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 |
|---|---|---|---|---|---|---|
4,901 | Why is softmax output not a good uncertainty measure for Deep Learning models? | What is being raised is just a basic misunderstanding of statistics coming from the ML "classification" not probability viewpoint.
a predicted probability is just a prediction, if you want confidence intervals you need to do something like bootstrapping/bayesian methods.
eg if I win 6/10 games or 600/1000 my predicted ... | Why is softmax output not a good uncertainty measure for Deep Learning models? | What is being raised is just a basic misunderstanding of statistics coming from the ML "classification" not probability viewpoint.
a predicted probability is just a prediction, if you want confidence | Why is softmax output not a good uncertainty measure for Deep Learning models?
What is being raised is just a basic misunderstanding of statistics coming from the ML "classification" not probability viewpoint.
a predicted probability is just a prediction, if you want confidence intervals you need to do something like b... | Why is softmax output not a good uncertainty measure for Deep Learning models?
What is being raised is just a basic misunderstanding of statistics coming from the ML "classification" not probability viewpoint.
a predicted probability is just a prediction, if you want confidence |
4,902 | Why are MA(q) time series models called "moving averages"? | A footnote in Pankratz (1983), on page 48, says:
The label "moving average" is technically incorrect since the MA
coefficients may be negative and may not sum to unity. This label is
used by convention.
Box and Jenkins (1976) also says something similar. On page 10:
The name "moving average" is somewhat misleadi... | Why are MA(q) time series models called "moving averages"? | A footnote in Pankratz (1983), on page 48, says:
The label "moving average" is technically incorrect since the MA
coefficients may be negative and may not sum to unity. This label is
used by conv | Why are MA(q) time series models called "moving averages"?
A footnote in Pankratz (1983), on page 48, says:
The label "moving average" is technically incorrect since the MA
coefficients may be negative and may not sum to unity. This label is
used by convention.
Box and Jenkins (1976) also says something similar. ... | Why are MA(q) time series models called "moving averages"?
A footnote in Pankratz (1983), on page 48, says:
The label "moving average" is technically incorrect since the MA
coefficients may be negative and may not sum to unity. This label is
used by conv |
4,903 | Why are MA(q) time series models called "moving averages"? | If you look at a zero-mean MA process:
$X_t = \varepsilon_t + \theta_1 \varepsilon_{t-1} + \cdots + \theta_q \varepsilon_{t-q} \,$
then you could regard the right hand side as akin to a weighted moving average of the $\varepsilon$ terms, but where the weights don't sum to 1.
For example, Hyndman and Athanasopoulos (20... | Why are MA(q) time series models called "moving averages"? | If you look at a zero-mean MA process:
$X_t = \varepsilon_t + \theta_1 \varepsilon_{t-1} + \cdots + \theta_q \varepsilon_{t-q} \,$
then you could regard the right hand side as akin to a weighted movi | Why are MA(q) time series models called "moving averages"?
If you look at a zero-mean MA process:
$X_t = \varepsilon_t + \theta_1 \varepsilon_{t-1} + \cdots + \theta_q \varepsilon_{t-q} \,$
then you could regard the right hand side as akin to a weighted moving average of the $\varepsilon$ terms, but where the weights ... | Why are MA(q) time series models called "moving averages"?
If you look at a zero-mean MA process:
$X_t = \varepsilon_t + \theta_1 \varepsilon_{t-1} + \cdots + \theta_q \varepsilon_{t-q} \,$
then you could regard the right hand side as akin to a weighted movi |
4,904 | How to interpret p-value of Kolmogorov-Smirnov test (python)? | As Stijn pointed out, the k-s test returns a D statistic and a p-value corresponding to the D statistic. The D statistic is the absolute max distance (supremum) between the CDFs of the two samples. The closer this number is to 0 the more likely it is that the two samples were drawn from the same distribution. Check out... | How to interpret p-value of Kolmogorov-Smirnov test (python)? | As Stijn pointed out, the k-s test returns a D statistic and a p-value corresponding to the D statistic. The D statistic is the absolute max distance (supremum) between the CDFs of the two samples. Th | How to interpret p-value of Kolmogorov-Smirnov test (python)?
As Stijn pointed out, the k-s test returns a D statistic and a p-value corresponding to the D statistic. The D statistic is the absolute max distance (supremum) between the CDFs of the two samples. The closer this number is to 0 the more likely it is that th... | How to interpret p-value of Kolmogorov-Smirnov test (python)?
As Stijn pointed out, the k-s test returns a D statistic and a p-value corresponding to the D statistic. The D statistic is the absolute max distance (supremum) between the CDFs of the two samples. Th |
4,905 | How to interpret p-value of Kolmogorov-Smirnov test (python)? | When doing a Google search for ks_2samp, the first hit is this website. On it, you can see the function specification:
This is a two-sided test for the null hypothesis that 2 independent samples are drawn from the same continuous distribution.
Parameters :
a, b : sequence of 1-D ndarrays
two arrays of sample obse... | How to interpret p-value of Kolmogorov-Smirnov test (python)? | When doing a Google search for ks_2samp, the first hit is this website. On it, you can see the function specification:
This is a two-sided test for the null hypothesis that 2 independent samples are d | How to interpret p-value of Kolmogorov-Smirnov test (python)?
When doing a Google search for ks_2samp, the first hit is this website. On it, you can see the function specification:
This is a two-sided test for the null hypothesis that 2 independent samples are drawn from the same continuous distribution.
Parameters : ... | How to interpret p-value of Kolmogorov-Smirnov test (python)?
When doing a Google search for ks_2samp, the first hit is this website. On it, you can see the function specification:
This is a two-sided test for the null hypothesis that 2 independent samples are d |
4,906 | Using lmer for repeated-measures linear mixed-effect model | I think that your approach is correct. Model m1 specifies a separate intercept for each subject. Model m2 adds a separate slope for each subject. Your slope is across days as subjects only participate in one treatment group. If you write model m2 as follows it's more obvious that you model a separate intercept and slop... | Using lmer for repeated-measures linear mixed-effect model | I think that your approach is correct. Model m1 specifies a separate intercept for each subject. Model m2 adds a separate slope for each subject. Your slope is across days as subjects only participate | Using lmer for repeated-measures linear mixed-effect model
I think that your approach is correct. Model m1 specifies a separate intercept for each subject. Model m2 adds a separate slope for each subject. Your slope is across days as subjects only participate in one treatment group. If you write model m2 as follows it'... | Using lmer for repeated-measures linear mixed-effect model
I think that your approach is correct. Model m1 specifies a separate intercept for each subject. Model m2 adds a separate slope for each subject. Your slope is across days as subjects only participate |
4,907 | Using lmer for repeated-measures linear mixed-effect model | I don't feel comfortable enough to comment on your autocorrelated errors issue (nor about the different implementations in lme4 vs. nlme), but I can speak to the rest.
Your model m1 is a random-intercept model, where you have included the cross-level interaction between Treatment and Day (the effect of Day is allowed t... | Using lmer for repeated-measures linear mixed-effect model | I don't feel comfortable enough to comment on your autocorrelated errors issue (nor about the different implementations in lme4 vs. nlme), but I can speak to the rest.
Your model m1 is a random-interc | Using lmer for repeated-measures linear mixed-effect model
I don't feel comfortable enough to comment on your autocorrelated errors issue (nor about the different implementations in lme4 vs. nlme), but I can speak to the rest.
Your model m1 is a random-intercept model, where you have included the cross-level interactio... | Using lmer for repeated-measures linear mixed-effect model
I don't feel comfortable enough to comment on your autocorrelated errors issue (nor about the different implementations in lme4 vs. nlme), but I can speak to the rest.
Your model m1 is a random-interc |
4,908 | What book is recommendable to start learning statistics using R at the same time? | I think one reason it is so hard to answer this is that R is so powerful and flexible that a real introduction to R programming goes well beyond what is normally needed in an introduction to statistics. The books that teach statistics using MiniTab, JMP or SPSS are doing relatively straightforward things with the soft... | What book is recommendable to start learning statistics using R at the same time? | I think one reason it is so hard to answer this is that R is so powerful and flexible that a real introduction to R programming goes well beyond what is normally needed in an introduction to statistic | What book is recommendable to start learning statistics using R at the same time?
