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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1,301 | When to use gamma GLMs? | In my opinion, it assumes that the errors lie on a family of gamma distributions, with the same shapes, and with the scales changing according the related formula.
But it is difficult to do model diagnosis. Note that the simple QQ plot is not suitable here, because it is about the same distribution, while ours is a fam... | When to use gamma GLMs? | In my opinion, it assumes that the errors lie on a family of gamma distributions, with the same shapes, and with the scales changing according the related formula.
But it is difficult to do model diag | When to use gamma GLMs?
In my opinion, it assumes that the errors lie on a family of gamma distributions, with the same shapes, and with the scales changing according the related formula.
But it is difficult to do model diagnosis. Note that the simple QQ plot is not suitable here, because it is about the same distribut... | When to use gamma GLMs?
In my opinion, it assumes that the errors lie on a family of gamma distributions, with the same shapes, and with the scales changing according the related formula.
But it is difficult to do model diag |
1,302 | Most interesting statistical paradoxes | It's not a paradox per se, but it is a puzzling comment, at least at first.
During World War II, Abraham Wald was a statistician for the U.S. government. He looked at the bombers that returned from missions and analyzed the pattern of the bullet "wounds" on the planes. He recommended that the Navy reinforce areas where... | Most interesting statistical paradoxes | It's not a paradox per se, but it is a puzzling comment, at least at first.
During World War II, Abraham Wald was a statistician for the U.S. government. He looked at the bombers that returned from mi | Most interesting statistical paradoxes
It's not a paradox per se, but it is a puzzling comment, at least at first.
During World War II, Abraham Wald was a statistician for the U.S. government. He looked at the bombers that returned from missions and analyzed the pattern of the bullet "wounds" on the planes. He recommen... | Most interesting statistical paradoxes
It's not a paradox per se, but it is a puzzling comment, at least at first.
During World War II, Abraham Wald was a statistician for the U.S. government. He looked at the bombers that returned from mi |
1,303 | Most interesting statistical paradoxes | Another example is the ecological fallacy.
Example
Suppose that we look for a relationship between voting and income by regressing the vote share for then-Senator Obama on the median income of a state (in thousands). We get an intercept of approximately 20 and a slope coefficient of 0.61.
Many would interpret this re... | Most interesting statistical paradoxes | Another example is the ecological fallacy.
Example
Suppose that we look for a relationship between voting and income by regressing the vote share for then-Senator Obama on the median income of a sta | Most interesting statistical paradoxes
Another example is the ecological fallacy.
Example
Suppose that we look for a relationship between voting and income by regressing the vote share for then-Senator Obama on the median income of a state (in thousands). We get an intercept of approximately 20 and a slope coefficien... | Most interesting statistical paradoxes
Another example is the ecological fallacy.
Example
Suppose that we look for a relationship between voting and income by regressing the vote share for then-Senator Obama on the median income of a sta |
1,304 | Most interesting statistical paradoxes | My contribution is Simpson's paradox because:
the reasons for the paradox are not intuitive to many people, so
it can be really hard to explain why the findings are the way they are to lay people in plain English.
tl;dr version of the paradox: the statistical significance of a result appears to differ depending on ho... | Most interesting statistical paradoxes | My contribution is Simpson's paradox because:
the reasons for the paradox are not intuitive to many people, so
it can be really hard to explain why the findings are the way they are to lay people in | Most interesting statistical paradoxes
My contribution is Simpson's paradox because:
the reasons for the paradox are not intuitive to many people, so
it can be really hard to explain why the findings are the way they are to lay people in plain English.
tl;dr version of the paradox: the statistical significance of a r... | Most interesting statistical paradoxes
My contribution is Simpson's paradox because:
the reasons for the paradox are not intuitive to many people, so
it can be really hard to explain why the findings are the way they are to lay people in |
1,305 | Most interesting statistical paradoxes | There are no paradoxes in statistics, only puzzles waiting to be solved.
Nevertheless, my favourite is the two envelope "paradox". Suppose I put two envelopes in front of you and tell you that one contains twice as much money as the other (but not which is which). You reason as follows. Suppose the left envelope contai... | Most interesting statistical paradoxes | There are no paradoxes in statistics, only puzzles waiting to be solved.
Nevertheless, my favourite is the two envelope "paradox". Suppose I put two envelopes in front of you and tell you that one con | Most interesting statistical paradoxes
There are no paradoxes in statistics, only puzzles waiting to be solved.
Nevertheless, my favourite is the two envelope "paradox". Suppose I put two envelopes in front of you and tell you that one contains twice as much money as the other (but not which is which). You reason as fo... | Most interesting statistical paradoxes
There are no paradoxes in statistics, only puzzles waiting to be solved.
Nevertheless, my favourite is the two envelope "paradox". Suppose I put two envelopes in front of you and tell you that one con |
1,306 | Most interesting statistical paradoxes | The Sleeping Beauty Problem.
This is a recent invention; it was heavily discussed within a small set of philosophy journals over the last decade. There are staunch advocates for two very different answers (the "Halfers" and "Thirders"). It raises questions about the nature of belief, probability, and conditioning, an... | Most interesting statistical paradoxes | The Sleeping Beauty Problem.
This is a recent invention; it was heavily discussed within a small set of philosophy journals over the last decade. There are staunch advocates for two very different an | Most interesting statistical paradoxes
The Sleeping Beauty Problem.
This is a recent invention; it was heavily discussed within a small set of philosophy journals over the last decade. There are staunch advocates for two very different answers (the "Halfers" and "Thirders"). It raises questions about the nature of be... | Most interesting statistical paradoxes
The Sleeping Beauty Problem.
This is a recent invention; it was heavily discussed within a small set of philosophy journals over the last decade. There are staunch advocates for two very different an |
1,307 | Most interesting statistical paradoxes | The St.Petersburg paradox, which makes you think differently on the concept and meaning of Expected Value. The intuition (mainly for people with background in statistics) and the calculations are giving different results. | Most interesting statistical paradoxes | The St.Petersburg paradox, which makes you think differently on the concept and meaning of Expected Value. The intuition (mainly for people with background in statistics) and the calculations are givi | Most interesting statistical paradoxes
The St.Petersburg paradox, which makes you think differently on the concept and meaning of Expected Value. The intuition (mainly for people with background in statistics) and the calculations are giving different results. | Most interesting statistical paradoxes
The St.Petersburg paradox, which makes you think differently on the concept and meaning of Expected Value. The intuition (mainly for people with background in statistics) and the calculations are givi |
1,308 | Most interesting statistical paradoxes | The Jeffreys-Lindley paradox, which shows that under some circumstances default frequentist and Bayesian methods of hypothesis testing can give completely contradictory answers. It really forces users to think about exactly what these forms of testing mean, and to consider whether that's what the really want. For a rec... | Most interesting statistical paradoxes | The Jeffreys-Lindley paradox, which shows that under some circumstances default frequentist and Bayesian methods of hypothesis testing can give completely contradictory answers. It really forces users | Most interesting statistical paradoxes
The Jeffreys-Lindley paradox, which shows that under some circumstances default frequentist and Bayesian methods of hypothesis testing can give completely contradictory answers. It really forces users to think about exactly what these forms of testing mean, and to consider whether... | Most interesting statistical paradoxes
The Jeffreys-Lindley paradox, which shows that under some circumstances default frequentist and Bayesian methods of hypothesis testing can give completely contradictory answers. It really forces users |
1,309 | Most interesting statistical paradoxes | Sorry, but I can't help myself (I, too, love statistical paradoxes!).
Again, perhaps not a paradox per se and another example of omitted variables bias.
Spurious causation/regression
Any variable with a time trend is going to be correlated with another variable that also has a time trend. For example, my weight from b... | Most interesting statistical paradoxes | Sorry, but I can't help myself (I, too, love statistical paradoxes!).
Again, perhaps not a paradox per se and another example of omitted variables bias.
Spurious causation/regression
Any variable wit | Most interesting statistical paradoxes
Sorry, but I can't help myself (I, too, love statistical paradoxes!).
Again, perhaps not a paradox per se and another example of omitted variables bias.
Spurious causation/regression
Any variable with a time trend is going to be correlated with another variable that also has a ti... | Most interesting statistical paradoxes
Sorry, but I can't help myself (I, too, love statistical paradoxes!).
Again, perhaps not a paradox per se and another example of omitted variables bias.
Spurious causation/regression
Any variable wit |
1,310 | Most interesting statistical paradoxes | One of my favorites is the Monty Hall problem. I remember learning about it in an elementary stats class, telling my dad, as both of us were in disbelief I simulated random numbers and we tried the problem. To our amazement it was true.
Basically the problem states that if you had three doors on a game show, behind... | Most interesting statistical paradoxes | One of my favorites is the Monty Hall problem. I remember learning about it in an elementary stats class, telling my dad, as both of us were in disbelief I simulated random numbers and we tried the p | Most interesting statistical paradoxes
One of my favorites is the Monty Hall problem. I remember learning about it in an elementary stats class, telling my dad, as both of us were in disbelief I simulated random numbers and we tried the problem. To our amazement it was true.
Basically the problem states that if you... | Most interesting statistical paradoxes
One of my favorites is the Monty Hall problem. I remember learning about it in an elementary stats class, telling my dad, as both of us were in disbelief I simulated random numbers and we tried the p |
1,311 | Most interesting statistical paradoxes | Parrondo's Paradox:
From wikipdedia: "Parrondo's paradox, a paradox in game theory, has been described as: A combination of losing strategies becomes a winning strategy. It is named after its creator, Juan Parrondo, who discovered the paradox in 1996. A more explanatory description is:
There exist pairs of games, each... | Most interesting statistical paradoxes | Parrondo's Paradox:
From wikipdedia: "Parrondo's paradox, a paradox in game theory, has been described as: A combination of losing strategies becomes a winning strategy. It is named after its creator, | Most interesting statistical paradoxes
Parrondo's Paradox:
From wikipdedia: "Parrondo's paradox, a paradox in game theory, has been described as: A combination of losing strategies becomes a winning strategy. It is named after its creator, Juan Parrondo, who discovered the paradox in 1996. A more explanatory descriptio... | Most interesting statistical paradoxes
Parrondo's Paradox:
From wikipdedia: "Parrondo's paradox, a paradox in game theory, has been described as: A combination of losing strategies becomes a winning strategy. It is named after its creator, |
1,312 | Most interesting statistical paradoxes | I like the following: The host is using an unknown distribution on $[0,1]$ to choose, independently, two numbers $x,y\in [0,1]$. The only thing known to the player about the distribution is that $P(x=y)=0$. The player is then shown the number $x$ and is asked to guess whether $y>x$ or $y<x$. Clearly, if player always g... | Most interesting statistical paradoxes | I like the following: The host is using an unknown distribution on $[0,1]$ to choose, independently, two numbers $x,y\in [0,1]$. The only thing known to the player about the distribution is that $P(x= | Most interesting statistical paradoxes
I like the following: The host is using an unknown distribution on $[0,1]$ to choose, independently, two numbers $x,y\in [0,1]$. The only thing known to the player about the distribution is that $P(x=y)=0$. The player is then shown the number $x$ and is asked to guess whether $y>x... | Most interesting statistical paradoxes
I like the following: The host is using an unknown distribution on $[0,1]$ to choose, independently, two numbers $x,y\in [0,1]$. The only thing known to the player about the distribution is that $P(x= |
1,313 | Most interesting statistical paradoxes | It's interesting that the Two Child Problem and the Monty Hall Problem so often get mentioned together in the context of paradox. Both illustrate an apparent paradox first illustrated in 1889, called Bertrand's Box Paradox, which can be generalized to represent either. I find it a most interesting "paradox" because the... | Most interesting statistical paradoxes | It's interesting that the Two Child Problem and the Monty Hall Problem so often get mentioned together in the context of paradox. Both illustrate an apparent paradox first illustrated in 1889, called | Most interesting statistical paradoxes
It's interesting that the Two Child Problem and the Monty Hall Problem so often get mentioned together in the context of paradox. Both illustrate an apparent paradox first illustrated in 1889, called Bertrand's Box Paradox, which can be generalized to represent either. I find it a... | Most interesting statistical paradoxes
It's interesting that the Two Child Problem and the Monty Hall Problem so often get mentioned together in the context of paradox. Both illustrate an apparent paradox first illustrated in 1889, called |
1,314 | Most interesting statistical paradoxes | This is Simpson's Paradox again but 'backwards' as well as forwards, comes from Judea Pearl's new book Causal Inference in Statistics: A primer[^1]
The classic Simpon's Paradox works as follows: consider trying to choose between two doctors. You automatically choose the one with the best outcomes. But suppose the one w... | Most interesting statistical paradoxes | This is Simpson's Paradox again but 'backwards' as well as forwards, comes from Judea Pearl's new book Causal Inference in Statistics: A primer[^1]
The classic Simpon's Paradox works as follows: consi | Most interesting statistical paradoxes
This is Simpson's Paradox again but 'backwards' as well as forwards, comes from Judea Pearl's new book Causal Inference in Statistics: A primer[^1]
The classic Simpon's Paradox works as follows: consider trying to choose between two doctors. You automatically choose the one with t... | Most interesting statistical paradoxes
This is Simpson's Paradox again but 'backwards' as well as forwards, comes from Judea Pearl's new book Causal Inference in Statistics: A primer[^1]
The classic Simpon's Paradox works as follows: consi |
1,315 | Most interesting statistical paradoxes | I find a simplified graphical illustration of the ecological fallacy (here the rich State/poor State voting paradox) helps me to understand on an intuitive level why we see a reversal of voting patterns when we aggregate State populations: | Most interesting statistical paradoxes | I find a simplified graphical illustration of the ecological fallacy (here the rich State/poor State voting paradox) helps me to understand on an intuitive level why we see a reversal of voting patter | Most interesting statistical paradoxes
I find a simplified graphical illustration of the ecological fallacy (here the rich State/poor State voting paradox) helps me to understand on an intuitive level why we see a reversal of voting patterns when we aggregate State populations: | Most interesting statistical paradoxes
I find a simplified graphical illustration of the ecological fallacy (here the rich State/poor State voting paradox) helps me to understand on an intuitive level why we see a reversal of voting patter |
1,316 | Most interesting statistical paradoxes | Suppose you obtained a data on births in royal family of some kingdom.
