Is it possible to prove a null hypothesis?
There is a case where a proof is possible. Suppose you have a school and your null hypothesis is that the numbers of boys and of girls is equal. As the sample size increases, the uncertainty in the |
6,988 | Is it possible to prove a null hypothesis? | I would like to discuss here a point a lot of users are somewhat confused. What is the real meaning of the Null Hypothesis statement H0: p=0? Are we trying to determine if the parameter p is zero? Of course not, there is no way to achieve such a goal.
What we intend to establish is that, given the data set, the evalu... | Is it possible to prove a null hypothesis? | I would like to discuss here a point a lot of users are somewhat confused. What is the real meaning of the Null Hypothesis statement H0: p=0? Are we trying to determine if the parameter p is zero? Of | Is it possible to prove a null hypothesis?
I would like to discuss here a point a lot of users are somewhat confused. What is the real meaning of the Null Hypothesis statement H0: p=0? Are we trying to determine if the parameter p is zero? Of course not, there is no way to achieve such a goal.
What we intend to estab... | Is it possible to prove a null hypothesis?
I would like to discuss here a point a lot of users are somewhat confused. What is the real meaning of the Null Hypothesis statement H0: p=0? Are we trying to determine if the parameter p is zero? Of |
6,989 | How to resolve Simpson's paradox? | In your question, you state that you don't know what "causal Bayesian networks" and "back door tests" are.
Suppose you have a causal Bayesian network. That is, a directed acyclic graph whose nodes represent propositions and whose directed edges represent potential causal relationships. You may have many such networks... | How to resolve Simpson's paradox? | In your question, you state that you don't know what "causal Bayesian networks" and "back door tests" are.
Suppose you have a causal Bayesian network. That is, a directed acyclic graph whose nodes re | How to resolve Simpson's paradox?
In your question, you state that you don't know what "causal Bayesian networks" and "back door tests" are.
Suppose you have a causal Bayesian network. That is, a directed acyclic graph whose nodes represent propositions and whose directed edges represent potential causal relationships... | How to resolve Simpson's paradox?
In your question, you state that you don't know what "causal Bayesian networks" and "back door tests" are.
Suppose you have a causal Bayesian network. That is, a directed acyclic graph whose nodes re |
6,990 | How to resolve Simpson's paradox? | I have a prior answer that discusses Simpson's paradox here: Basic Simpson's paradox. It may help you to read that to better understand the phenomenon.
In short, Simpson's paradox occurs because of confounding. In your example, the treatment is confounded* with the kind of kidney stones each patient had. We know f... | How to resolve Simpson's paradox? | I have a prior answer that discusses Simpson's paradox here: Basic Simpson's paradox. It may help you to read that to better understand the phenomenon.
In short, Simpson's paradox occurs because of | How to resolve Simpson's paradox?
I have a prior answer that discusses Simpson's paradox here: Basic Simpson's paradox. It may help you to read that to better understand the phenomenon.
In short, Simpson's paradox occurs because of confounding. In your example, the treatment is confounded* with the kind of kidney s... | How to resolve Simpson's paradox?
I have a prior answer that discusses Simpson's paradox here: Basic Simpson's paradox. It may help you to read that to better understand the phenomenon.
In short, Simpson's paradox occurs because of |
6,991 | How to resolve Simpson's paradox? | This nice article by Judea Pearl published in 2013 deals exactly with the problem of which option to choose when confronted with Simpson's paradox:
Understanding Simpson's paradox (PDF) | How to resolve Simpson's paradox? | This nice article by Judea Pearl published in 2013 deals exactly with the problem of which option to choose when confronted with Simpson's paradox:
Understanding Simpson's paradox (PDF) | How to resolve Simpson's paradox?
This nice article by Judea Pearl published in 2013 deals exactly with the problem of which option to choose when confronted with Simpson's paradox:
Understanding Simpson's paradox (PDF) | How to resolve Simpson's paradox?
This nice article by Judea Pearl published in 2013 deals exactly with the problem of which option to choose when confronted with Simpson's paradox:
Understanding Simpson's paradox (PDF) |
6,992 | How to resolve Simpson's paradox? | One important "take away" is that if treatment assignments are disproportionate between subgroups, one must take subgroups into account when analyzing the data.