I think one reason it is so hard to answer this is that R is so powerful and flexible that a real introduction to R programming goes well beyond what is normally needed in an introduction to statistics. The books that teach statistics us... | What book is recommendable to start learning statistics using R at the same time?
I think one reason it is so hard to answer this is that R is so powerful and flexible that a real introduction to R programming goes well beyond what is normally needed in an introduction to statistic |
4,909 | What book is recommendable to start learning statistics using R at the same time? | May be "Introduction to Statistical Thought"? | What book is recommendable to start learning statistics using R at the same time? | May be "Introduction to Statistical Thought"? | What book is recommendable to start learning statistics using R at the same time?
May be "Introduction to Statistical Thought"? | What book is recommendable to start learning statistics using R at the same time?
May be "Introduction to Statistical Thought"? |
4,910 | What book is recommendable to start learning statistics using R at the same time? | @Julie's post of Verzani's book is a real nice choice for someone who has neither R or statistics experience. It's soft enough on both the R and the statistics that it's used by the political science department at UC Davis, and those students have neither programming classes nor higher-level math. His work is available... | What book is recommendable to start learning statistics using R at the same time? | @Julie's post of Verzani's book is a real nice choice for someone who has neither R or statistics experience. It's soft enough on both the R and the statistics that it's used by the political science | What book is recommendable to start learning statistics using R at the same time?
@Julie's post of Verzani's book is a real nice choice for someone who has neither R or statistics experience. It's soft enough on both the R and the statistics that it's used by the political science department at UC Davis, and those stud... | What book is recommendable to start learning statistics using R at the same time?
@Julie's post of Verzani's book is a real nice choice for someone who has neither R or statistics experience. It's soft enough on both the R and the statistics that it's used by the political science |
4,911 | What book is recommendable to start learning statistics using R at the same time? | I found this book to be of great use, but it does assume some knowledge of basic statistical terms, such as p-value, ANOVA, et cetera.
This book offers a much gentler introduction to statistical concepts themselves... | What book is recommendable to start learning statistics using R at the same time? | I found this book to be of great use, but it does assume some knowledge of basic statistical terms, such as p-value, ANOVA, et cetera.
This book offers a much gentler introduction to statistical conce | What book is recommendable to start learning statistics using R at the same time?
I found this book to be of great use, but it does assume some knowledge of basic statistical terms, such as p-value, ANOVA, et cetera.
This book offers a much gentler introduction to statistical concepts themselves... | What book is recommendable to start learning statistics using R at the same time?
I found this book to be of great use, but it does assume some knowledge of basic statistical terms, such as p-value, ANOVA, et cetera.
This book offers a much gentler introduction to statistical conce |
4,912 | What book is recommendable to start learning statistics using R at the same time? | A good book is produced via Adelaide University it is available free online and as a purchase for hardcopy.
Learning Statistics with R
It is very well broken up in its structure and does cover an introduction to R as well as basic introduction to Statistics before moving into more in-depth topics.
There is a very deep ... | What book is recommendable to start learning statistics using R at the same time? | A good book is produced via Adelaide University it is available free online and as a purchase for hardcopy.
Learning Statistics with R
It is very well broken up in its structure and does cover an intr | What book is recommendable to start learning statistics using R at the same time?
A good book is produced via Adelaide University it is available free online and as a purchase for hardcopy.
Learning Statistics with R
It is very well broken up in its structure and does cover an introduction to R as well as basic introdu... | What book is recommendable to start learning statistics using R at the same time?
A good book is produced via Adelaide University it is available free online and as a purchase for hardcopy.
Learning Statistics with R
It is very well broken up in its structure and does cover an intr |
4,913 | What book is recommendable to start learning statistics using R at the same time? | Learning Statistics Using R by Randall E. Schumacker is coming out January 2014 from SAGE Publications. It contains all the material in the posting. | What book is recommendable to start learning statistics using R at the same time? | Learning Statistics Using R by Randall E. Schumacker is coming out January 2014 from SAGE Publications. It contains all the material in the posting. | What book is recommendable to start learning statistics using R at the same time?
Learning Statistics Using R by Randall E. Schumacker is coming out January 2014 from SAGE Publications. It contains all the material in the posting. | What book is recommendable to start learning statistics using R at the same time?
Learning Statistics Using R by Randall E. Schumacker is coming out January 2014 from SAGE Publications. It contains all the material in the posting. |
4,914 | Different ways to write interaction terms in lm? | The results are different because the way lm sets up the model with the interaction is different from how it is set up when you set it up yourself. If you look at the residual sd, it's the same, which indicates (not definitively) that the underlying models are the same, just expressed (to the lm internals) differently... | Different ways to write interaction terms in lm? | The results are different because the way lm sets up the model with the interaction is different from how it is set up when you set it up yourself. If you look at the residual sd, it's the same, whic | Different ways to write interaction terms in lm?
The results are different because the way lm sets up the model with the interaction is different from how it is set up when you set it up yourself. If you look at the residual sd, it's the same, which indicates (not definitively) that the underlying models are the same,... | Different ways to write interaction terms in lm?
The results are different because the way lm sets up the model with the interaction is different from how it is set up when you set it up yourself. If you look at the residual sd, it's the same, whic |
4,915 | Different ways to write interaction terms in lm? | You might understand this behavior better if you look at the model matrices.
model.matrix(lm1 <- lm(y ~ r*s, data=d))
model.matrix(lm2 <- lm(y ~ r + s + rs, data=d))
When you look at these matrices, you can compare the constellations of s2=1 with the other variables (i.e. when s2=1, which values do the other variab... | Different ways to write interaction terms in lm? | You might understand this behavior better if you look at the model matrices.
model.matrix(lm1 <- lm(y ~ r*s, data=d))
model.matrix(lm2 <- lm(y ~ r + s + rs, data=d))
When you look at these matrice | Different ways to write interaction terms in lm?
You might understand this behavior better if you look at the model matrices.
model.matrix(lm1 <- lm(y ~ r*s, data=d))
model.matrix(lm2 <- lm(y ~ r + s + rs, data=d))
When you look at these matrices, you can compare the constellations of s2=1 with the other variables ... | Different ways to write interaction terms in lm?
You might understand this behavior better if you look at the model matrices.
model.matrix(lm1 <- lm(y ~ r*s, data=d))
model.matrix(lm2 <- lm(y ~ r + s + rs, data=d))
When you look at these matrice |
4,916 | Different ways to write interaction terms in lm? | I think there are good reasons not to use
lm(y ~ r + s + rs, data=d)
When you create rs and put it into the formula, R will think of rs as just another variable, it has no way of knowing that it is an interaction of r and s.
This matters if you use drop1() or stepwise regression.
It is invalid to drop a variable x whil... | Different ways to write interaction terms in lm? | I think there are good reasons not to use
lm(y ~ r + s + rs, data=d)
When you create rs and put it into the formula, R will think of rs as just another variable, it has no way of knowing that it is an | Different ways to write interaction terms in lm?
I think there are good reasons not to use
lm(y ~ r + s + rs, data=d)
When you create rs and put it into the formula, R will think of rs as just another variable, it has no way of knowing that it is an interaction of r and s.
This matters if you use drop1() or stepwise re... | Different ways to write interaction terms in lm?