In the family tree each birth was noted. What is peculiar about this
family was that parents were trying to have a baby only as soon first
boy was born and then did not have any more children.
So your data potentially looks similar to this:
G... | Most interesting statistical paradoxes | Suppose you obtained a data on births in royal family of some kingdom.
In the family tree each birth was noted. What is peculiar about this
family was that parents were trying to have a baby only | Most interesting statistical paradoxes
Suppose you obtained a data on births in royal family of some kingdom.
In the family tree each birth was noted. What is peculiar about this
family was that parents were trying to have a baby only as soon first
boy was born and then did not have any more children.
So your da... | Most interesting statistical paradoxes
Suppose you obtained a data on births in royal family of some kingdom.
In the family tree each birth was noted. What is peculiar about this
family was that parents were trying to have a baby only |
1,317 | Most interesting statistical paradoxes | One of my "favorites", meaning that it's what drives me crazy about the interpretation of many studies (and often by the authors themselves, not just the media) is that of Survivorship Bias.
One way to imagine it is suppose there's some effect that is very detrimental to the subjects, so much so that it has a very good... | Most interesting statistical paradoxes | One of my "favorites", meaning that it's what drives me crazy about the interpretation of many studies (and often by the authors themselves, not just the media) is that of Survivorship Bias.
One way t | Most interesting statistical paradoxes
One of my "favorites", meaning that it's what drives me crazy about the interpretation of many studies (and often by the authors themselves, not just the media) is that of Survivorship Bias.
One way to imagine it is suppose there's some effect that is very detrimental to the subje... | Most interesting statistical paradoxes
One of my "favorites", meaning that it's what drives me crazy about the interpretation of many studies (and often by the authors themselves, not just the media) is that of Survivorship Bias.
One way t |
1,318 | Most interesting statistical paradoxes | Try the Borel–Kolmogorov paradox, where conditional probabilities behave badly. One example had the question
Let $X_1, X_2$ be independent exponential random variables with
parameter $1$.
Find the conditional PDF of $X_1+X_2$ given that $\frac{X_1}{X_2}=1.$
Find the conditional PDF of $X_1+X_2$ given that $X_1-X_2=0... | Most interesting statistical paradoxes | Try the Borel–Kolmogorov paradox, where conditional probabilities behave badly. One example had the question
Let $X_1, X_2$ be independent exponential random variables with
parameter $1$.
Find the | Most interesting statistical paradoxes
Try the Borel–Kolmogorov paradox, where conditional probabilities behave badly. One example had the question
Let $X_1, X_2$ be independent exponential random variables with
parameter $1$.
Find the conditional PDF of $X_1+X_2$ given that $\frac{X_1}{X_2}=1.$
Find the conditional... | Most interesting statistical paradoxes
Try the Borel–Kolmogorov paradox, where conditional probabilities behave badly. One example had the question
Let $X_1, X_2$ be independent exponential random variables with
parameter $1$.
Find the |
1,319 | Most interesting statistical paradoxes | Misspecification paradox
If $T$ is a method of statistical inference with a certain model assumption, say the true $P$ is assumed to be in some set ${\cal P}$ (e.g., $P$ may be assumed to be an i.i.d. normal distribution model for data $X_1,\ldots,X_n$), it is standard practice (in some quarters) to run a model misspec... | Most interesting statistical paradoxes | Misspecification paradox
If $T$ is a method of statistical inference with a certain model assumption, say the true $P$ is assumed to be in some set ${\cal P}$ (e.g., $P$ may be assumed to be an i.i.d. | Most interesting statistical paradoxes
Misspecification paradox
If $T$ is a method of statistical inference with a certain model assumption, say the true $P$ is assumed to be in some set ${\cal P}$ (e.g., $P$ may be assumed to be an i.i.d. normal distribution model for data $X_1,\ldots,X_n$), it is standard practice (i... | Most interesting statistical paradoxes
Misspecification paradox
If $T$ is a method of statistical inference with a certain model assumption, say the true $P$ is assumed to be in some set ${\cal P}$ (e.g., $P$ may be assumed to be an i.i.d. |
1,320 | Most interesting statistical paradoxes | 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.
I'm surprised no one has mentioned Newcombe's Paradox ... | Most interesting statistical paradoxes | 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.
| Most interesting statistical paradoxes
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.
I'm surprised n... | Most interesting statistical paradoxes
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.
|
1,321 | Most interesting statistical paradoxes | There are lists of paradoxes on Wikipedia!
https://en.wikipedia.org/wiki/Category:Statistical_paradoxes
https://en.wikipedia.org/wiki/Category:Probability_theory_paradoxes | Most interesting statistical paradoxes | There are lists of paradoxes on Wikipedia!
https://en.wikipedia.org/wiki/Category:Statistical_paradoxes
https://en.wikipedia.org/wiki/Category:Probability_theory_paradoxes | Most interesting statistical paradoxes
There are lists of paradoxes on Wikipedia!
https://en.wikipedia.org/wiki/Category:Statistical_paradoxes
https://en.wikipedia.org/wiki/Category:Probability_theory_paradoxes | Most interesting statistical paradoxes
There are lists of paradoxes on Wikipedia!
https://en.wikipedia.org/wiki/Category:Statistical_paradoxes
https://en.wikipedia.org/wiki/Category:Probability_theory_paradoxes |
1,322 | Most interesting statistical paradoxes | The hot hand paradox.
Quoting Miller and Sanjurjo's paper:
Jack takes a coin from his pocket and decides that he will flip it 4 times in a row, writing down the outcome of each flip on a scrap of paper. After he is done flipping, he will look at the flips that immediately followed an outcome of heads, and compute the ... | Most interesting statistical paradoxes | The hot hand paradox.
Quoting Miller and Sanjurjo's paper:
Jack takes a coin from his pocket and decides that he will flip it 4 times in a row, writing down the outcome of each flip on a scrap of pap | Most interesting statistical paradoxes
The hot hand paradox.
Quoting Miller and Sanjurjo's paper:
Jack takes a coin from his pocket and decides that he will flip it 4 times in a row, writing down the outcome of each flip on a scrap of paper. After he is done flipping, he will look at the flips that immediately followe... | Most interesting statistical paradoxes
The hot hand paradox.
Quoting Miller and Sanjurjo's paper:
Jack takes a coin from his pocket and decides that he will flip it 4 times in a row, writing down the outcome of each flip on a scrap of pap |
1,323 | Most interesting statistical paradoxes | Let x, y, and z be uncorrelated vectors. Yet x/z and y/z will be correlated. | Most interesting statistical paradoxes | Let x, y, and z be uncorrelated vectors. Yet x/z and y/z will be correlated. | Most interesting statistical paradoxes
Let x, y, and z be uncorrelated vectors. Yet x/z and y/z will be correlated. | Most interesting statistical paradoxes
Let x, y, and z be uncorrelated vectors. Yet x/z and y/z will be correlated. |
1,324 | Maximum Likelihood Estimation (MLE) in layman terms | Say you have some data. Say you're willing to assume that the data comes from some distribution -- perhaps Gaussian. There are an infinite number of different Gaussians that the data could have come from (which correspond to the combination of the infinite number of means and variances that a Gaussian distribution ca... | Maximum Likelihood Estimation (MLE) in layman terms | Say you have some data. Say you're willing to assume that the data comes from some distribution -- perhaps Gaussian. There are an infinite number of different Gaussians that the data could have come | Maximum Likelihood Estimation (MLE) in layman terms
Say you have some data. Say you're willing to assume that the data comes from some distribution -- perhaps Gaussian. There are an infinite number of different Gaussians that the data could have come from (which correspond to the combination of the infinite number of... | Maximum Likelihood Estimation (MLE) in layman terms
Say you have some data. Say you're willing to assume that the data comes from some distribution -- perhaps Gaussian. There are an infinite number of different Gaussians that the data could have come |
1,325 | Maximum Likelihood Estimation (MLE) in layman terms | Maximum Likelihood Estimation (MLE) is a technique to find the most likely
function that explains observed data. I think math is necessary, but don't let it
scare you!
Let's say that we have a set of points in the $x,y$ plane, and we want to know
the function parameters $\beta$ and $\sigma$ that most likely fit the d... | Maximum Likelihood Estimation (MLE) in layman terms | Maximum Likelihood Estimation (MLE) is a technique to find the most likely
function that explains observed data. I think math is necessary, but don't let it
scare you!
Let's say that we have a set of | Maximum Likelihood Estimation (MLE) in layman terms
Maximum Likelihood Estimation (MLE) is a technique to find the most likely
function that explains observed data. I think math is necessary, but don't let it
scare you!
Let's say that we have a set of points in the $x,y$ plane, and we want to know
the function parame... | Maximum Likelihood Estimation (MLE) in layman terms
Maximum Likelihood Estimation (MLE) is a technique to find the most likely
function that explains observed data. I think math is necessary, but don't let it
scare you!
Let's say that we have a set of |
1,326 | Maximum Likelihood Estimation (MLE) in layman terms | The maximum likelihood (ML) estimate of a parameter is the value of that parameter under which your actual observed data are most likely, relative to any other possible values of the parameter.
The idea is that there are any number of "true" parameter values that could have led to your actually observed data with some ... | Maximum Likelihood Estimation (MLE) in layman terms | The maximum likelihood (ML) estimate of a parameter is the value of that parameter under which your actual observed data are most likely, relative to any other possible values of the parameter.
The id | Maximum Likelihood Estimation (MLE) in layman terms
The maximum likelihood (ML) estimate of a parameter is the value of that parameter under which your actual observed data are most likely, relative to any other possible values of the parameter.
The idea is that there are any number of "true" parameter values that coul... | Maximum Likelihood Estimation (MLE) in layman terms
The maximum likelihood (ML) estimate of a parameter is the value of that parameter under which your actual observed data are most likely, relative to any other possible values of the parameter.
The id |
1,327 | Maximum Likelihood Estimation (MLE) in layman terms | It is possible to say something without using (much) math, but for actual statistical applications of maximum likelihood you need mathematics.
Maximum likelihood estimation is related to what philosophers call inference to the best explanation, or abduction. We use this all the time! Note, I do not say that maximum lik... | Maximum Likelihood Estimation (MLE) in layman terms | It is possible to say something without using (much) math, but for actual statistical applications of maximum likelihood you need mathematics.