A second important "take away" is that observational studies are especially prone to delivering wrong answers due to the unknown presence of Simpson's paradox.... | How to resolve Simpson's paradox? | One important "take away" is that if treatment assignments are disproportionate between subgroups, one must take subgroups into account when analyzing the data.
A second important "take away" is that | How to resolve Simpson's paradox?
One important "take away" is that if treatment assignments are disproportionate between subgroups, one must take subgroups into account when analyzing the data.
A second important "take away" is that observational studies are especially prone to delivering wrong answers due to the unkn... | How to resolve Simpson's paradox?
One important "take away" is that if treatment assignments are disproportionate between subgroups, one must take subgroups into account when analyzing the data.
A second important "take away" is that |
6,993 | How to resolve Simpson's paradox? | Do you want the solution to the one example or the paradox in general? There is none for the latter because the paradox can arise for more than one reason and needs to be assessed on a case by case basis.
The paradox is primarily problematic when reporting summary data and is critical in training individuals how to an... | How to resolve Simpson's paradox? | Do you want the solution to the one example or the paradox in general? There is none for the latter because the paradox can arise for more than one reason and needs to be assessed on a case by case ba | How to resolve Simpson's paradox?
Do you want the solution to the one example or the paradox in general? There is none for the latter because the paradox can arise for more than one reason and needs to be assessed on a case by case basis.
The paradox is primarily problematic when reporting summary data and is critical... | How to resolve Simpson's paradox?
Do you want the solution to the one example or the paradox in general? There is none for the latter because the paradox can arise for more than one reason and needs to be assessed on a case by case ba |
6,994 | Estimating same model over multiple time series | You could do a grid search: start with ARIMA(1,0,0) and try all the possibilities up to ARIMA(5,2,5) or something. Fit the model to each series, and estimate a scale-independent error measurement like MAPE or MASE (MASE would probably be better). Choose the ARIMA model with the lowest average MASE across all your mod... | Estimating same model over multiple time series | You could do a grid search: start with ARIMA(1,0,0) and try all the possibilities up to ARIMA(5,2,5) or something. Fit the model to each series, and estimate a scale-independent error measurement lik | Estimating same model over multiple time series
You could do a grid search: start with ARIMA(1,0,0) and try all the possibilities up to ARIMA(5,2,5) or something. Fit the model to each series, and estimate a scale-independent error measurement like MAPE or MASE (MASE would probably be better). Choose the ARIMA model ... | Estimating same model over multiple time series
You could do a grid search: start with ARIMA(1,0,0) and try all the possibilities up to ARIMA(5,2,5) or something. Fit the model to each series, and estimate a scale-independent error measurement lik |
6,995 | Estimating same model over multiple time series | One way to do that is to construct a long time series with all of your data, and with sequences of missing values between the series to separate them. For example, in R, if you have three series (x, y and z) each of length 100 and frequency 12, you can join them as follows
combined <- ts(c(x,rep(NA,56),y,rep(NA,56),z,r... | Estimating same model over multiple time series | One way to do that is to construct a long time series with all of your data, and with sequences of missing values between the series to separate them. For example, in R, if you have three series (x, y | Estimating same model over multiple time series
One way to do that is to construct a long time series with all of your data, and with sequences of missing values between the series to separate them. For example, in R, if you have three series (x, y and z) each of length 100 and frequency 12, you can join them as follow... | Estimating same model over multiple time series
One way to do that is to construct a long time series with all of your data, and with sequences of missing values between the series to separate them. For example, in R, if you have three series (x, y |
6,996 | Estimating same model over multiple time series | Estimating single model for multiple time series is the realm of panel data econometrics. However in your case with no explanatory variable @Rob Hyndman answer is probably the best fit. However if it turns out that the means of time series are different (test it, since in this case @Rob Hyndman's method should fail!),... | Estimating same model over multiple time series | Estimating single model for multiple time series is the realm of panel data econometrics. However in your case with no explanatory variable @Rob Hyndman answer is probably the best fit. However if it | Estimating same model over multiple time series
Estimating single model for multiple time series is the realm of panel data econometrics. However in your case with no explanatory variable @Rob Hyndman answer is probably the best fit. However if it turns out that the means of time series are different (test it, since i... | Estimating same model over multiple time series
Estimating single model for multiple time series is the realm of panel data econometrics. However in your case with no explanatory variable @Rob Hyndman answer is probably the best fit. However if it |
6,997 | Estimating same model over multiple time series | An alternative to Rob Hyndman's approach, to make a single data series, is to merge the data. This might be appropriate if your multiple time series represent noisy readings from a set of machines recording the same event. (If each time series is on a different scale you need to normalize the data first.)