I think there are good reasons not to use
lm(y ~ r + s + rs, data=d)
When you create rs and put it into the formula, R will think of rs as just another variable, it has no way of knowing that it is an |
4,917 | Data APIs/feeds available as packages in R | Instructions for using R to download netCDF data can be found here, a common format used for storing Earth science data, e.g. as in marine geospatial data from OpenEarth or climate model driver and forecasts from UCAR
rnpn (under development) enables you to get data from the National Phenology Network - a citizen scien... | Data APIs/feeds available as packages in R | Instructions for using R to download netCDF data can be found here, a common format used for storing Earth science data, e.g. as in marine geospatial data from OpenEarth or climate model driver and fo | Data APIs/feeds available as packages in R
Instructions for using R to download netCDF data can be found here, a common format used for storing Earth science data, e.g. as in marine geospatial data from OpenEarth or climate model driver and forecasts from UCAR
rnpn (under development) enables you to get data from the N... | Data APIs/feeds available as packages in R
Instructions for using R to download netCDF data can be found here, a common format used for storing Earth science data, e.g. as in marine geospatial data from OpenEarth or climate model driver and fo |
4,918 | Data APIs/feeds available as packages in R | There's a project aimed at creating R packages with this objective (R interface to real-time APIs) called rOpenSci, which has 18 packages currently available or in development. Some (rnpn, rfishbase) are on your list already.
Great list! and full disclosure - I'm part of the rOpenSci project. | Data APIs/feeds available as packages in R | There's a project aimed at creating R packages with this objective (R interface to real-time APIs) called rOpenSci, which has 18 packages currently available or in development. Some (rnpn, rfishbase) | Data APIs/feeds available as packages in R
There's a project aimed at creating R packages with this objective (R interface to real-time APIs) called rOpenSci, which has 18 packages currently available or in development. Some (rnpn, rfishbase) are on your list already.
Great list! and full disclosure - I'm part of th... | Data APIs/feeds available as packages in R
There's a project aimed at creating R packages with this objective (R interface to real-time APIs) called rOpenSci, which has 18 packages currently available or in development. Some (rnpn, rfishbase) |
4,919 | Data APIs/feeds available as packages in R | ONETr - efficient interaction with the O*NET™ API, offering occupational descriptor data from the U.S. Department of Labor. | Data APIs/feeds available as packages in R | ONETr - efficient interaction with the O*NET™ API, offering occupational descriptor data from the U.S. Department of Labor. | Data APIs/feeds available as packages in R
ONETr - efficient interaction with the O*NET™ API, offering occupational descriptor data from the U.S. Department of Labor. | Data APIs/feeds available as packages in R
ONETr - efficient interaction with the O*NET™ API, offering occupational descriptor data from the U.S. Department of Labor. |
4,920 | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | I agree with many of the other answers here but think the statement is even worse than they make it out to be.
The statement is an explicit version of an implicit claim in many shoddy analyses of small datasets. These hint that because they have found a significant result in a small sample, their claimed result must b... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | I agree with many of the other answers here but think the statement is even worse than they make it out to be.
The statement is an explicit version of an implicit claim in many shoddy analyses of sma | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
I agree with many of the other answers here but think the statement is even worse than they make it out to be.
The statement is an explicit version of an implicit claim in many shoddy analyses of small datasets. These hint t... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
I agree with many of the other answers here but think the statement is even worse than they make it out to be.
The statement is an explicit version of an implicit claim in many shoddy analyses of sma |
4,921 | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | "It's counterintuitive, but the smaller the sample size of a clinical test, the more significant its results are. The differences in a sample of 20 people may be more significant than in a sample of 10,000 people. If we need such a sample, there is a risk of being wrong. With 10,000 people, when the differences are sm... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | "It's counterintuitive, but the smaller the sample size of a clinical test, the more significant its results are. The differences in a sample of 20 people may be more significant than in a sample of 1 | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
"It's counterintuitive, but the smaller the sample size of a clinical test, the more significant its results are. The differences in a sample of 20 people may be more significant than in a sample of 10,000 people. If we need... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
"It's counterintuitive, but the smaller the sample size of a clinical test, the more significant its results are. The differences in a sample of 20 people may be more significant than in a sample of 1 |
4,922 | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | (I think the phrasing is deliberately provocative.)
If you have 10 observations and want to show that their mean is not zero, it will have to be quite a bit different from 0 if you want to have any kind of chance (power) of detecting the difference.
If you have a trillion observations and want to show that their mean i... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | (I think the phrasing is deliberately provocative.)
If you have 10 observations and want to show that their mean is not zero, it will have to be quite a bit different from 0 if you want to have any ki | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
(I think the phrasing is deliberately provocative.)
If you have 10 observations and want to show that their mean is not zero, it will have to be quite a bit different from 0 if you want to have any kind of chance (power) of d... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
(I think the phrasing is deliberately provocative.)
If you have 10 observations and want to show that their mean is not zero, it will have to be quite a bit different from 0 if you want to have any ki |
4,923 | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | Can you confirm that it is a FALSE statement in statistics
I think the statement is phrased poorly. In this context, the word "significant" seems to have the flavor of "importance". Difference detected in smaller datasets are not somehow more important or meaningful by virtue of being detected in small datasets. Rath... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | Can you confirm that it is a FALSE statement in statistics
I think the statement is phrased poorly. In this context, the word "significant" seems to have the flavor of "importance". Difference detect | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
Can you confirm that it is a FALSE statement in statistics
I think the statement is phrased poorly. In this context, the word "significant" seems to have the flavor of "importance". Difference detected in smaller datasets ar... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
Can you confirm that it is a FALSE statement in statistics
I think the statement is phrased poorly. In this context, the word "significant" seems to have the flavor of "importance". Difference detect |
4,924 | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | The quote in question seems to originate from marianne.net (in French) and, as it stands, is definitely wrong. But, as Demetri and Dave pointed out, with some language bending there might be some truth to it.
In my understanding, Prof. Raoult confuses significance and effect size. In a small sample, the effect size has... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | The quote in question seems to originate from marianne.net (in French) and, as it stands, is definitely wrong. But, as Demetri and Dave pointed out, with some language bending there might be some trut | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
The quote in question seems to originate from marianne.net (in French) and, as it stands, is definitely wrong. But, as Demetri and Dave pointed out, with some language bending there might be some truth to it.
In my understand... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
The quote in question seems to originate from marianne.net (in French) and, as it stands, is definitely wrong. But, as Demetri and Dave pointed out, with some language bending there might be some trut |
4,925 | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | A smaller sample size is not better.
A small sample size needs a more significant* result if you want to draw a conclusion from it.
Let's consider some results and their interpretation:
If your drug cures 30% of 10 people, the percentage of the general population cured could be anywhere between around 0% and 65% of pe... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | A smaller sample size is not better.
A small sample size needs a more significant* result if you want to draw a conclusion from it.
Let's consider some results and their interpretation:
If your drug | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
A smaller sample size is not better.
A small sample size needs a more significant* result if you want to draw a conclusion from it.
Let's consider some results and their interpretation:
If your drug cures 30% of 10 people, t... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
A smaller sample size is not better.
A small sample size needs a more significant* result if you want to draw a conclusion from it.
Let's consider some results and their interpretation:
If your drug |
4,926 | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | There are a few things that are true, and worth understanding for where the confusion might slip in.
First, it is possible to get high levels of confidence from small samples, so long as the effect is sufficiently pronounced. For example, a treatment that goes from 10% control recovery to 90% experimental recovery will... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | There are a few things that are true, and worth understanding for where the confusion might slip in.
First, it is possible to get high levels of confidence from small samples, so long as the effect is | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
There are a few things that are true, and worth understanding for where the confusion might slip in.
First, it is possible to get high levels of confidence from small samples, so long as the effect is sufficiently pronounced.... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
There are a few things that are true, and worth understanding for where the confusion might slip in.
First, it is possible to get high levels of confidence from small samples, so long as the effect is |
4,927 | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | This statement is misleading because it is unclear what he means by significant.
In the case of a clinical trial, what you want to show is that people are more likely to heal when given a test treatment than when given a placebo. So you have two (random) groups of equal size, one of which gets a the treatment while the... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | This statement is misleading because it is unclear what he means by significant.
In the case of a clinical trial, what you want to show is that people are more likely to heal when given a test treatme | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
This statement is misleading because it is unclear what he means by significant.