Maximum likelihood estimation is related to what philosop | Maximum Likelihood Estimation (MLE) in layman terms
It is possible to say something without using (much) math, but for actual statistical applications of maximum likelihood you need mathematics.
Maximum likelihood estimation is related to what philosophers call inference to the best explanation, or abduction. We use th... | Maximum Likelihood Estimation (MLE) in layman terms
It is possible to say something without using (much) math, but for actual statistical applications of maximum likelihood you need mathematics.
Maximum likelihood estimation is related to what philosop |
1,328 | Maximum Likelihood Estimation (MLE) in layman terms | The MLE is the value of the parameter of interest that maximizes the probability of observing the data that you observed. In other words, it is the value of the parameter that makes the observed data most likely to have been observed. | Maximum Likelihood Estimation (MLE) in layman terms | The MLE is the value of the parameter of interest that maximizes the probability of observing the data that you observed. In other words, it is the value of the parameter that makes the observed data | Maximum Likelihood Estimation (MLE) in layman terms
The MLE is the value of the parameter of interest that maximizes the probability of observing the data that you observed. In other words, it is the value of the parameter that makes the observed data most likely to have been observed. | Maximum Likelihood Estimation (MLE) in layman terms
The MLE is the value of the parameter of interest that maximizes the probability of observing the data that you observed. In other words, it is the value of the parameter that makes the observed data |
1,329 | Maximum Likelihood Estimation (MLE) in layman terms | If your data come from a probability distribution with an unknown parameter $\theta$, the maximum likelihood estimate of $\theta$ is that which makes the data you actually observed most probable.
In the case where your data are independent samples from that probability distribution, the likelihood (for a given value of... | Maximum Likelihood Estimation (MLE) in layman terms | If your data come from a probability distribution with an unknown parameter $\theta$, the maximum likelihood estimate of $\theta$ is that which makes the data you actually observed most probable.
In t | Maximum Likelihood Estimation (MLE) in layman terms
If your data come from a probability distribution with an unknown parameter $\theta$, the maximum likelihood estimate of $\theta$ is that which makes the data you actually observed most probable.
In the case where your data are independent samples from that probabilit... | Maximum Likelihood Estimation (MLE) in layman terms
If your data come from a probability distribution with an unknown parameter $\theta$, the maximum likelihood estimate of $\theta$ is that which makes the data you actually observed most probable.
In t |
1,330 | Maximum Likelihood Estimation (MLE) in layman terms | Let's play a game: I am in a dark room, no one can see what I do but you know that either (a) I throw a dice and count the number of '1's as 'success' or (b) I toss a coin and I count the number of heads as 'success'.
As I said, you can not see which of the two I do but I give you just one single piece of informatio... | Maximum Likelihood Estimation (MLE) in layman terms | Let's play a game: I am in a dark room, no one can see what I do but you know that either (a) I throw a dice and count the number of '1's as 'success' or (b) I toss a coin and I count the number of h | Maximum Likelihood Estimation (MLE) in layman terms
Let's play a game: I am in a dark room, no one can see what I do but you know that either (a) I throw a dice and count the number of '1's as 'success' or (b) I toss a coin and I count the number of heads as 'success'.
As I said, you can not see which of the two I d... | Maximum Likelihood Estimation (MLE) in layman terms
Let's play a game: I am in a dark room, no one can see what I do but you know that either (a) I throw a dice and count the number of '1's as 'success' or (b) I toss a coin and I count the number of h |
1,331 | Maximum Likelihood Estimation (MLE) in layman terms | Say you have some data $X$ that comes from Normal distribution with unknown mean $\mu$. You want to find what is the value of $\mu$, however you have no idea how to achieve it. One thing you could do is to try several values of $\mu$ and check which of them is the best one. To do this you need however some method for c... | Maximum Likelihood Estimation (MLE) in layman terms | Say you have some data $X$ that comes from Normal distribution with unknown mean $\mu$. You want to find what is the value of $\mu$, however you have no idea how to achieve it. One thing you could do | Maximum Likelihood Estimation (MLE) in layman terms
Say you have some data $X$ that comes from Normal distribution with unknown mean $\mu$. You want to find what is the value of $\mu$, however you have no idea how to achieve it. One thing you could do is to try several values of $\mu$ and check which of them is the bes... | Maximum Likelihood Estimation (MLE) in layman terms
Say you have some data $X$ that comes from Normal distribution with unknown mean $\mu$. You want to find what is the value of $\mu$, however you have no idea how to achieve it. One thing you could do |
1,332 | Maximum Likelihood Estimation (MLE) in layman terms | One task in statistics is to fit a distribution function to a set of data points to generalize what's intrinsic about the data. When one is fitting a distribution a)choose an appropriate distribution b)set the movable parts (parameters), for example mean, variance, etc. When doing all this one also needs an objective, ... | Maximum Likelihood Estimation (MLE) in layman terms | One task in statistics is to fit a distribution function to a set of data points to generalize what's intrinsic about the data. When one is fitting a distribution a)choose an appropriate distribution | Maximum Likelihood Estimation (MLE) in layman terms
One task in statistics is to fit a distribution function to a set of data points to generalize what's intrinsic about the data. When one is fitting a distribution a)choose an appropriate distribution b)set the movable parts (parameters), for example mean, variance, et... | Maximum Likelihood Estimation (MLE) in layman terms
One task in statistics is to fit a distribution function to a set of data points to generalize what's intrinsic about the data. When one is fitting a distribution a)choose an appropriate distribution |
1,333 | Maximum Likelihood Estimation (MLE) in layman terms | As you wanted, I will use very naive terms. Suppose you have collected some data $\{y_1, y_2,\ldots,y_n\}$ and have reasonable assumption that they follow some probability distribution. But you don't usually know the parameter(s) of that distribution from such samples. Parameters are the "population characteristics" of... | Maximum Likelihood Estimation (MLE) in layman terms | As you wanted, I will use very naive terms. Suppose you have collected some data $\{y_1, y_2,\ldots,y_n\}$ and have reasonable assumption that they follow some probability distribution. But you don't | Maximum Likelihood Estimation (MLE) in layman terms
As you wanted, I will use very naive terms. Suppose you have collected some data $\{y_1, y_2,\ldots,y_n\}$ and have reasonable assumption that they follow some probability distribution. But you don't usually know the parameter(s) of that distribution from such samples... | Maximum Likelihood Estimation (MLE) in layman terms
As you wanted, I will use very naive terms. Suppose you have collected some data $\{y_1, y_2,\ldots,y_n\}$ and have reasonable assumption that they follow some probability distribution. But you don't |
1,334 | Maximum Likelihood Estimation (MLE) in layman terms | Suppose you have a coin. Tossing it can give either heads or tails. But you don't know if it's a fair coin. So you toss it 1000 times. It comes up as heads 1000 times, and never as tails.
Now, it's possible that this is actually a fair coin with a 50/50 chance for heads/tails, but it doesn't seem likely, does it? The ... | Maximum Likelihood Estimation (MLE) in layman terms | Suppose you have a coin. Tossing it can give either heads or tails. But you don't know if it's a fair coin. So you toss it 1000 times. It comes up as heads 1000 times, and never as tails.
Now, it's p | Maximum Likelihood Estimation (MLE) in layman terms
Suppose you have a coin. Tossing it can give either heads or tails. But you don't know if it's a fair coin. So you toss it 1000 times. It comes up as heads 1000 times, and never as tails.
Now, it's possible that this is actually a fair coin with a 50/50 chance for he... | Maximum Likelihood Estimation (MLE) in layman terms
Suppose you have a coin. Tossing it can give either heads or tails. But you don't know if it's a fair coin. So you toss it 1000 times. It comes up as heads 1000 times, and never as tails.
Now, it's p |
1,335 | Maximum Likelihood Estimation (MLE) in layman terms | Just to show very simple graphics and R code for MLEs in
binomial and Poisson models.
Binomial. Suppose you know there are $n = 50$ trials of which $x=19$ are Successes. Then for what value of $p$ is the binomial PDF maximized?
This PDF considered as a function of $p$ and (possibly) without its norming constant) is cal... | Maximum Likelihood Estimation (MLE) in layman terms | Just to show very simple graphics and R code for MLEs in
binomial and Poisson models.
Binomial. Suppose you know there are $n = 50$ trials of which $x=19$ are Successes. Then for what value of $p$ is | Maximum Likelihood Estimation (MLE) in layman terms
Just to show very simple graphics and R code for MLEs in
binomial and Poisson models.
Binomial. Suppose you know there are $n = 50$ trials of which $x=19$ are Successes. Then for what value of $p$ is the binomial PDF maximized?
This PDF considered as a function of $p$... | Maximum Likelihood Estimation (MLE) in layman terms
Just to show very simple graphics and R code for MLEs in
binomial and Poisson models.
Binomial. Suppose you know there are $n = 50$ trials of which $x=19$ are Successes. Then for what value of $p$ is |
1,336 | Maximum Likelihood Estimation (MLE) in layman terms | You have a model, which you impose that the data comes from. In a way, you wanna reconcile between the model and reality. To do so, you wanna minimize the discrepancy between the two. How would you do that? You have $\Theta$ vector of parameters that you can tune in order to achieve so. Minimizing the discrepancy betwe... | Maximum Likelihood Estimation (MLE) in layman terms | You have a model, which you impose that the data comes from. In a way, you wanna reconcile between the model and reality. To do so, you wanna minimize the discrepancy between the two. How would you do | Maximum Likelihood Estimation (MLE) in layman terms
You have a model, which you impose that the data comes from. In a way, you wanna reconcile between the model and reality. To do so, you wanna minimize the discrepancy between the two. How would you do that? You have $\Theta$ vector of parameters that you can tune in o... | Maximum Likelihood Estimation (MLE) in layman terms
You have a model, which you impose that the data comes from. In a way, you wanna reconcile between the model and reality. To do so, you wanna minimize the discrepancy between the two. How would you do |
1,337 | Maximum Likelihood Estimation (MLE) in layman terms | The way I understand MLE is this: You only get to see what the nature wants you to see. Things you see are facts. These facts have an underlying process that generated it. These process are hidden, unknown, needs to be discovered. Then the question is: Given the observed fact, what is the likelihood that process P1 gen... | Maximum Likelihood Estimation (MLE) in layman terms | The way I understand MLE is this: You only get to see what the nature wants you to see. Things you see are facts. These facts have an underlying process that generated it. These process are hidden, un | Maximum Likelihood Estimation (MLE) in layman terms
The way I understand MLE is this: You only get to see what the nature wants you to see. Things you see are facts. These facts have an underlying process that generated it. These process are hidden, unknown, needs to be discovered. Then the question is: Given the obser... | Maximum Likelihood Estimation (MLE) in layman terms
The way I understand MLE is this: You only get to see what the nature wants you to see. Things you see are facts. These facts have an underlying process that generated it. These process are hidden, un |
1,338 | Using k-fold cross-validation for time-series model selection | Time-series (or other intrinsically ordered data) can be problematic for cross-validation. If some pattern emerges in year 3 and stays for years 4-6, then your model can pick up on it, even though it wasn't part of years 1 & 2.
An approach that's sometimes more principled for time series is forward chaining, where you... | Using k-fold cross-validation for time-series model selection | Time-series (or other intrinsically ordered data) can be problematic for cross-validation. If some pattern emerges in year 3 and stays for years 4-6, then your model can pick up on it, even though it | Using k-fold cross-validation for time-series model selection
Time-series (or other intrinsically ordered data) can be problematic for cross-validation. If some pattern emerges in year 3 and stays for years 4-6, then your model can pick up on it, even though it wasn't part of years 1 & 2.