NOTE: you sti... | Estimating same model over multiple time series | An alternative to Rob Hyndman's approach, to make a single data series, is to merge the data. This might be appropriate if your multiple time series represent noisy readings from a set of machines rec | Estimating same model over multiple time series
An alternative to Rob Hyndman's approach, to make a single data series, is to merge the data. This might be appropriate if your multiple time series represent noisy readings from a set of machines recording the same event. (If each time series is on a different scale you ... | Estimating same model over multiple time series
An alternative to Rob Hyndman's approach, to make a single data series, is to merge the data. This might be appropriate if your multiple time series represent noisy readings from a set of machines rec |
6,998 | Estimating same model over multiple time series | I would look at hidden Markov models and dynamic Bayesian networks. They model time series data. Also they are trained using multiple time series instances e.g. multiple blood pressure time series from various individuals .
You should find packages in Python and R to build those. You might have to define structure for... | Estimating same model over multiple time series | I would look at hidden Markov models and dynamic Bayesian networks. They model time series data. Also they are trained using multiple time series instances e.g. multiple blood pressure time series fro | Estimating same model over multiple time series
I would look at hidden Markov models and dynamic Bayesian networks. They model time series data. Also they are trained using multiple time series instances e.g. multiple blood pressure time series from various individuals .
You should find packages in Python and R to bui... | Estimating same model over multiple time series
I would look at hidden Markov models and dynamic Bayesian networks. They model time series data. Also they are trained using multiple time series instances e.g. multiple blood pressure time series fro |
6,999 | Is there a way to use the covariance matrix to find coefficients for multiple regression? | Yes, the covariance matrix of all the variables--explanatory and response--contains the information needed to find all the coefficients, provided an intercept (constant) term is included in the model. (Although the covariances provide no information about the constant term, it can be found from the means of the data.)... | Is there a way to use the covariance matrix to find coefficients for multiple regression? | Yes, the covariance matrix of all the variables--explanatory and response--contains the information needed to find all the coefficients, provided an intercept (constant) term is included in the model. | Is there a way to use the covariance matrix to find coefficients for multiple regression?
Yes, the covariance matrix of all the variables--explanatory and response--contains the information needed to find all the coefficients, provided an intercept (constant) term is included in the model. (Although the covariances pr... | Is there a way to use the covariance matrix to find coefficients for multiple regression?
Yes, the covariance matrix of all the variables--explanatory and response--contains the information needed to find all the coefficients, provided an intercept (constant) term is included in the model. |
7,000 | How to draw neat polygons around scatterplot regions in ggplot2 [closed] | With some googling I came across the website of Gota Morota who has an example of doing this already on her website. Below is that example extended to your data.
library(ggplot2)
library(plyr)
work <- "E:\\Forum_Post_Stuff\\convex_hull_ggplot2"
setwd(work)
#note you have some missing data
mydata <- read.table(file = ... | How to draw neat polygons around scatterplot regions in ggplot2 [closed] | With some googling I came across the website of Gota Morota who has an example of doing this already on her website. Below is that example extended to your data.
library(ggplot2)
library(plyr)
work < | How to draw neat polygons around scatterplot regions in ggplot2 [closed]
With some googling I came across the website of Gota Morota who has an example of doing this already on her website. Below is that example extended to your data.
library(ggplot2)
library(plyr)
work <- "E:\\Forum_Post_Stuff\\convex_hull_ggplot2"
s... | How to draw neat polygons around scatterplot regions in ggplot2 [closed]
With some googling I came across the website of Gota Morota who has an example of doing this already on her website. Below is that example extended to your data.
library(ggplot2)
library(plyr)
work < |
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