In the case of a clinical trial, what you want to show is that people are more likely to heal when given a test treatment than when given a plac... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
This statement is misleading because it is unclear what he means by significant.
In the case of a clinical trial, what you want to show is that people are more likely to heal when given a test treatme |
4,928 | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | A smaller sample size is definitely not better than a larger one.
Other answers do a good job of parsing what he might have meant (e.g., effect size, etc.). However, these miss the fact that the underlying effect is the same whether we use a larger or small sample size.
This is more obvious if we look at a binary outco... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | A smaller sample size is definitely not better than a larger one.
Other answers do a good job of parsing what he might have meant (e.g., effect size, etc.). However, these miss the fact that the under | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
A smaller sample size is definitely not better than a larger one.
Other answers do a good job of parsing what he might have meant (e.g., effect size, etc.). However, these miss the fact that the underlying effect is the same ... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
A smaller sample size is definitely not better than a larger one.
Other answers do a good job of parsing what he might have meant (e.g., effect size, etc.). However, these miss the fact that the under |
4,929 | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | Before really answering the question, I have to point out that the study being discussed was a non-randomized open label study where the controls were possibly in a different facility than the treatment subjects, and they tossed out dead, ICU patients and dropouts due to side effects from the treatment group. The poor... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | Before really answering the question, I have to point out that the study being discussed was a non-randomized open label study where the controls were possibly in a different facility than the treatme | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
Before really answering the question, I have to point out that the study being discussed was a non-randomized open label study where the controls were possibly in a different facility than the treatment subjects, and they tos... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
Before really answering the question, I have to point out that the study being discussed was a non-randomized open label study where the controls were possibly in a different facility than the treatme |
4,930 | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | First of I would like to state the following:
Biostatistics is a really difficult field; many biostatisticians are better data scientists than people with a maths background.
Biostatistics has create it own tools that we can use today.
The experiments they make must be really regulated (at least from pharmaceutical vi... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | First of I would like to state the following:
Biostatistics is a really difficult field; many biostatisticians are better data scientists than people with a maths background.
Biostatistics has create | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
First of I would like to state the following:
Biostatistics is a really difficult field; many biostatisticians are better data scientists than people with a maths background.
Biostatistics has create it own tools that we can... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
First of I would like to state the following:
Biostatistics is a really difficult field; many biostatisticians are better data scientists than people with a maths background.
Biostatistics has create |
4,931 | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | tl;dr– It sounds like they're arguing that smaller data sets are superior because larger data sets imply $p$-hacking or/and a less observable finding. But, obviously, doing a particular experiment with more data is better than with less data when the data analysis is done correctly.
Translating the argument.
Raw ar... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | tl;dr– It sounds like they're arguing that smaller data sets are superior because larger data sets imply $p$-hacking or/and a less observable finding. But, obviously, doing a particular experiment w | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
tl;dr– It sounds like they're arguing that smaller data sets are superior because larger data sets imply $p$-hacking or/and a less observable finding. But, obviously, doing a particular experiment with more data is better t... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
tl;dr– It sounds like they're arguing that smaller data sets are superior because larger data sets imply $p$-hacking or/and a less observable finding. But, obviously, doing a particular experiment w |
4,932 | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | The requirement that sample sizes be a certain size to have statistical inference confidence stems from I think the emperical law. And that is as you take more random SAMPLES the average of the MEANS converge to the actual population mean. But I've heard in order to be valid a sample size of greater than 32 is required... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | The requirement that sample sizes be a certain size to have statistical inference confidence stems from I think the emperical law. And that is as you take more random SAMPLES the average of the MEANS | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
The requirement that sample sizes be a certain size to have statistical inference confidence stems from I think the emperical law. And that is as you take more random SAMPLES the average of the MEANS converge to the actual po... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
The requirement that sample sizes be a certain size to have statistical inference confidence stems from I think the emperical law. And that is as you take more random SAMPLES the average of the MEANS |
4,933 | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | Dr. Raoult's statement is false.
A bigger dataset (on your domain of discourse subject) is always better. It yields a better average, thus better certainty.
You may apply the principle of charity.
Probably what he is trying to say is:
A small (but most significant) sample set is better than a bigger (but less signific... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | Dr. Raoult's statement is false.
A bigger dataset (on your domain of discourse subject) is always better. It yields a better average, thus better certainty.
You may apply the principle of charity.
Pro | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
Dr. Raoult's statement is false.
A bigger dataset (on your domain of discourse subject) is always better. It yields a better average, thus better certainty.
You may apply the principle of charity.
Probably what he is trying t... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
Dr. Raoult's statement is false.
A bigger dataset (on your domain of discourse subject) is always better. It yields a better average, thus better certainty.
You may apply the principle of charity.
Pro |
4,934 | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | Yes, a smaller sample CAN be more informative due to the confluence of similar significant discriminating attributes. For example, a small sample of Detriot African Americans with similar income levels and associated access to healthcare, occupations, stress, diets and pre-existing conditions (high blood pressure,...) ... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly? | Yes, a smaller sample CAN be more informative due to the confluence of similar significant discriminating attributes. For example, a small sample of Detriot African Americans with similar income level | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
Yes, a smaller sample CAN be more informative due to the confluence of similar significant discriminating attributes. For example, a small sample of Detriot African Americans with similar income levels and associated access t... | A smaller dataset is better: Is this statement false in statistics? How to refute it properly?
Yes, a smaller sample CAN be more informative due to the confluence of similar significant discriminating attributes. For example, a small sample of Detriot African Americans with similar income level |
4,935 | Famous easy to understand examples of a confounding variable invalidating a study | Coffee Drinking & Lung Cancer
My favorite example is that supposedly, "coffee drinkers have a greater risk of lung cancer", despite most coffee drinkers... well... drinking coffee, rather than inhaling it.
There have been various studies about this, but the consensus remains that studies with this conclusion usually ju... | Famous easy to understand examples of a confounding variable invalidating a study | Coffee Drinking & Lung Cancer
My favorite example is that supposedly, "coffee drinkers have a greater risk of lung cancer", despite most coffee drinkers... well... drinking coffee, rather than inhalin | Famous easy to understand examples of a confounding variable invalidating a study
Coffee Drinking & Lung Cancer
My favorite example is that supposedly, "coffee drinkers have a greater risk of lung cancer", despite most coffee drinkers... well... drinking coffee, rather than inhaling it.
There have been various studies ... | Famous easy to understand examples of a confounding variable invalidating a study
Coffee Drinking & Lung Cancer
My favorite example is that supposedly, "coffee drinkers have a greater risk of lung cancer", despite most coffee drinkers... well... drinking coffee, rather than inhalin |
4,936 | Famous easy to understand examples of a confounding variable invalidating a study | You might want to introduce Simpson's Paradox.
The first example that page is the UC Berkeley gender bias case where it was thought that there was gender bias (towards males) in admissions when looking at overall acceptance rates, but this was eliminated or reversed when investigated by department. The confounding vari... | Famous easy to understand examples of a confounding variable invalidating a study | You might want to introduce Simpson's Paradox.
The first example that page is the UC Berkeley gender bias case where it was thought that there was gender bias (towards males) in admissions when lookin | Famous easy to understand examples of a confounding variable invalidating a study
You might want to introduce Simpson's Paradox.
The first example that page is the UC Berkeley gender bias case where it was thought that there was gender bias (towards males) in admissions when looking at overall acceptance rates, but thi... | Famous easy to understand examples of a confounding variable invalidating a study
You might want to introduce Simpson's Paradox.
The first example that page is the UC Berkeley gender bias case where it was thought that there was gender bias (towards males) in admissions when lookin |
4,937 | Famous easy to understand examples of a confounding variable invalidating a study | Power Lines and Cancer
After an initial study finding a link between living next to high-voltage transmission lines and cancer, follow-up studies found that when you include income in the model the effect of the power lines goes away.