An approach that's sometimes ... | Using k-fold cross-validation for time-series model selection
Time-series (or other intrinsically ordered data) can be problematic for cross-validation. If some pattern emerges in year 3 and stays for years 4-6, then your model can pick up on it, even though it |
1,339 | Using k-fold cross-validation for time-series model selection | The method I use for cross-validating my time-series model is cross-validation on a rolling basis. Start with a small subset of data for training purpose, forecast for the later data points and then checking the accuracy for the forecasted data points. The same forecasted data points are then included as part of the ne... | Using k-fold cross-validation for time-series model selection | The method I use for cross-validating my time-series model is cross-validation on a rolling basis. Start with a small subset of data for training purpose, forecast for the later data points and then c | Using k-fold cross-validation for time-series model selection
The method I use for cross-validating my time-series model is cross-validation on a rolling basis. Start with a small subset of data for training purpose, forecast for the later data points and then checking the accuracy for the forecasted data points. The s... | Using k-fold cross-validation for time-series model selection
The method I use for cross-validating my time-series model is cross-validation on a rolling basis. Start with a small subset of data for training purpose, forecast for the later data points and then c |
1,340 | Using k-fold cross-validation for time-series model selection | The "canonical" way to do time-series cross-validation (at least as described by @Rob Hyndman) is to "roll" through the dataset.
i.e.:
fold 1 : training [1], test [2]
fold 2 : training [1 2], test [3]
fold 3 : training [1 2 3], test [4]
fold 4 : training [1 2 3 4], test [5]
fold 5 : training [1 2 3 4 5], test [6]
Bas... | Using k-fold cross-validation for time-series model selection | The "canonical" way to do time-series cross-validation (at least as described by @Rob Hyndman) is to "roll" through the dataset.
i.e.:
fold 1 : training [1], test [2]
fold 2 : training [1 2], test [3 | Using k-fold cross-validation for time-series model selection
The "canonical" way to do time-series cross-validation (at least as described by @Rob Hyndman) is to "roll" through the dataset.
i.e.:
fold 1 : training [1], test [2]
fold 2 : training [1 2], test [3]
fold 3 : training [1 2 3], test [4]
fold 4 : training [1... | Using k-fold cross-validation for time-series model selection
The "canonical" way to do time-series cross-validation (at least as described by @Rob Hyndman) is to "roll" through the dataset.
i.e.:
fold 1 : training [1], test [2]
fold 2 : training [1 2], test [3 |
1,341 | Using k-fold cross-validation for time-series model selection | There is nothing wrong with using blocks of "future" data for time series cross validation in most situations. By most situations I refer to models for stationary data, which are the models that we typically use. E.g. when you fit an $\mathit{ARIMA}(p,d,q)$, with $d>0$ to a series, you take $d$ differences of the serie... | Using k-fold cross-validation for time-series model selection | There is nothing wrong with using blocks of "future" data for time series cross validation in most situations. By most situations I refer to models for stationary data, which are the models that we ty | Using k-fold cross-validation for time-series model selection
There is nothing wrong with using blocks of "future" data for time series cross validation in most situations. By most situations I refer to models for stationary data, which are the models that we typically use. E.g. when you fit an $\mathit{ARIMA}(p,d,q)$,... | Using k-fold cross-validation for time-series model selection
There is nothing wrong with using blocks of "future" data for time series cross validation in most situations. By most situations I refer to models for stationary data, which are the models that we ty |
1,342 | Using k-fold cross-validation for time-series model selection | As commented by @thebigdog, "On the use of cross-validation for time series predictor evaluation" by Bergmeir et al. discusses cross-validation in the context of stationary time-series and determine Forward Chaining (proposed by other answerers) to be unhelpful. Note, Forward Chaining is called Last-Block Evaluation in... | Using k-fold cross-validation for time-series model selection | As commented by @thebigdog, "On the use of cross-validation for time series predictor evaluation" by Bergmeir et al. discusses cross-validation in the context of stationary time-series and determine F | Using k-fold cross-validation for time-series model selection
As commented by @thebigdog, "On the use of cross-validation for time series predictor evaluation" by Bergmeir et al. discusses cross-validation in the context of stationary time-series and determine Forward Chaining (proposed by other answerers) to be unhelp... | Using k-fold cross-validation for time-series model selection
As commented by @thebigdog, "On the use of cross-validation for time series predictor evaluation" by Bergmeir et al. discusses cross-validation in the context of stationary time-series and determine F |
1,343 | How would you explain the difference between correlation and covariance? | The problem with covariances is that they are hard to compare: when you calculate the covariance of a set of heights and weights, as expressed in (respectively) meters and kilograms, you will get a different covariance from when you do it in other units (which already gives a problem for people doing the same thing wit... | How would you explain the difference between correlation and covariance? | The problem with covariances is that they are hard to compare: when you calculate the covariance of a set of heights and weights, as expressed in (respectively) meters and kilograms, you will get a di | How would you explain the difference between correlation and covariance?
The problem with covariances is that they are hard to compare: when you calculate the covariance of a set of heights and weights, as expressed in (respectively) meters and kilograms, you will get a different covariance from when you do it in other... | How would you explain the difference between correlation and covariance?
The problem with covariances is that they are hard to compare: when you calculate the covariance of a set of heights and weights, as expressed in (respectively) meters and kilograms, you will get a di |
1,344 | How would you explain the difference between correlation and covariance? | The requirements of these types of questions strike me as a bit bizarre. Here is a mathematical concept/formula, yet I want to talk about it in some context completely devoid of mathematical symbols. I also think it should be stated that the actual algebra necessary to understand the formulas, I would think, should be ... | How would you explain the difference between correlation and covariance? | The requirements of these types of questions strike me as a bit bizarre. Here is a mathematical concept/formula, yet I want to talk about it in some context completely devoid of mathematical symbols. | How would you explain the difference between correlation and covariance?
The requirements of these types of questions strike me as a bit bizarre. Here is a mathematical concept/formula, yet I want to talk about it in some context completely devoid of mathematical symbols. I also think it should be stated that the actua... | How would you explain the difference between correlation and covariance?
The requirements of these types of questions strike me as a bit bizarre. Here is a mathematical concept/formula, yet I want to talk about it in some context completely devoid of mathematical symbols. |
1,345 | How would you explain the difference between correlation and covariance? | Correlation (r) is the covariance (cov) of your variables (x & y) divided by (or adjusted by, in other words) each of their standard deviations ($\sqrt{Var[x]Var[y]}$).
That is, correlation is simply a representation of covariance so the result must lay between -1 (perfectly inversely correlated) an +1 (perfectly posi... | How would you explain the difference between correlation and covariance? | Correlation (r) is the covariance (cov) of your variables (x & y) divided by (or adjusted by, in other words) each of their standard deviations ($\sqrt{Var[x]Var[y]}$).
That is, correlation is simply | How would you explain the difference between correlation and covariance?
Correlation (r) is the covariance (cov) of your variables (x & y) divided by (or adjusted by, in other words) each of their standard deviations ($\sqrt{Var[x]Var[y]}$).
That is, correlation is simply a representation of covariance so the result m... | How would you explain the difference between correlation and covariance?
Correlation (r) is the covariance (cov) of your variables (x & y) divided by (or adjusted by, in other words) each of their standard deviations ($\sqrt{Var[x]Var[y]}$).
That is, correlation is simply |
1,346 | How would you explain the difference between correlation and covariance? | If you are familiar with the idea of centering and standardizing, x-xbar is to center x at its mean. Same applies to y. So covariance simply centers the data. Correlation, however, not only centers the data but also scales using the standard deviation (standardize). The multiplication and summation is the dot-produ... | How would you explain the difference between correlation and covariance? | If you are familiar with the idea of centering and standardizing, x-xbar is to center x at its mean. Same applies to y. So covariance simply centers the data. Correlation, however, not only centers | How would you explain the difference between correlation and covariance?
If you are familiar with the idea of centering and standardizing, x-xbar is to center x at its mean. Same applies to y. So covariance simply centers the data. Correlation, however, not only centers the data but also scales using the standard de... | How would you explain the difference between correlation and covariance?
If you are familiar with the idea of centering and standardizing, x-xbar is to center x at its mean. Same applies to y. So covariance simply centers the data. Correlation, however, not only centers |
1,347 | How would you explain the difference between correlation and covariance? | 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.
As far as I've understood it. Correlation is a "normal... | How would you explain the difference between correlation and covariance? | 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.
| How would you explain the difference between correlation and covariance?
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.
... | How would you explain the difference between correlation and covariance?
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.
|
1,348 | How would you explain the difference between correlation and covariance? | Correlation is scaled to be between -1 and +1 depending on whether there is positive or negative correlation, and is dimensionless. The covariance however, ranges from zero, in the case of two independent variables, to Var(X), in the case where the two sets of data are equal. The units of COV(X,Y) are the units of X ti... | How would you explain the difference between correlation and covariance? | Correlation is scaled to be between -1 and +1 depending on whether there is positive or negative correlation, and is dimensionless. The covariance however, ranges from zero, in the case of two indepen | How would you explain the difference between correlation and covariance?
Correlation is scaled to be between -1 and +1 depending on whether there is positive or negative correlation, and is dimensionless. The covariance however, ranges from zero, in the case of two independent variables, to Var(X), in the case where th... | How would you explain the difference between correlation and covariance?
Correlation is scaled to be between -1 and +1 depending on whether there is positive or negative correlation, and is dimensionless. The covariance however, ranges from zero, in the case of two indepen |
1,349 | PCA and proportion of variance explained | In case of PCA, "variance" means summative variance or multivariate variability or overall variability or total variability. Below is the covariance matrix of some 3 variables. Their variances are on the diagonal, and the sum of the 3 values (3.448) is the overall variability.
1.343730519 -.160152268 .186470243... | PCA and proportion of variance explained | In case of PCA, "variance" means summative variance or multivariate variability or overall variability or total variability. Below is the covariance matrix of some 3 variables. Their variances are on | PCA and proportion of variance explained
In case of PCA, "variance" means summative variance or multivariate variability or overall variability or total variability. Below is the covariance matrix of some 3 variables. Their variances are on the diagonal, and the sum of the 3 values (3.448) is the overall variability.
... | PCA and proportion of variance explained
In case of PCA, "variance" means summative variance or multivariate variability or overall variability or total variability. Below is the covariance matrix of some 3 variables. Their variances are on |
1,350 | PCA and proportion of variance explained | @ttnphns has provided a good answer, perhaps I can add a few points. First, I want to point out that there was a relevant question on CV, with a really strong answer—you definitely want to check it out. In what follows, I will refer to the plots shown in that answer.
All three plots display the same data. Notice t... | PCA and proportion of variance explained | @ttnphns has provided a good answer, perhaps I can add a few points. First, I want to point out that there was a relevant question on CV, with a really strong answer—you definitely want to check it o | PCA and proportion of variance explained
@ttnphns has provided a good answer, perhaps I can add a few points. First, I want to point out that there was a relevant question on CV, with a really strong answer—you definitely want to check it out. In what follows, I will refer to the plots shown in that answer.
All thr... | PCA and proportion of variance explained
@ttnphns has provided a good answer, perhaps I can add a few points. First, I want to point out that there was a relevant question on CV, with a really strong answer—you definitely want to check it o |
1,351 | PCA and proportion of variance explained | There is a very simple, direct, and precise mathematical answer to the original question.
The first PC is a linear combination of the original variables $Y_1$, $Y_2$, $\dots$, $Y_p$ that maximizes the total of the $R_i^2$ statistics when predicting the original variables as a regression function of the linear combinat... | PCA and proportion of variance explained | There is a very simple, direct, and precise mathematical answer to the original question.
The first PC is a linear combination of the original variables $Y_1$, $Y_2$, $\dots$, $Y_p$ that maximizes th | PCA and proportion of variance explained
There is a very simple, direct, and precise mathematical answer to the original question.
The first PC is a linear combination of the original variables $Y_1$, $Y_2$, $\dots$, $Y_p$ that maximizes the total of the $R_i^2$ statistics when predicting the original variables as a r... | PCA and proportion of variance explained
There is a very simple, direct, and precise mathematical answer to the original question.
The first PC is a linear combination of the original variables $Y_1$, $Y_2$, $\dots$, $Y_p$ that maximizes th |
1,352 | PCA and proportion of variance explained | Think about $Y=A+B$ as random variable $Y$ being explained by two new random variables $A$ and $B$. why we do this? Maybe $Y$ is complex but $A$ and $B$ are less complex. Anyhow, the portion of variance of $Y$ is explained by those of $A$ and $B$. $var(Y) = var(A) + var (B) + 2cov(A,B)$. Application of this to the line... | PCA and proportion of variance explained | Think about $Y=A+B$ as random variable $Y$ being explained by two new random variables $A$ and $B$. why we do this? Maybe $Y$ is complex but $A$ and $B$ are less complex. Anyhow, the portion of varian | PCA and proportion of variance explained
Think about $Y=A+B$ as random variable $Y$ being explained by two new random variables $A$ and $B$. why we do this? Maybe $Y$ is complex but $A$ and $B$ are less complex. Anyhow, the portion of variance of $Y$ is explained by those of $A$ and $B$. $var(Y) = var(A) + var (B) + 2c... | PCA and proportion of variance explained
Think about $Y=A+B$ as random variable $Y$ being explained by two new random variables $A$ and $B$. why we do this? Maybe $Y$ is complex but $A$ and $B$ are less complex. Anyhow, the portion of varian |
1,353 | How is it possible that validation loss is increasing while validation accuracy is increasing as well | Other answers explain well how accuracy and loss are not necessarily exactly (inversely) correlated, as loss measures a difference between raw output (float) and a class (0 or 1 in the case of binary classification), while accuracy measures the difference between thresholded output (0 or 1) and class. So if raw outputs... | How is it possible that validation loss is increasing while validation accuracy is increasing as wel | Other answers explain well how accuracy and loss are not necessarily exactly (inversely) correlated, as loss measures a difference between raw output (float) and a class (0 or 1 in the case of binary | How is it possible that validation loss is increasing while validation accuracy is increasing as well
Other answers explain well how accuracy and loss are not necessarily exactly (inversely) correlated, as loss measures a difference between raw output (float) and a class (0 or 1 in the case of binary classification), w... | How is it possible that validation loss is increasing while validation accuracy is increasing as wel
Other answers explain well how accuracy and loss are not necessarily exactly (inversely) correlated, as loss measures a difference between raw output (float) and a class (0 or 1 in the case of binary |
1,354 | How is it possible that validation loss is increasing while validation accuracy is increasing as well | Accuracy of a set is evaluated by just cross-checking the highest softmax output and the correct labeled class.It is not depended on how high is the softmax output.
To make it clearer, here are some numbers.
Suppose there are 2 classes - horse and dog. For our case, the correct class is horse . Now, the output of the s... | How is it possible that validation loss is increasing while validation accuracy is increasing as wel | Accuracy of a set is evaluated by just cross-checking the highest softmax output and the correct labeled class.It is not depended on how high is the softmax output.
To make it clearer, here are some n | How is it possible that validation loss is increasing while validation accuracy is increasing as well
Accuracy of a set is evaluated by just cross-checking the highest softmax output and the correct labeled class.It is not depended on how high is the softmax output.
To make it clearer, here are some numbers.
Suppose th... | How is it possible that validation loss is increasing while validation accuracy is increasing as wel
Accuracy of a set is evaluated by just cross-checking the highest softmax output and the correct labeled class.It is not depended on how high is the softmax output.
To make it clearer, here are some n |
1,355 | How is it possible that validation loss is increasing while validation accuracy is increasing as well | Many answers focus on the mathematical calculation explaining how is this possible. But they don't explain why it becomes so. And they cannot suggest how to digger further to be more clear.
I have 3 hypothesis. And suggest some experiments to verify them. Hopefully it can help explain this problem.
Label is noisy. Co... | How is it possible that validation loss is increasing while validation accuracy is increasing as wel | Many answers focus on the mathematical calculation explaining how is this possible. But they don't explain why it becomes so. And they cannot suggest how to digger further to be more clear.
I have 3 | How is it possible that validation loss is increasing while validation accuracy is increasing as well
Many answers focus on the mathematical calculation explaining how is this possible. But they don't explain why it becomes so. And they cannot suggest how to digger further to be more clear.
I have 3 hypothesis. And su... | How is it possible that validation loss is increasing while validation accuracy is increasing as wel
Many answers focus on the mathematical calculation explaining how is this possible. But they don't explain why it becomes so. And they cannot suggest how to digger further to be more clear.
I have 3 |
1,356 | How is it possible that validation loss is increasing while validation accuracy is increasing as well | From Ankur's answer, it seems to me that:
Accuracy measures the percentage correctness of the prediction i.e. $\frac{correct-classes}{total-classes}$
while
Loss actually tracks the inverse-confidence (for want of a better word) of the prediction. A high Loss score indicates that, even when the model is making good p... | How is it possible that validation loss is increasing while validation accuracy is increasing as wel | From Ankur's answer, it seems to me that:
Accuracy measures the percentage correctness of the prediction i.e. $\frac{correct-classes}{total-classes}$
while
Loss actually tracks the inverse-confiden | How is it possible that validation loss is increasing while validation accuracy is increasing as well
From Ankur's answer, it seems to me that:
Accuracy measures the percentage correctness of the prediction i.e. $\frac{correct-classes}{total-classes}$
while
Loss actually tracks the inverse-confidence (for want of a ... | How is it possible that validation loss is increasing while validation accuracy is increasing as wel
From Ankur's answer, it seems to me that:
Accuracy measures the percentage correctness of the prediction i.e. $\frac{correct-classes}{total-classes}$
while
Loss actually tracks the inverse-confiden |
1,357 | How is it possible that validation loss is increasing while validation accuracy is increasing as well | A model can overfit to cross entropy loss without over overfitting to accuracy.
There is a key difference between the two types of loss:
Accuracy measures whether you get the prediction right
Cross entropy measures how confident you are about a prediction
For example, if an image of a cat is passed into two models. ... | How is it possible that validation loss is increasing while validation accuracy is increasing as wel | A model can overfit to cross entropy loss without over overfitting to accuracy.
There is a key difference between the two types of loss:
Accuracy measures whether you get the prediction right
Cross | How is it possible that validation loss is increasing while validation accuracy is increasing as well
A model can overfit to cross entropy loss without over overfitting to accuracy.
There is a key difference between the two types of loss:
Accuracy measures whether you get the prediction right
Cross entropy measures h... | How is it possible that validation loss is increasing while validation accuracy is increasing as wel
A model can overfit to cross entropy loss without over overfitting to accuracy.
There is a key difference between the two types of loss:
Accuracy measures whether you get the prediction right
Cross |
1,358 | How is it possible that validation loss is increasing while validation accuracy is increasing as well | Let's say a label is horse and a prediction is:
cat (25%)
dog (35%)
horse (40%)
So, your model is predicting correct, but it's less sure about it. This is how you get high accuracy and high loss | How is it possible that validation loss is increasing while validation accuracy is increasing as wel | Let's say a label is horse and a prediction is:
cat (25%)
dog (35%)
horse (40%)
So, your model is predicting correct, but it's less sure about it. This is how you get high accuracy and high loss | How is it possible that validation loss is increasing while validation accuracy is increasing as well
Let's say a label is horse and a prediction is:
cat (25%)
dog (35%)
horse (40%)
So, your model is predicting correct, but it's less sure about it. This is how you get high accuracy and high loss | How is it possible that validation loss is increasing while validation accuracy is increasing as wel
Let's say a label is horse and a prediction is:
cat (25%)
dog (35%)
horse (40%)
So, your model is predicting correct, but it's less sure about it. This is how you get high accuracy and high loss |
1,359 | What are the main differences between K-means and K-nearest neighbours? | These are completely different methods. The fact that they both have the letter K in their name is a coincidence.
K-means is a clustering algorithm that tries to partition a set of points into K sets (clusters) such that the points in each cluster tend to be near each other. It is unsupervised because the points have n... | What are the main differences between K-means and K-nearest neighbours? | These are completely different methods. The fact that they both have the letter K in their name is a coincidence.
K-means is a clustering algorithm that tries to partition a set of points into K sets | What are the main differences between K-means and K-nearest neighbours?
These are completely different methods. The fact that they both have the letter K in their name is a coincidence.
K-means is a clustering algorithm that tries to partition a set of points into K sets (clusters) such that the points in each cluster ... | What are the main differences between K-means and K-nearest neighbours?
These are completely different methods. The fact that they both have the letter K in their name is a coincidence.
K-means is a clustering algorithm that tries to partition a set of points into K sets |
1,360 | What are the main differences between K-means and K-nearest neighbours? | As noted by Bitwise in their answer, k-means is a clustering algorithm. If it comes to k-nearest neighbours (k-NN) the terminology is a bit fuzzy:
in the context of classification, it is a classification algorithm, as also noted in the aforementioned answer
in general it is a problem, for which various solutions (alg... | What are the main differences between K-means and K-nearest neighbours? | As noted by Bitwise in their answer, k-means is a clustering algorithm. If it comes to k-nearest neighbours (k-NN) the terminology is a bit fuzzy:
in the context of classification, it is a classific | What are the main differences between K-means and K-nearest neighbours?
As noted by Bitwise in their answer, k-means is a clustering algorithm. If it comes to k-nearest neighbours (k-NN) the terminology is a bit fuzzy:
in the context of classification, it is a classification algorithm, as also noted in the aforementi... | What are the main differences between K-means and K-nearest neighbours?
As noted by Bitwise in their answer, k-means is a clustering algorithm. If it comes to k-nearest neighbours (k-NN) the terminology is a bit fuzzy:
in the context of classification, it is a classific |
1,361 | What are the main differences between K-means and K-nearest neighbours? | You can have a supervised k-means. You can build centroids (as in k-means) based on your labeled data. Nothing stops you. If you want to improve this, Euclidean space and Euclidean distance might not provide you the best results. You will need to choose your space (could be Riemannian space for example) and define the ... | What are the main differences between K-means and K-nearest neighbours? | You can have a supervised k-means. You can build centroids (as in k-means) based on your labeled data. Nothing stops you. If you want to improve this, Euclidean space and Euclidean distance might not | What are the main differences between K-means and K-nearest neighbours?
You can have a supervised k-means. You can build centroids (as in k-means) based on your labeled data. Nothing stops you. If you want to improve this, Euclidean space and Euclidean distance might not provide you the best results. You will need to c... | What are the main differences between K-means and K-nearest neighbours?
You can have a supervised k-means. You can build centroids (as in k-means) based on your labeled data. Nothing stops you. If you want to improve this, Euclidean space and Euclidean distance might not |
1,362 | What are the main differences between K-means and K-nearest neighbours? | K-means can create the cluster information for neighbour nodes
while KNN cannot find the cluster for a given neighbour node. | What are the main differences between K-means and K-nearest neighbours? | K-means can create the cluster information for neighbour nodes
while KNN cannot find the cluster for a given neighbour node. | What are the main differences between K-means and K-nearest neighbours?
K-means can create the cluster information for neighbour nodes
while KNN cannot find the cluster for a given neighbour node. | What are the main differences between K-means and K-nearest neighbours?
K-means can create the cluster information for neighbour nodes
while KNN cannot find the cluster for a given neighbour node. |
1,363 | What are the main differences between K-means and K-nearest neighbours? | k Means can be used as the training phase before knn is deployed in the actual classification stage. K means creates the classes represented by the centroid and class label ofthe samples belonging to each class. knn uses these parameters as well as the k number to classify an unseen new sample and assign it to one of t... | What are the main differences between K-means and K-nearest neighbours? | k Means can be used as the training phase before knn is deployed in the actual classification stage. K means creates the classes represented by the centroid and class label ofthe samples belonging to | What are the main differences between K-means and K-nearest neighbours?
k Means can be used as the training phase before knn is deployed in the actual classification stage. K means creates the classes represented by the centroid and class label ofthe samples belonging to each class. knn uses these parameters as well as... | What are the main differences between K-means and K-nearest neighbours?
k Means can be used as the training phase before knn is deployed in the actual classification stage. K means creates the classes represented by the centroid and class label ofthe samples belonging to |
1,364 | Difference between confidence intervals and prediction intervals | Your question isn't quite correct. A confidence interval gives a range for $\text{E}[y \mid x]$, as you say. A prediction interval gives a range for $y$ itself. Naturally, our best guess for $y$ is $\text{E}[y \mid x]$, so the intervals will both be centered around the same value, $x\hat{\beta}$.