Living next to power lines is a moderately accurate predictor of low household income... | Famous easy to understand examples of a confounding variable invalidating a study | Power Lines and Cancer
After an initial study finding a link between living next to high-voltage transmission lines and cancer, follow-up studies found that when you include income in the model the ef | Famous easy to understand examples of a confounding variable invalidating a study
Power Lines and Cancer
After an initial study finding a link between living next to high-voltage transmission lines and cancer, follow-up studies found that when you include income in the model the effect of the power lines goes away.
Liv... | Famous easy to understand examples of a confounding variable invalidating a study
Power Lines and Cancer
After an initial study finding a link between living next to high-voltage transmission lines and cancer, follow-up studies found that when you include income in the model the ef |
4,938 | Famous easy to understand examples of a confounding variable invalidating a study | Consider the following examples. I am not sure they are necessarily very famous but they help to demonstrate the potential negative effects of confounding variables.
Say one is studying the relation between birth order (1st child, 2nd child, etc.) and the presence of Down Syndrome in the child. In this scenario, mater... | Famous easy to understand examples of a confounding variable invalidating a study | Consider the following examples. I am not sure they are necessarily very famous but they help to demonstrate the potential negative effects of confounding variables.
Say one is studying the relation | Famous easy to understand examples of a confounding variable invalidating a study
Consider the following examples. I am not sure they are necessarily very famous but they help to demonstrate the potential negative effects of confounding variables.
Say one is studying the relation between birth order (1st child, 2nd ch... | Famous easy to understand examples of a confounding variable invalidating a study
Consider the following examples. I am not sure they are necessarily very famous but they help to demonstrate the potential negative effects of confounding variables.
Say one is studying the relation |
4,939 | Famous easy to understand examples of a confounding variable invalidating a study | There was one about diet that looked at diet in different countries and concluded that meat caused all sorts of problems (e.g. heart disease), but failed to account for the average lifespan in each country: The countries that ate very little meat also had lower life expectancies and the problems that meat "caused" were... | Famous easy to understand examples of a confounding variable invalidating a study | There was one about diet that looked at diet in different countries and concluded that meat caused all sorts of problems (e.g. heart disease), but failed to account for the average lifespan in each co | Famous easy to understand examples of a confounding variable invalidating a study
There was one about diet that looked at diet in different countries and concluded that meat caused all sorts of problems (e.g. heart disease), but failed to account for the average lifespan in each country: The countries that ate very lit... | Famous easy to understand examples of a confounding variable invalidating a study
There was one about diet that looked at diet in different countries and concluded that meat caused all sorts of problems (e.g. heart disease), but failed to account for the average lifespan in each co |
4,940 | Famous easy to understand examples of a confounding variable invalidating a study | I'm not sure it entirely counts as a confounding variable so much as confounding situations, but animals' abilities to find their way through a maze may qualify.
As described in this ScienceDirect summary, studies of rats (or other animals) in mazes were popular for a large part of the 20th century, and continue today ... | Famous easy to understand examples of a confounding variable invalidating a study | I'm not sure it entirely counts as a confounding variable so much as confounding situations, but animals' abilities to find their way through a maze may qualify.
As described in this ScienceDirect sum | Famous easy to understand examples of a confounding variable invalidating a study
I'm not sure it entirely counts as a confounding variable so much as confounding situations, but animals' abilities to find their way through a maze may qualify.
As described in this ScienceDirect summary, studies of rats (or other animal... | Famous easy to understand examples of a confounding variable invalidating a study
I'm not sure it entirely counts as a confounding variable so much as confounding situations, but animals' abilities to find their way through a maze may qualify.
As described in this ScienceDirect sum |
4,941 | Famous easy to understand examples of a confounding variable invalidating a study | There was a great study of mobile phone use and brain cancer. Most people with a lateral brain cancer, when asked which hand they hold their phone in, answer the diseased side. This seemed to show that phone use caused cancer.
However, maybe the answers are informed by hindsight. Someone thought of a great test for thi... | Famous easy to understand examples of a confounding variable invalidating a study | There was a great study of mobile phone use and brain cancer. Most people with a lateral brain cancer, when asked which hand they hold their phone in, answer the diseased side. This seemed to show tha | Famous easy to understand examples of a confounding variable invalidating a study
There was a great study of mobile phone use and brain cancer. Most people with a lateral brain cancer, when asked which hand they hold their phone in, answer the diseased side. This seemed to show that phone use caused cancer.
However, ma... | Famous easy to understand examples of a confounding variable invalidating a study
There was a great study of mobile phone use and brain cancer. Most people with a lateral brain cancer, when asked which hand they hold their phone in, answer the diseased side. This seemed to show tha |
4,942 | Famous easy to understand examples of a confounding variable invalidating a study | 'Statistics' by Freedman, Purvis et al. has a number of examples in the first couple of chapters. My personal favorite is that ice cream causes polio. The confounding variable is that they are both prevalent in the summertime when young children are out, about, and spreading polio. The book is "Statistics (Fourth E... | Famous easy to understand examples of a confounding variable invalidating a study | 'Statistics' by Freedman, Purvis et al. has a number of examples in the first couple of chapters. My personal favorite is that ice cream causes polio. The confounding variable is that they are both | Famous easy to understand examples of a confounding variable invalidating a study
'Statistics' by Freedman, Purvis et al. has a number of examples in the first couple of chapters. My personal favorite is that ice cream causes polio. The confounding variable is that they are both prevalent in the summertime when youn... | Famous easy to understand examples of a confounding variable invalidating a study
'Statistics' by Freedman, Purvis et al. has a number of examples in the first couple of chapters. My personal favorite is that ice cream causes polio. The confounding variable is that they are both |
4,943 | Famous easy to understand examples of a confounding variable invalidating a study | See: Subversive Subjects: Rule-Breaking and Deception in Clinical Trials
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4520402/ | Famous easy to understand examples of a confounding variable invalidating a study | See: Subversive Subjects: Rule-Breaking and Deception in Clinical Trials
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4520402/ | Famous easy to understand examples of a confounding variable invalidating a study
See: Subversive Subjects: Rule-Breaking and Deception in Clinical Trials
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4520402/ | Famous easy to understand examples of a confounding variable invalidating a study
See: Subversive Subjects: Rule-Breaking and Deception in Clinical Trials
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4520402/ |
4,944 | Famous easy to understand examples of a confounding variable invalidating a study | Hormone replacement Therapy and heart disease?
https://www.teachepi.org/wp-content/uploads/OldTE/documents/courses/bfiles/The%20B%20Files_File1_HRT_Final_Complete.pdf
The benefits were determined by observation, and essentially it appears that the people who chose to do hrt had higher socioeconomic status, healthier l... | Famous easy to understand examples of a confounding variable invalidating a study | Hormone replacement Therapy and heart disease?
https://www.teachepi.org/wp-content/uploads/OldTE/documents/courses/bfiles/The%20B%20Files_File1_HRT_Final_Complete.pdf
The benefits were determined by o | Famous easy to understand examples of a confounding variable invalidating a study
Hormone replacement Therapy and heart disease?
https://www.teachepi.org/wp-content/uploads/OldTE/documents/courses/bfiles/The%20B%20Files_File1_HRT_Final_Complete.pdf
The benefits were determined by observation, and essentially it appears... | Famous easy to understand examples of a confounding variable invalidating a study
Hormone replacement Therapy and heart disease?
https://www.teachepi.org/wp-content/uploads/OldTE/documents/courses/bfiles/The%20B%20Files_File1_HRT_Final_Complete.pdf
The benefits were determined by o |
4,945 | Famous easy to understand examples of a confounding variable invalidating a study | There are lots of good examples in Howard Weiner's books. In particular, Chapter 1 "The most dangerous equation" in "How to understand, communicate and control uncertainty through graphical display"
Examples include:
The small schools movement.