As @Greg says, the st... | Difference between confidence intervals and prediction intervals | Your question isn't quite correct. A confidence interval gives a range for $\text{E}[y \mid x]$, as you say. A prediction interval gives a range for $y$ itself. Naturally, our best guess for $y$ is $\ | Difference between confidence intervals and prediction intervals
Your question isn't quite correct. A confidence interval gives a range for $\text{E}[y \mid x]$, as you say. A prediction interval gives a range for $y$ itself. Naturally, our best guess for $y$ is $\text{E}[y \mid x]$, so the intervals will both be cente... | Difference between confidence intervals and prediction intervals
Your question isn't quite correct. A confidence interval gives a range for $\text{E}[y \mid x]$, as you say. A prediction interval gives a range for $y$ itself. Naturally, our best guess for $y$ is $\ |
1,365 | Difference between confidence intervals and prediction intervals | One is a prediction of a future observation, and the other is a predicted mean response. I will give a more detailed answer to hopefully explain the difference and where it comes from, as well as how this difference manifests itself in wider intervals for prediction than for confidence.
This example might illustrate th... | Difference between confidence intervals and prediction intervals | One is a prediction of a future observation, and the other is a predicted mean response. I will give a more detailed answer to hopefully explain the difference and where it comes from, as well as how | Difference between confidence intervals and prediction intervals
One is a prediction of a future observation, and the other is a predicted mean response. I will give a more detailed answer to hopefully explain the difference and where it comes from, as well as how this difference manifests itself in wider intervals for... | Difference between confidence intervals and prediction intervals
One is a prediction of a future observation, and the other is a predicted mean response. I will give a more detailed answer to hopefully explain the difference and where it comes from, as well as how |
1,366 | Difference between confidence intervals and prediction intervals | The difference between a prediction interval and a confidence interval is the standard error.
The standard error for a confidence interval on the mean takes into account the uncertainty due to sampling. The line you computed from your sample will be different from the line that would have been computed if you had th... | Difference between confidence intervals and prediction intervals | The difference between a prediction interval and a confidence interval is the standard error.
The standard error for a confidence interval on the mean takes into account the uncertainty due to sampl | Difference between confidence intervals and prediction intervals
The difference between a prediction interval and a confidence interval is the standard error.
The standard error for a confidence interval on the mean takes into account the uncertainty due to sampling. The line you computed from your sample will be di... | Difference between confidence intervals and prediction intervals
The difference between a prediction interval and a confidence interval is the standard error.
The standard error for a confidence interval on the mean takes into account the uncertainty due to sampl |
1,367 | Difference between confidence intervals and prediction intervals | I found the following explanation helpful:
Confidence intervals tell you about how well you have determined the mean. Assume that the data really are randomly sampled from a
Gaussian distribution. If you do this many times, and calculate a
confidence interval of the mean from each sample, you'd expect about
95 %... | Difference between confidence intervals and prediction intervals | I found the following explanation helpful:
Confidence intervals tell you about how well you have determined the mean. Assume that the data really are randomly sampled from a
Gaussian distribution. | Difference between confidence intervals and prediction intervals
I found the following explanation helpful:
Confidence intervals tell you about how well you have determined the mean. Assume that the data really are randomly sampled from a
Gaussian distribution. If you do this many times, and calculate a
confidence... | Difference between confidence intervals and prediction intervals
I found the following explanation helpful:
Confidence intervals tell you about how well you have determined the mean. Assume that the data really are randomly sampled from a
Gaussian distribution. |
1,368 | Difference between confidence intervals and prediction intervals | Short answer:
A prediction interval is an interval associated with a random variable yet to be observed (forecasting).
A confidence interval is an interval associated with a parameter and is a frequentist concept.
Check full answer here from Rob Hyndman, the creator of forecast package in R. | Difference between confidence intervals and prediction intervals | Short answer:
A prediction interval is an interval associated with a random variable yet to be observed (forecasting).
A confidence interval is an interval associated with a parameter and is a frequen | Difference between confidence intervals and prediction intervals
Short answer:
A prediction interval is an interval associated with a random variable yet to be observed (forecasting).
A confidence interval is an interval associated with a parameter and is a frequentist concept.
Check full answer here from Rob Hyndman, ... | Difference between confidence intervals and prediction intervals
Short answer:
A prediction interval is an interval associated with a random variable yet to be observed (forecasting).
A confidence interval is an interval associated with a parameter and is a frequen |
1,369 | Difference between confidence intervals and prediction intervals | This answer is for those readers who could not fully understand the previous answers. Let's discuss a specific example. Suppose you try to predict the people's weight from their height, sex (male, female) and diet (standard, low carb, vegetarian). Currently, there are more than 8 billion people on Earth. Of course, you... | Difference between confidence intervals and prediction intervals | This answer is for those readers who could not fully understand the previous answers. Let's discuss a specific example. Suppose you try to predict the people's weight from their height, sex (male, fem | Difference between confidence intervals and prediction intervals
This answer is for those readers who could not fully understand the previous answers. Let's discuss a specific example. Suppose you try to predict the people's weight from their height, sex (male, female) and diet (standard, low carb, vegetarian). Current... | Difference between confidence intervals and prediction intervals
This answer is for those readers who could not fully understand the previous answers. Let's discuss a specific example. Suppose you try to predict the people's weight from their height, sex (male, fem |
1,370 | What does a "closed-form solution" mean? | "An equation is said to be a closed-form solution if it solves a given
problem in terms of functions and mathematical operations from a given
generally accepted set. For example, an infinite sum would generally
not be considered closed-form. However, the choice of what to call
closed-form and what not is rather... | What does a "closed-form solution" mean? | "An equation is said to be a closed-form solution if it solves a given
problem in terms of functions and mathematical operations from a given
generally accepted set. For example, an infinite sum w | What does a "closed-form solution" mean?
"An equation is said to be a closed-form solution if it solves a given
problem in terms of functions and mathematical operations from a given
generally accepted set. For example, an infinite sum would generally
not be considered closed-form. However, the choice of what to ... | What does a "closed-form solution" mean?
"An equation is said to be a closed-form solution if it solves a given
problem in terms of functions and mathematical operations from a given
generally accepted set. For example, an infinite sum w |
1,371 | What does a "closed-form solution" mean? | Most estimation procedures involve finding parameters that minimize (or maximize) some objective function. For example, with OLS, we minimize the sum of squared residuals. With Maximum Likelihood Estimation, we maximize the log-likelihood function. The difference is trivial: minimization can be converted to maximizatio... | What does a "closed-form solution" mean? | Most estimation procedures involve finding parameters that minimize (or maximize) some objective function. For example, with OLS, we minimize the sum of squared residuals. With Maximum Likelihood Esti | What does a "closed-form solution" mean?
Most estimation procedures involve finding parameters that minimize (or maximize) some objective function. For example, with OLS, we minimize the sum of squared residuals. With Maximum Likelihood Estimation, we maximize the log-likelihood function. The difference is trivial: min... | What does a "closed-form solution" mean?
Most estimation procedures involve finding parameters that minimize (or maximize) some objective function. For example, with OLS, we minimize the sum of squared residuals. With Maximum Likelihood Esti |
1,372 | What does a "closed-form solution" mean? | I think that this website provides a simple intuition, an excerpt of which is:
A closed-form solution (or closed form expression) is any formula that
can be evaluated in a finite number of standard operations. ... A
numerical solution is any approximation that can be evaluated in a
finite number of standard oper... | What does a "closed-form solution" mean? | I think that this website provides a simple intuition, an excerpt of which is:
A closed-form solution (or closed form expression) is any formula that
can be evaluated in a finite number of standard | What does a "closed-form solution" mean?
I think that this website provides a simple intuition, an excerpt of which is:
A closed-form solution (or closed form expression) is any formula that
can be evaluated in a finite number of standard operations. ... A
numerical solution is any approximation that can be evalua... | What does a "closed-form solution" mean?
I think that this website provides a simple intuition, an excerpt of which is:
A closed-form solution (or closed form expression) is any formula that
can be evaluated in a finite number of standard |
1,373 | What does a "closed-form solution" mean? | Looking for lay terms or the painful verbiage that rigorously defines the meaning? I'll presume lay terms as the other can be found everywhere. Let's say you wanted the closed form solution of the square root of 8. The closed form solution is 2 * (2)^1/2 or two times the square root of two. This is in contrast to the n... | What does a "closed-form solution" mean? | Looking for lay terms or the painful verbiage that rigorously defines the meaning? I'll presume lay terms as the other can be found everywhere. Let's say you wanted the closed form solution of the squ | What does a "closed-form solution" mean?
Looking for lay terms or the painful verbiage that rigorously defines the meaning? I'll presume lay terms as the other can be found everywhere. Let's say you wanted the closed form solution of the square root of 8. The closed form solution is 2 * (2)^1/2 or two times the square ... | What does a "closed-form solution" mean?
Looking for lay terms or the painful verbiage that rigorously defines the meaning? I'll presume lay terms as the other can be found everywhere. Let's say you wanted the closed form solution of the squ |
1,374 | Softmax vs Sigmoid function in Logistic classifier? | The sigmoid function is used for the two-class logistic regression, whereas the softmax function is used for the multiclass logistic regression (a.k.a. MaxEnt, multinomial logistic regression, softmax Regression, Maximum Entropy Classifier).
In the two-class logistic regression, the predicted probablies are as follows... | Softmax vs Sigmoid function in Logistic classifier? | The sigmoid function is used for the two-class logistic regression, whereas the softmax function is used for the multiclass logistic regression (a.k.a. MaxEnt, multinomial logistic regression, softmax | Softmax vs Sigmoid function in Logistic classifier?
The sigmoid function is used for the two-class logistic regression, whereas the softmax function is used for the multiclass logistic regression (a.k.a. MaxEnt, multinomial logistic regression, softmax Regression, Maximum Entropy Classifier).
In the two-class logistic... | Softmax vs Sigmoid function in Logistic classifier?
The sigmoid function is used for the two-class logistic regression, whereas the softmax function is used for the multiclass logistic regression (a.k.a. MaxEnt, multinomial logistic regression, softmax |
1,375 | Softmax vs Sigmoid function in Logistic classifier? | I've noticed people often get directed to this question when searching whether to use sigmoid vs softmax in neural networks. If you are one of those people building a neural network classifier, here is how to decide whether to apply sigmoid or softmax to the raw output values from your network:
If you have a multi-la... | Softmax vs Sigmoid function in Logistic classifier? | I've noticed people often get directed to this question when searching whether to use sigmoid vs softmax in neural networks. If you are one of those people building a neural network classifier, here i | Softmax vs Sigmoid function in Logistic classifier?
I've noticed people often get directed to this question when searching whether to use sigmoid vs softmax in neural networks. If you are one of those people building a neural network classifier, here is how to decide whether to apply sigmoid or softmax to the raw outpu... | Softmax vs Sigmoid function in Logistic classifier?
I've noticed people often get directed to this question when searching whether to use sigmoid vs softmax in neural networks. If you are one of those people building a neural network classifier, here i |
1,376 | Softmax vs Sigmoid function in Logistic classifier? | They are, in fact, equivalent, in the sense that one can be transformed into the other.
Suppose that your data is represented by a vector $\boldsymbol{x}$, of arbitrary dimension, and you built a binary classifier $P$ for it, using an affine transformation followed by a softmax:
\begin{equation}
\begin{pmatrix} z_0 \\ ... | Softmax vs Sigmoid function in Logistic classifier? | They are, in fact, equivalent, in the sense that one can be transformed into the other.
Suppose that your data is represented by a vector $\boldsymbol{x}$, of arbitrary dimension, and you built a bina | Softmax vs Sigmoid function in Logistic classifier?
They are, in fact, equivalent, in the sense that one can be transformed into the other.
Suppose that your data is represented by a vector $\boldsymbol{x}$, of arbitrary dimension, and you built a binary classifier $P$ for it, using an affine transformation followed by... | Softmax vs Sigmoid function in Logistic classifier?
They are, in fact, equivalent, in the sense that one can be transformed into the other.
Suppose that your data is represented by a vector $\boldsymbol{x}$, of arbitrary dimension, and you built a bina |
1,377 | Softmax vs Sigmoid function in Logistic classifier? | Adding to all the previous answers - I would like to mention the fact that any multi-class classification problem can be reduced to multiple binary classification problems using "one-vs-all" method, i.e. having C sigmoids (when C is the number of classes) and interpreting every sigmoid to be the probability of being in... | Softmax vs Sigmoid function in Logistic classifier? | Adding to all the previous answers - I would like to mention the fact that any multi-class classification problem can be reduced to multiple binary classification problems using "one-vs-all" method, i | Softmax vs Sigmoid function in Logistic classifier?