People noticed that some small schools had better performance than large... | Famous easy to understand examples of a confounding variable invalidating a study | There are lots of good examples in Howard Weiner's books. In particular, Chapter 1 "The most dangerous equation" in "How to understand, communicate and control uncertainty through graphical display" | Famous easy to understand examples of a confounding variable invalidating a study
There are lots of good examples in Howard Weiner's books. In particular, Chapter 1 "The most dangerous equation" in "How to understand, communicate and control uncertainty through graphical display"
Examples include:
The small schools ... | Famous easy to understand examples of a confounding variable invalidating a study
There are lots of good examples in Howard Weiner's books. In particular, Chapter 1 "The most dangerous equation" in "How to understand, communicate and control uncertainty through graphical display" |
4,946 | Why is polynomial regression considered a special case of multiple linear regression? | When you fit a regression model such as $\hat y_i = \hat\beta_0 + \hat\beta_1x_i + \hat\beta_2x^2_i$, the model and the OLS estimator doesn't 'know' that $x^2_i$ is simply the square of $x_i$, it just 'thinks' it's another variable. Of course there is some collinearity, and that gets incorporated into the fit (e.g., t... | Why is polynomial regression considered a special case of multiple linear regression? | When you fit a regression model such as $\hat y_i = \hat\beta_0 + \hat\beta_1x_i + \hat\beta_2x^2_i$, the model and the OLS estimator doesn't 'know' that $x^2_i$ is simply the square of $x_i$, it just | Why is polynomial regression considered a special case of multiple linear regression?
When you fit a regression model such as $\hat y_i = \hat\beta_0 + \hat\beta_1x_i + \hat\beta_2x^2_i$, the model and the OLS estimator doesn't 'know' that $x^2_i$ is simply the square of $x_i$, it just 'thinks' it's another variable. ... | Why is polynomial regression considered a special case of multiple linear regression?
When you fit a regression model such as $\hat y_i = \hat\beta_0 + \hat\beta_1x_i + \hat\beta_2x^2_i$, the model and the OLS estimator doesn't 'know' that $x^2_i$ is simply the square of $x_i$, it just |
4,947 | Why is polynomial regression considered a special case of multiple linear regression? | So a general linear model is function that is linear in the unknown parameters. A polynomial regression, for example $y = a + bx + cx^2$ is quadratic as a function of $x$ but linear in the coefficients $a$, $b$ and $c$. More generally, a general linear model can be expressed as $y = \sum_{i=0}^N a_i h_i(x)$, where the ... | Why is polynomial regression considered a special case of multiple linear regression? | So a general linear model is function that is linear in the unknown parameters. A polynomial regression, for example $y = a + bx + cx^2$ is quadratic as a function of $x$ but linear in the coefficient | Why is polynomial regression considered a special case of multiple linear regression?
So a general linear model is function that is linear in the unknown parameters. A polynomial regression, for example $y = a + bx + cx^2$ is quadratic as a function of $x$ but linear in the coefficients $a$, $b$ and $c$. More generally... | Why is polynomial regression considered a special case of multiple linear regression?
So a general linear model is function that is linear in the unknown parameters. A polynomial regression, for example $y = a + bx + cx^2$ is quadratic as a function of $x$ but linear in the coefficient |
4,948 | Why is polynomial regression considered a special case of multiple linear regression? | Consider a model
$$
y_i = b_0+b_1 x^{n_1}_i + \cdots+ b_px^{n_p}_i + \epsilon_i.
$$
This can be rewritten
$$
y =
X b + \epsilon;\\
X= \begin{pmatrix}
1 & x_{1}^{n_1} & \cdots & x_{1}^{n_p} \\
1 & x_{2}^{n_1} & \cdots & x_{2}^{n_p} \\
\vdots & \vdots & \ddots & \vdots \\
1 & x_{n}^{n_1} & \cdots & x_{n}^{n_p... | Why is polynomial regression considered a special case of multiple linear regression? | Consider a model
$$
y_i = b_0+b_1 x^{n_1}_i + \cdots+ b_px^{n_p}_i + \epsilon_i.
$$
This can be rewritten
$$
y =
X b + \epsilon;\\
X= \begin{pmatrix}
1 & x_{1}^{n_1} & \cdots & x_{1}^{n_p} \\
1 & | Why is polynomial regression considered a special case of multiple linear regression?
Consider a model
$$
y_i = b_0+b_1 x^{n_1}_i + \cdots+ b_px^{n_p}_i + \epsilon_i.
$$
This can be rewritten
$$
y =
X b + \epsilon;\\
X= \begin{pmatrix}
1 & x_{1}^{n_1} & \cdots & x_{1}^{n_p} \\
1 & x_{2}^{n_1} & \cdots & x_{2}^{n_p... | Why is polynomial regression considered a special case of multiple linear regression?
Consider a model
$$
y_i = b_0+b_1 x^{n_1}_i + \cdots+ b_px^{n_p}_i + \epsilon_i.
$$
This can be rewritten
$$
y =
X b + \epsilon;\\
X= \begin{pmatrix}
1 & x_{1}^{n_1} & \cdots & x_{1}^{n_p} \\
1 & |
4,949 | What kind of information is Fisher information? | Trying to complement the other answers... What kind of information is Fisher information? Start with the loglikelihood function
$$
\ell (\theta) = \log f(x;\theta)
$$
as a function of $\theta$ for $\theta \in \Theta$, the parameter space.
Assuming some regularity conditions we do not discuss here, we have
$\Declare... | What kind of information is Fisher information? | Trying to complement the other answers... What kind of information is Fisher information? Start with the loglikelihood function
$$
\ell (\theta) = \log f(x;\theta)
$$
as a function of $\theta$ for | What kind of information is Fisher information?
Trying to complement the other answers... What kind of information is Fisher information? Start with the loglikelihood function
$$
\ell (\theta) = \log f(x;\theta)
$$
as a function of $\theta$ for $\theta \in \Theta$, the parameter space.
Assuming some regularity cond... | What kind of information is Fisher information?
Trying to complement the other answers... What kind of information is Fisher information? Start with the loglikelihood function
$$
\ell (\theta) = \log f(x;\theta)
$$
as a function of $\theta$ for |
4,950 | What kind of information is Fisher information? | Let's think in terms of the negative log-likelihood function $\ell$. The negative score is its gradient with respect to the parameter value. At the true parameter, the score is zero. Otherwise, it gives the direction towards the minimum $\ell$ (or in the case of non-convex $\ell$, a saddle point or local minimum or ... | What kind of information is Fisher information? | Let's think in terms of the negative log-likelihood function $\ell$. The negative score is its gradient with respect to the parameter value. At the true parameter, the score is zero. Otherwise, it | What kind of information is Fisher information?
Let's think in terms of the negative log-likelihood function $\ell$. The negative score is its gradient with respect to the parameter value. At the true parameter, the score is zero. Otherwise, it gives the direction towards the minimum $\ell$ (or in the case of non-co... | What kind of information is Fisher information?
Let's think in terms of the negative log-likelihood function $\ell$. The negative score is its gradient with respect to the parameter value. At the true parameter, the score is zero. Otherwise, it |
4,951 | What kind of information is Fisher information? | Complementary to @NeilG's nice answer (+1) and to address your specific questions:
I would say it counts the "precision" rather than the "error" itself.
Remember that the Hessian of the log-likelihood evaluated at the ML estimates is the observed Fisher information. The estimated standard errors are the square ro... | What kind of information is Fisher information? | Complementary to @NeilG's nice answer (+1) and to address your specific questions:
I would say it counts the "precision" rather than the "error" itself.
Remember that the Hessian of the log-like | What kind of information is Fisher information?
Complementary to @NeilG's nice answer (+1) and to address your specific questions:
I would say it counts the "precision" rather than the "error" itself.
Remember that the Hessian of the log-likelihood evaluated at the ML estimates is the observed Fisher information.... | What kind of information is Fisher information?
Complementary to @NeilG's nice answer (+1) and to address your specific questions:
I would say it counts the "precision" rather than the "error" itself.