Adding to all the previous answers - I would like to mention the fact that any multi-class classification problem can be reduced to multiple binary classification problems using "one-vs-all" method, i.e. having C sigmoids (when C is the number of classes) and interpre... | Softmax vs Sigmoid function in Logistic classifier?
Adding to all the previous answers - I would like to mention the fact that any multi-class classification problem can be reduced to multiple binary classification problems using "one-vs-all" method, i |
1,378 | What loss function for multi-class, multi-label classification tasks in neural networks? | If you are using keras, just put sigmoids on your output layer and binary_crossentropy on your cost function.
If you are using tensorflow, then can use sigmoid_cross_entropy_with_logits. But for my case this direct loss function was not converging. So I ended up using explicit sigmoid cross entropy loss $(y \cdot \ln(\... | What loss function for multi-class, multi-label classification tasks in neural networks? | If you are using keras, just put sigmoids on your output layer and binary_crossentropy on your cost function.
If you are using tensorflow, then can use sigmoid_cross_entropy_with_logits. But for my ca | What loss function for multi-class, multi-label classification tasks in neural networks?
If you are using keras, just put sigmoids on your output layer and binary_crossentropy on your cost function.
If you are using tensorflow, then can use sigmoid_cross_entropy_with_logits. But for my case this direct loss function wa... | What loss function for multi-class, multi-label classification tasks in neural networks?
If you are using keras, just put sigmoids on your output layer and binary_crossentropy on your cost function.
If you are using tensorflow, then can use sigmoid_cross_entropy_with_logits. But for my ca |
1,379 | What loss function for multi-class, multi-label classification tasks in neural networks? | UPDATE (18/04/18): The old answer still proved to be useful on my model. The trick is to model the partition function and the distribution separately, thus exploiting the power of softmax.
Consider your observation vector $y$ to contain $m$ labels. $y_{im}=\delta_{im}$ (1 if sample i contains label m, 0 otherwise). S... | What loss function for multi-class, multi-label classification tasks in neural networks? | UPDATE (18/04/18): The old answer still proved to be useful on my model. The trick is to model the partition function and the distribution separately, thus exploiting the power of softmax.
Consider y | What loss function for multi-class, multi-label classification tasks in neural networks?
UPDATE (18/04/18): The old answer still proved to be useful on my model. The trick is to model the partition function and the distribution separately, thus exploiting the power of softmax.
Consider your observation vector $y$ to c... | What loss function for multi-class, multi-label classification tasks in neural networks?
UPDATE (18/04/18): The old answer still proved to be useful on my model. The trick is to model the partition function and the distribution separately, thus exploiting the power of softmax.
Consider y |
1,380 | What loss function for multi-class, multi-label classification tasks in neural networks? | I was going through same problem, After some research here is my solution:
If you are using tensorflow :
Multi label loss:
cross_entropy = tf.nn.sigmoid_cross_entropy_with_logits(logits=logits, labels=tf.cast(targets,tf.float32))
loss = tf.reduce_mean(tf.reduce_sum(cross_entropy, axis=1))
prediction... | What loss function for multi-class, multi-label classification tasks in neural networks? | I was going through same problem, After some research here is my solution:
If you are using tensorflow :
Multi label loss:
cross_entropy = tf.nn.sigmoid_cross_entropy_with_logits(logits=logits, la | What loss function for multi-class, multi-label classification tasks in neural networks?
I was going through same problem, After some research here is my solution:
If you are using tensorflow :
Multi label loss:
cross_entropy = tf.nn.sigmoid_cross_entropy_with_logits(logits=logits, labels=tf.cast(targets,tf.float32... | What loss function for multi-class, multi-label classification tasks in neural networks?
I was going through same problem, After some research here is my solution:
If you are using tensorflow :
Multi label loss:
cross_entropy = tf.nn.sigmoid_cross_entropy_with_logits(logits=logits, la |
1,381 | What loss function for multi-class, multi-label classification tasks in neural networks? | I haven't used keras yet. Taking caffe for example, you can use SigmoidCrossEntropyLossLayer for multi-label problems. | What loss function for multi-class, multi-label classification tasks in neural networks? | I haven't used keras yet. Taking caffe for example, you can use SigmoidCrossEntropyLossLayer for multi-label problems. | What loss function for multi-class, multi-label classification tasks in neural networks?
I haven't used keras yet. Taking caffe for example, you can use SigmoidCrossEntropyLossLayer for multi-label problems. | What loss function for multi-class, multi-label classification tasks in neural networks?
I haven't used keras yet. Taking caffe for example, you can use SigmoidCrossEntropyLossLayer for multi-label problems. |
1,382 | What loss function for multi-class, multi-label classification tasks in neural networks? | Actually in tensorsflow you can still use the sigmoid_cross_entropy_mean as the loss calculation function in multi-label, I am very confirm it | What loss function for multi-class, multi-label classification tasks in neural networks? | Actually in tensorsflow you can still use the sigmoid_cross_entropy_mean as the loss calculation function in multi-label, I am very confirm it | What loss function for multi-class, multi-label classification tasks in neural networks?
Actually in tensorsflow you can still use the sigmoid_cross_entropy_mean as the loss calculation function in multi-label, I am very confirm it | What loss function for multi-class, multi-label classification tasks in neural networks?
Actually in tensorsflow you can still use the sigmoid_cross_entropy_mean as the loss calculation function in multi-label, I am very confirm it |
1,383 | What loss function for multi-class, multi-label classification tasks in neural networks? | I'm a newbie here but I'll try give it a shot with this question. I was searching the same thing as you, and finally I found a very good keras multi-class classification tutorial @ http://machinelearningmastery.com/multi-class-classification-tutorial-keras-deep-learning-library/.
The author of that tutorial use catego... | What loss function for multi-class, multi-label classification tasks in neural networks? | I'm a newbie here but I'll try give it a shot with this question. I was searching the same thing as you, and finally I found a very good keras multi-class classification tutorial @ http://machinelear | What loss function for multi-class, multi-label classification tasks in neural networks?
I'm a newbie here but I'll try give it a shot with this question. I was searching the same thing as you, and finally I found a very good keras multi-class classification tutorial @ http://machinelearningmastery.com/multi-class-cla... | What loss function for multi-class, multi-label classification tasks in neural networks?
I'm a newbie here but I'll try give it a shot with this question. I was searching the same thing as you, and finally I found a very good keras multi-class classification tutorial @ http://machinelear |
1,384 | Intuitive explanation of unit root | He had just come to the bridge; and not looking where he was going,
he tripped over something, and the fir-cone jerked out of his
paw into the river.
"Bother," said Pooh, as it floated slowly under the bridge, and he went back to get another fir-cone which had a rhyme
to it. But then he thought that he w... | Intuitive explanation of unit root | He had just come to the bridge; and not looking where he was going,
he tripped over something, and the fir-cone jerked out of his
paw into the river.
"Bother," said Pooh, as it floated slo | Intuitive explanation of unit root
He had just come to the bridge; and not looking where he was going,
he tripped over something, and the fir-cone jerked out of his
paw into the river.
"Bother," said Pooh, as it floated slowly under the bridge, and he went back to get another fir-cone which had a rhyme
t... | Intuitive explanation of unit root
He had just come to the bridge; and not looking where he was going,
he tripped over something, and the fir-cone jerked out of his
paw into the river.
"Bother," said Pooh, as it floated slo |
1,385 | Intuitive explanation of unit root | Imagine two $AR(1)$ processes:
Process 1: $v_k = 0.5 v_{k-1} + \epsilon_{k-1}$
Process 2: $v_k = v_{k-1} + \epsilon_{k-1}$
$\epsilon_i$ is drawn from $N(0,1)$
Process 1 has no unit root. Process 2 has a unit root. You can confirm this by calculating characteristic polynomials per Michael's answer.
Imagine we start ... | Intuitive explanation of unit root | Imagine two $AR(1)$ processes:
Process 1: $v_k = 0.5 v_{k-1} + \epsilon_{k-1}$
Process 2: $v_k = v_{k-1} + \epsilon_{k-1}$
$\epsilon_i$ is drawn from $N(0,1)$
Process 1 has no unit root. Process 2 | Intuitive explanation of unit root
Imagine two $AR(1)$ processes:
Process 1: $v_k = 0.5 v_{k-1} + \epsilon_{k-1}$
Process 2: $v_k = v_{k-1} + \epsilon_{k-1}$
$\epsilon_i$ is drawn from $N(0,1)$
Process 1 has no unit root. Process 2 has a unit root. You can confirm this by calculating characteristic polynomials per ... | Intuitive explanation of unit root
Imagine two $AR(1)$ processes:
Process 1: $v_k = 0.5 v_{k-1} + \epsilon_{k-1}$
Process 2: $v_k = v_{k-1} + \epsilon_{k-1}$
$\epsilon_i$ is drawn from $N(0,1)$
Process 1 has no unit root. Process 2 |
1,386 | Intuitive explanation of unit root | Consider the first-order autoregressive process
$$X_t= aX_{t-1} + e_t$$ where $e_t$ is white noise. The model can also be expressed with all $X$'s on one side as $$X_t-aX_{t-1} = e_t.$$
Using the backshift operator $BX_t = X_{t-1}$ we can re-express the model compactly as $X_t-aBX_t =e_t$ or, equivalently, $$(1-aB)X_... | Intuitive explanation of unit root | Consider the first-order autoregressive process
$$X_t= aX_{t-1} + e_t$$ where $e_t$ is white noise. The model can also be expressed with all $X$'s on one side as $$X_t-aX_{t-1} = e_t.$$
Using the ba | Intuitive explanation of unit root
Consider the first-order autoregressive process
$$X_t= aX_{t-1} + e_t$$ where $e_t$ is white noise. The model can also be expressed with all $X$'s on one side as $$X_t-aX_{t-1} = e_t.$$
Using the backshift operator $BX_t = X_{t-1}$ we can re-express the model compactly as $X_t-aBX_t... | Intuitive explanation of unit root
Consider the first-order autoregressive process
$$X_t= aX_{t-1} + e_t$$ where $e_t$ is white noise. The model can also be expressed with all $X$'s on one side as $$X_t-aX_{t-1} = e_t.$$
Using the ba |
1,387 | Comprehensive list of activation functions in neural networks with pros/cons | I'll start making a list here of the ones I've learned so far. As @marcodena said, pros and cons are more difficult because it's mostly just heuristics learned from trying these things, but I figure at least having a list of what they are can't hurt.
First, I'll define notation explicitly so there is no confusion:
Nota... | Comprehensive list of activation functions in neural networks with pros/cons | I'll start making a list here of the ones I've learned so far. As @marcodena said, pros and cons are more difficult because it's mostly just heuristics learned from trying these things, but I figure a | Comprehensive list of activation functions in neural networks with pros/cons
I'll start making a list here of the ones I've learned so far. As @marcodena said, pros and cons are more difficult because it's mostly just heuristics learned from trying these things, but I figure at least having a list of what they are can'... | Comprehensive list of activation functions in neural networks with pros/cons
I'll start making a list here of the ones I've learned so far. As @marcodena said, pros and cons are more difficult because it's mostly just heuristics learned from trying these things, but I figure a |
1,388 | Comprehensive list of activation functions in neural networks with pros/cons | One such a list, though not very exhaustive: http://cs231n.github.io/neural-networks-1/
Commonly used activation functions
Every activation function (or non-linearity) takes a single number
and performs a certain fixed mathematical operation on it. There are
several activation functions you may encounter in practice:
... | Comprehensive list of activation functions in neural networks with pros/cons | One such a list, though not very exhaustive: http://cs231n.github.io/neural-networks-1/
Commonly used activation functions
Every activation function (or non-linearity) takes a single number
and perfo | Comprehensive list of activation functions in neural networks with pros/cons
One such a list, though not very exhaustive: http://cs231n.github.io/neural-networks-1/
Commonly used activation functions
Every activation function (or non-linearity) takes a single number
and performs a certain fixed mathematical operation ... | Comprehensive list of activation functions in neural networks with pros/cons
One such a list, though not very exhaustive: http://cs231n.github.io/neural-networks-1/
Commonly used activation functions
Every activation function (or non-linearity) takes a single number
and perfo |
1,389 | Comprehensive list of activation functions in neural networks with pros/cons | I don't think that a list with pros and cons exists. The activation functions are highly application dependent, and they depends also on the architecture of your neural network (here for example you see the application of two softmax functions, that are similar to the sigmoid one).
You can find some studies about the ... | Comprehensive list of activation functions in neural networks with pros/cons | I don't think that a list with pros and cons exists. The activation functions are highly application dependent, and they depends also on the architecture of your neural network (here for example you s | Comprehensive list of activation functions in neural networks with pros/cons
I don't think that a list with pros and cons exists. The activation functions are highly application dependent, and they depends also on the architecture of your neural network (here for example you see the application of two softmax functions... | Comprehensive list of activation functions in neural networks with pros/cons
I don't think that a list with pros and cons exists. The activation functions are highly application dependent, and they depends also on the architecture of your neural network (here for example you s |
1,390 | Comprehensive list of activation functions in neural networks with pros/cons | Just for the sake of completeness on Danielle's great answer, there are other paradigms, where one randomly 'spins the wheel' on the weights and / or the type of activations: liquid state machines,
extreme learning machines and echo state networks.
One way to think about these architectures: the reservoir is a sort of... | Comprehensive list of activation functions in neural networks with pros/cons | Just for the sake of completeness on Danielle's great answer, there are other paradigms, where one randomly 'spins the wheel' on the weights and / or the type of activations: liquid state machines,
e | Comprehensive list of activation functions in neural networks with pros/cons
Just for the sake of completeness on Danielle's great answer, there are other paradigms, where one randomly 'spins the wheel' on the weights and / or the type of activations: liquid state machines,
extreme learning machines and echo state net... | Comprehensive list of activation functions in neural networks with pros/cons
Just for the sake of completeness on Danielle's great answer, there are other paradigms, where one randomly 'spins the wheel' on the weights and / or the type of activations: liquid state machines,
e |
1,391 | Comprehensive list of activation functions in neural networks with pros/cons | An article reviewing recent activation functions can be found in
"Activation Functions: Comparison of Trends in Practice and Research for Deep Learning" by Chigozie Enyinna Nwankpa, Winifred Ijomah, Anthony Gachagan, and Stephen Marshall
Deep neural networks have been successfully used in diverse emerging domains to s... | Comprehensive list of activation functions in neural networks with pros/cons | An article reviewing recent activation functions can be found in
"Activation Functions: Comparison of Trends in Practice and Research for Deep Learning" by Chigozie Enyinna Nwankpa, Winifred Ijomah, A | Comprehensive list of activation functions in neural networks with pros/cons
An article reviewing recent activation functions can be found in
"Activation Functions: Comparison of Trends in Practice and Research for Deep Learning" by Chigozie Enyinna Nwankpa, Winifred Ijomah, Anthony Gachagan, and Stephen Marshall
Deep... | Comprehensive list of activation functions in neural networks with pros/cons
An article reviewing recent activation functions can be found in
"Activation Functions: Comparison of Trends in Practice and Research for Deep Learning" by Chigozie Enyinna Nwankpa, Winifred Ijomah, A |
1,392 | Why use gradient descent for linear regression, when a closed-form math solution is available? | The main reason why gradient descent is used for linear regression is the computational complexity: it's computationally cheaper (faster) to find the solution using the gradient descent in some cases.
The formula which you wrote looks very simple, even computationally, because it only works for univariate case, i.e. wh... | Why use gradient descent for linear regression, when a closed-form math solution is available? | The main reason why gradient descent is used for linear regression is the computational complexity: it's computationally cheaper (faster) to find the solution using the gradient descent in some cases. | Why use gradient descent for linear regression, when a closed-form math solution is available?
The main reason why gradient descent is used for linear regression is the computational complexity: it's computationally cheaper (faster) to find the solution using the gradient descent in some cases.
The formula which you wr... | Why use gradient descent for linear regression, when a closed-form math solution is available?
The main reason why gradient descent is used for linear regression is the computational complexity: it's computationally cheaper (faster) to find the solution using the gradient descent in some cases. |
1,393 | Why use gradient descent for linear regression, when a closed-form math solution is available? | In short, suppose we want to solve the linear regression problem with squared loss
$$\text{minimize}~ \|Ax-b\|^2$$ We can set the derivative $2A^T(Ax-b)$ to $0$, and it is solving the linear system
$$A^TAx=A^Tb$$
In high level, there are two ways to solve a linear system. Direct method and the iterative method. Note di... | Why use gradient descent for linear regression, when a closed-form math solution is available? | In short, suppose we want to solve the linear regression problem with squared loss
$$\text{minimize}~ \|Ax-b\|^2$$ We can set the derivative $2A^T(Ax-b)$ to $0$, and it is solving the linear system
$$ | Why use gradient descent for linear regression, when a closed-form math solution is available?
In short, suppose we want to solve the linear regression problem with squared loss
$$\text{minimize}~ \|Ax-b\|^2$$ We can set the derivative $2A^T(Ax-b)$ to $0$, and it is solving the linear system
$$A^TAx=A^Tb$$
In high leve... | Why use gradient descent for linear regression, when a closed-form math solution is available?
In short, suppose we want to solve the linear regression problem with squared loss
$$\text{minimize}~ \|Ax-b\|^2$$ We can set the derivative $2A^T(Ax-b)$ to $0$, and it is solving the linear system
$$ |
1,394 | Why use gradient descent for linear regression, when a closed-form math solution is available? | Sycorax is correct that you don't need gradient descent when estimating linear regression. Your course might be using a simple example to teach you gradient descent to preface more complicated versions.
One neat thing I want to add, though, is that there's currently a small research niche involving terminating gradien... | Why use gradient descent for linear regression, when a closed-form math solution is available? | Sycorax is correct that you don't need gradient descent when estimating linear regression. Your course might be using a simple example to teach you gradient descent to preface more complicated versio | Why use gradient descent for linear regression, when a closed-form math solution is available?
Sycorax is correct that you don't need gradient descent when estimating linear regression. Your course might be using a simple example to teach you gradient descent to preface more complicated versions.
One neat thing I want... | Why use gradient descent for linear regression, when a closed-form math solution is available?
Sycorax is correct that you don't need gradient descent when estimating linear regression. Your course might be using a simple example to teach you gradient descent to preface more complicated versio |
1,395 | Why use gradient descent for linear regression, when a closed-form math solution is available? | If I am not wrong, I think you are pointing towards the MOOC offered by Prof Andrew Ng. To find the optimal regression coefficients, grossly two methods are available. One is by using Normal Equations i.e. by simply finding out $(\mathbf{X}^T\mathbf{X})^{-1}\mathbf{X}^T\mathbf{y}$ and the second is by minimizing the le... | Why use gradient descent for linear regression, when a closed-form math solution is available? | If I am not wrong, I think you are pointing towards the MOOC offered by Prof Andrew Ng. To find the optimal regression coefficients, grossly two methods are available. One is by using Normal Equations | Why use gradient descent for linear regression, when a closed-form math solution is available?
If I am not wrong, I think you are pointing towards the MOOC offered by Prof Andrew Ng. To find the optimal regression coefficients, grossly two methods are available. One is by using Normal Equations i.e. by simply finding o... | Why use gradient descent for linear regression, when a closed-form math solution is available?
If I am not wrong, I think you are pointing towards the MOOC offered by Prof Andrew Ng. To find the optimal regression coefficients, grossly two methods are available. One is by using Normal Equations |
1,396 | Why use gradient descent for linear regression, when a closed-form math solution is available? | First, yes, the real reason is the one given by Tim Atreides; this is a pedagogical exercise.
However, it is possible, albeit unlikely, that one would want to do a linear regression on, say, several trillion datapoints being streamed in from a network socket. In this case, the naive evaluation of the analytic solution ... | Why use gradient descent for linear regression, when a closed-form math solution is available? | First, yes, the real reason is the one given by Tim Atreides; this is a pedagogical exercise.
However, it is possible, albeit unlikely, that one would want to do a linear regression on, say, several t | Why use gradient descent for linear regression, when a closed-form math solution is available?
First, yes, the real reason is the one given by Tim Atreides; this is a pedagogical exercise.
However, it is possible, albeit unlikely, that one would want to do a linear regression on, say, several trillion datapoints being ... | Why use gradient descent for linear regression, when a closed-form math solution is available?
First, yes, the real reason is the one given by Tim Atreides; this is a pedagogical exercise.
However, it is possible, albeit unlikely, that one would want to do a linear regression on, say, several t |
1,397 | Why use gradient descent for linear regression, when a closed-form math solution is available? | One other reason is that gradient descent is more of a general method. For many machine learning problems, the cost function is not convex (e.g., matrix factorization, neural networks) so you cannot use a closed form solution. In those cases, gradient descent is used to find some good local optimum points. Or if you wa... | Why use gradient descent for linear regression, when a closed-form math solution is available? | One other reason is that gradient descent is more of a general method. For many machine learning problems, the cost function is not convex (e.g., matrix factorization, neural networks) so you cannot u | Why use gradient descent for linear regression, when a closed-form math solution is available?
One other reason is that gradient descent is more of a general method. For many machine learning problems, the cost function is not convex (e.g., matrix factorization, neural networks) so you cannot use a closed form solution... | Why use gradient descent for linear regression, when a closed-form math solution is available?
One other reason is that gradient descent is more of a general method. For many machine learning problems, the cost function is not convex (e.g., matrix factorization, neural networks) so you cannot u |
1,398 | Why use gradient descent for linear regression, when a closed-form math solution is available? | In fact, you can solve your linear regression problem by different methods: normal equations (the way you mentioned), QR/SVD decomposition or an iterative method to minimize the error directly (like what the gradient descent method is doing).
Note that the other methods give you the exact solution (ignoring the round-o... | Why use gradient descent for linear regression, when a closed-form math solution is available? | In fact, you can solve your linear regression problem by different methods: normal equations (the way you mentioned), QR/SVD decomposition or an iterative method to minimize the error directly (like w | Why use gradient descent for linear regression, when a closed-form math solution is available?
In fact, you can solve your linear regression problem by different methods: normal equations (the way you mentioned), QR/SVD decomposition or an iterative method to minimize the error directly (like what the gradient descent ... | Why use gradient descent for linear regression, when a closed-form math solution is available?
In fact, you can solve your linear regression problem by different methods: normal equations (the way you mentioned), QR/SVD decomposition or an iterative method to minimize the error directly (like w |
1,399 | tanh activation function vs sigmoid activation function | Yes it matters for technical reasons. Basically for optimization. It is worth reading Efficient Backprop by LeCun et al.
There are two reasons for that choice (assuming you have normalized your data, and this is very important):
Having stronger gradients: since data is centered around 0, the derivatives are higher. To... | tanh activation function vs sigmoid activation function | Yes it matters for technical reasons. Basically for optimization. It is worth reading Efficient Backprop by LeCun et al.
There are two reasons for that choice (assuming you have normalized your data, | tanh activation function vs sigmoid activation function
Yes it matters for technical reasons. Basically for optimization. It is worth reading Efficient Backprop by LeCun et al.
There are two reasons for that choice (assuming you have normalized your data, and this is very important):
Having stronger gradients: since d... | tanh activation function vs sigmoid activation function
Yes it matters for technical reasons. Basically for optimization. It is worth reading Efficient Backprop by LeCun et al.
There are two reasons for that choice (assuming you have normalized your data, |
1,400 | tanh activation function vs sigmoid activation function | Thanks a lot @jpmuc ! Inspired by your answer, I calculated and plotted the derivative of the tanh function and the standard sigmoid function seperately. I'd like to share with you all. Here is what I got.
This is the derivative of the tanh function. For input between [-1,1], we have derivative between [0.42, 1].
This... | tanh activation function vs sigmoid activation function | Thanks a lot @jpmuc ! Inspired by your answer, I calculated and plotted the derivative of the tanh function and the standard sigmoid function seperately. I'd like to share with you all. Here is what I | tanh activation function vs sigmoid activation function
Thanks a lot @jpmuc ! Inspired by your answer, I calculated and plotted the derivative of the tanh function and the standard sigmoid function seperately. I'd like to share with you all. Here is what I got.
This is the derivative of the tanh function. For input bet... | tanh activation function vs sigmoid activation function
Thanks a lot @jpmuc ! Inspired by your answer, I calculated and plotted the derivative of the tanh function and the standard sigmoid function seperately. I'd like to share with you all. Here is what I |
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