Remember that the Hessian of the log-like |
4,952 | Why is there a difference between manually calculating a logistic regression 95% confidence interval, and using the confint() function in R? | After having fetched the data from the accompanying website, here is how I would do it:
chdage <- read.table("chdage.dat", header=F, col.names=c("id","age","chd"))
chdage$aged <- ifelse(chdage$age>=55, 1, 0)
mod.lr <- glm(chd ~ aged, data=chdage, family=binomial)
summary(mod.lr)
The 95% CIs based on profile likelihood... | Why is there a difference between manually calculating a logistic regression 95% confidence interval | After having fetched the data from the accompanying website, here is how I would do it:
chdage <- read.table("chdage.dat", header=F, col.names=c("id","age","chd"))
chdage$aged <- ifelse(chdage$age>=55 | Why is there a difference between manually calculating a logistic regression 95% confidence interval, and using the confint() function in R?
After having fetched the data from the accompanying website, here is how I would do it:
chdage <- read.table("chdage.dat", header=F, col.names=c("id","age","chd"))
chdage$aged <- ... | Why is there a difference between manually calculating a logistic regression 95% confidence interval
After having fetched the data from the accompanying website, here is how I would do it:
chdage <- read.table("chdage.dat", header=F, col.names=c("id","age","chd"))
chdage$aged <- ifelse(chdage$age>=55 |
4,953 | Why is there a difference between manually calculating a logistic regression 95% confidence interval, and using the confint() function in R? | Following up: profile confidence intervals are more reliable (choosing the appropriate cutoff for the likelihood does involve an asymptotic (large sample) assumption, but this is a much weaker assumption than the quadratic-likelihood-surface assumption underlying the Wald confidence intervals). As far as I know, there ... | Why is there a difference between manually calculating a logistic regression 95% confidence interval | Following up: profile confidence intervals are more reliable (choosing the appropriate cutoff for the likelihood does involve an asymptotic (large sample) assumption, but this is a much weaker assumpt | Why is there a difference between manually calculating a logistic regression 95% confidence interval, and using the confint() function in R?
Following up: profile confidence intervals are more reliable (choosing the appropriate cutoff for the likelihood does involve an asymptotic (large sample) assumption, but this is ... | Why is there a difference between manually calculating a logistic regression 95% confidence interval
Following up: profile confidence intervals are more reliable (choosing the appropriate cutoff for the likelihood does involve an asymptotic (large sample) assumption, but this is a much weaker assumpt |
4,954 | Why is there a difference between manually calculating a logistic regression 95% confidence interval, and using the confint() function in R? | I believe if you look into the help file for confint() you will find that the confidence interval being constructed is a "profile" interval instead of a Wald confidence interval (your formula from HL). | Why is there a difference between manually calculating a logistic regression 95% confidence interval | I believe if you look into the help file for confint() you will find that the confidence interval being constructed is a "profile" interval instead of a Wald confidence interval (your formula from HL) | Why is there a difference between manually calculating a logistic regression 95% confidence interval, and using the confint() function in R?
I believe if you look into the help file for confint() you will find that the confidence interval being constructed is a "profile" interval instead of a Wald confidence interval (... | Why is there a difference between manually calculating a logistic regression 95% confidence interval
I believe if you look into the help file for confint() you will find that the confidence interval being constructed is a "profile" interval instead of a Wald confidence interval (your formula from HL) |
4,955 | How to perform a test using R to see if data follows normal distribution | If I understand your question correctly, then to test if word occurrences in a set of documents follows a Normal distribution you can just use a shapiro-Wilk test and some qqplots. For example,
## Generate two data sets
## First Normal, second from a t-distribution
words1 = rnorm(100); words2 = rt(100, df=3)
## Have a... | How to perform a test using R to see if data follows normal distribution | If I understand your question correctly, then to test if word occurrences in a set of documents follows a Normal distribution you can just use a shapiro-Wilk test and some qqplots. For example,
## Gen | How to perform a test using R to see if data follows normal distribution
If I understand your question correctly, then to test if word occurrences in a set of documents follows a Normal distribution you can just use a shapiro-Wilk test and some qqplots. For example,
## Generate two data sets
## First Normal, second fro... | How to perform a test using R to see if data follows normal distribution
If I understand your question correctly, then to test if word occurrences in a set of documents follows a Normal distribution you can just use a shapiro-Wilk test and some qqplots. For example,
## Gen |
4,956 | How to perform a test using R to see if data follows normal distribution | Assuming your dataset is called words and has a counts column, you can plot the histogram to have a visualization of the distribution:
hist(words$counts, 100, col="black")
where 100 is the number of bins
You can also do a normal Q-Q plot using
qqnorm(words$counts)
Finally, you can also use the Shapiro-Wilk test for n... | How to perform a test using R to see if data follows normal distribution | Assuming your dataset is called words and has a counts column, you can plot the histogram to have a visualization of the distribution:
hist(words$counts, 100, col="black")
where 100 is the number of | How to perform a test using R to see if data follows normal distribution
Assuming your dataset is called words and has a counts column, you can plot the histogram to have a visualization of the distribution:
hist(words$counts, 100, col="black")
where 100 is the number of bins
You can also do a normal Q-Q plot using
qq... | How to perform a test using R to see if data follows normal distribution
Assuming your dataset is called words and has a counts column, you can plot the histogram to have a visualization of the distribution:
hist(words$counts, 100, col="black")
where 100 is the number of |
4,957 | How to perform a test using R to see if data follows normal distribution | No test will show you that your data has a normal distribution - it will only be able to show you when the data is sufficiently inconsistent with a normal that you would reject the null.
But counts are not normal in any case, they're positive integers - what's the probability that an observation from a normal distribu... | How to perform a test using R to see if data follows normal distribution | No test will show you that your data has a normal distribution - it will only be able to show you when the data is sufficiently inconsistent with a normal that you would reject the null.
But counts a | How to perform a test using R to see if data follows normal distribution
No test will show you that your data has a normal distribution - it will only be able to show you when the data is sufficiently inconsistent with a normal that you would reject the null.
But counts are not normal in any case, they're positive int... | How to perform a test using R to see if data follows normal distribution
No test will show you that your data has a normal distribution - it will only be able to show you when the data is sufficiently inconsistent with a normal that you would reject the null.
But counts a |
4,958 | How to perform a test using R to see if data follows normal distribution | A more formal way of looking at the normality is by testing whether the kurtosis and skewness are significantly different from zero.
To do this, we need to get:
kurtosis.test <- function (x) {
m4 <- sum((x-mean(x))^4)/length(x)
s4 <- var(x)^2
kurt <- (m4/s4) - 3
sek <- sqrt(24/length(x))
totest <- kurt/sek
pvalue <-... | How to perform a test using R to see if data follows normal distribution | A more formal way of looking at the normality is by testing whether the kurtosis and skewness are significantly different from zero.
To do this, we need to get:
kurtosis.test <- function (x) {
m4 < | How to perform a test using R to see if data follows normal distribution
A more formal way of looking at the normality is by testing whether the kurtosis and skewness are significantly different from zero.
To do this, we need to get:
kurtosis.test <- function (x) {
m4 <- sum((x-mean(x))^4)/length(x)
s4 <- var(x)^2
k... | How to perform a test using R to see if data follows normal distribution
A more formal way of looking at the normality is by testing whether the kurtosis and skewness are significantly different from zero.
To do this, we need to get:
kurtosis.test <- function (x) {
m4 < |
4,959 | How to perform a test using R to see if data follows normal distribution | By using the nortest package of R, these tests can be conducted:
Perform Anderson-Darling normality test
ad.test(data1)
Perform Cramér-von Mises test for normality
cvm.test(data1)
Perform Pearson chi-square test for normality
pearson.test(data1)
Perform Shapiro-Francia test for normality
sf.test(data1)
Many other... | How to perform a test using R to see if data follows normal distribution | By using the nortest package of R, these tests can be conducted:
Perform Anderson-Darling normality test
ad.test(data1)
Perform Cramér-von Mises test for normality
cvm.test(data1)
Perform Pearson c | How to perform a test using R to see if data follows normal distribution
By using the nortest package of R, these tests can be conducted:
Perform Anderson-Darling normality test
ad.test(data1)
Perform Cramér-von Mises test for normality
cvm.test(data1)
Perform Pearson chi-square test for normality
pearson.test(data1... | How to perform a test using R to see if data follows normal distribution
By using the nortest package of R, these tests can be conducted:
Perform Anderson-Darling normality test
ad.test(data1)
Perform Cramér-von Mises test for normality
cvm.test(data1)
Perform Pearson c |
4,960 | How to perform a test using R to see if data follows normal distribution | In addition to the Shapiro-Wilk test of the stats package, the nortest package (available on CRAN) provides other normality tests. | How to perform a test using R to see if data follows normal distribution | In addition to the Shapiro-Wilk test of the stats package, the nortest package (available on CRAN) provides other normality tests. | How to perform a test using R to see if data follows normal distribution
In addition to the Shapiro-Wilk test of the stats package, the nortest package (available on CRAN) provides other normality tests. | How to perform a test using R to see if data follows normal distribution
In addition to the Shapiro-Wilk test of the stats package, the nortest package (available on CRAN) provides other normality tests. |
4,961 | Alternatives to one-way ANOVA for heteroskedastic data | There are a number of options available when dealing with heteroscedastic data. Unfortunately, none of them is guaranteed to always work. Here are some options I'm familiar with:
transformations
Welch ANOVA
weighted least squares
robust regression
heteroscedasticity consistent standard errors
bootstrap
Kruskal-Walli... | Alternatives to one-way ANOVA for heteroskedastic data | There are a number of options available when dealing with heteroscedastic data. Unfortunately, none of them is guaranteed to always work. Here are some options I'm familiar with:
transformations
We | Alternatives to one-way ANOVA for heteroskedastic data
There are a number of options available when dealing with heteroscedastic data. Unfortunately, none of them is guaranteed to always work. Here are some options I'm familiar with:
transformations
Welch ANOVA
weighted least squares
robust regression
heteroscedasti... | Alternatives to one-way ANOVA for heteroskedastic data
There are a number of options available when dealing with heteroscedastic data. Unfortunately, none of them is guaranteed to always work. Here are some options I'm familiar with:
transformations
We |
4,962 | What is Deviance? (specifically in CART/rpart) | Deviance and GLM
Formally, one can view deviance as a sort of distance between two probabilistic models; in GLM context, it amounts to two times the log ratio of likelihoods between two nested models $\ell_1/\ell_0$ where $\ell_0$ is the "smaller" model; that is, a linear restriction on model parameters (cf. the Neyman... | What is Deviance? (specifically in CART/rpart) | Deviance and GLM
Formally, one can view deviance as a sort of distance between two probabilistic models; in GLM context, it amounts to two times the log ratio of likelihoods between two nested models | What is Deviance? (specifically in CART/rpart)
Deviance and GLM
Formally, one can view deviance as a sort of distance between two probabilistic models; in GLM context, it amounts to two times the log ratio of likelihoods between two nested models $\ell_1/\ell_0$ where $\ell_0$ is the "smaller" model; that is, a linear ... | What is Deviance? (specifically in CART/rpart)
Deviance and GLM
Formally, one can view deviance as a sort of distance between two probabilistic models; in GLM context, it amounts to two times the log ratio of likelihoods between two nested models |
4,963 | What is Deviance? (specifically in CART/rpart) | It might be a bit clearer if we think about a perfect model with as many parameters as observations such that it explains all variance in the response. This is the saturated model. Deviance simply measures the difference in "fit" of a candidate model and that of the saturated model.
In a regression tree, the saturated ... | What is Deviance? (specifically in CART/rpart) | It might be a bit clearer if we think about a perfect model with as many parameters as observations such that it explains all variance in the response. This is the saturated model. Deviance simply mea | What is Deviance? (specifically in CART/rpart)
It might be a bit clearer if we think about a perfect model with as many parameters as observations such that it explains all variance in the response. This is the saturated model. Deviance simply measures the difference in "fit" of a candidate model and that of the satura... | What is Deviance? (specifically in CART/rpart)
It might be a bit clearer if we think about a perfect model with as many parameters as observations such that it explains all variance in the response. This is the saturated model. Deviance simply mea |
4,964 | What is Deviance? (specifically in CART/rpart) | Deviance is the likelihood-ratio statistic for testing the null hypothesis that the model holds agains the general alternative (i.e., the saturated model). For some Poisson and binomial GLMs, the number of observations $N$ stays fixed as the individual counts increase in size. Then the deviance has a chi-squared asymp... | What is Deviance? (specifically in CART/rpart) | Deviance is the likelihood-ratio statistic for testing the null hypothesis that the model holds agains the general alternative (i.e., the saturated model). For some Poisson and binomial GLMs, the numb | What is Deviance? (specifically in CART/rpart)
Deviance is the likelihood-ratio statistic for testing the null hypothesis that the model holds agains the general alternative (i.e., the saturated model). For some Poisson and binomial GLMs, the number of observations $N$ stays fixed as the individual counts increase in ... | What is Deviance? (specifically in CART/rpart)
Deviance is the likelihood-ratio statistic for testing the null hypothesis that the model holds agains the general alternative (i.e., the saturated model). For some Poisson and binomial GLMs, the numb |
4,965 | Rank in R - descending order [closed] | You could negate x:
> rank(-x)
[1] 5 3 6 2 4 1 | Rank in R - descending order [closed] | You could negate x:
> rank(-x)
[1] 5 3 6 2 4 1 | Rank in R - descending order [closed]
You could negate x:
> rank(-x)
[1] 5 3 6 2 4 1 | Rank in R - descending order [closed]
You could negate x:
> rank(-x)
[1] 5 3 6 2 4 1 |
4,966 | Deriving Bellman's Equation in Reinforcement Learning | There are already a great many answers to this question, but most involve few words describing what is going on in the manipulations. I'm going to answer it using way more words, I think. To start,
$$G_{t} \doteq \sum_{k=t+1}^{T} \gamma^{k-t-1} R_{k}$$
is defined in equation 3.11 of Sutton and Barto, with a constant... | Deriving Bellman's Equation in Reinforcement Learning | There are already a great many answers to this question, but most involve few words describing what is going on in the manipulations. I'm going to answer it using way more words, I think. To start, | Deriving Bellman's Equation in Reinforcement Learning
There are already a great many answers to this question, but most involve few words describing what is going on in the manipulations. I'm going to answer it using way more words, I think. To start,
$$G_{t} \doteq \sum_{k=t+1}^{T} \gamma^{k-t-1} R_{k}$$
is defined... | Deriving Bellman's Equation in Reinforcement Learning
There are already a great many answers to this question, but most involve few words describing what is going on in the manipulations. I'm going to answer it using way more words, I think. To start, |
4,967 | Deriving Bellman's Equation in Reinforcement Learning | Here is my proof. It is based on the manipulation of conditional distributions, which makes it easier to follow. Hope this one helps you.
\begin{align}
v_{\pi}(s)&=E{\left[G_t|S_t=s\right]} \nonumber \\
&=E{\left[R_{t+1}+\gamma G_{t+1}|S_t=s\right]} \nonumber \\
&= \sum_{s'}\sum_{r}\sum_{g_{t+1}}\sum_{a}p(s',r,g_{t+1},... | Deriving Bellman's Equation in Reinforcement Learning | Here is my proof. It is based on the manipulation of conditional distributions, which makes it easier to follow. Hope this one helps you.
\begin{align}
v_{\pi}(s)&=E{\left[G_t|S_t=s\right]} \nonumber | Deriving Bellman's Equation in Reinforcement Learning
Here is my proof. It is based on the manipulation of conditional distributions, which makes it easier to follow. Hope this one helps you.
\begin{align}
v_{\pi}(s)&=E{\left[G_t|S_t=s\right]} \nonumber \\
&=E{\left[R_{t+1}+\gamma G_{t+1}|S_t=s\right]} \nonumber \\
&= ... | Deriving Bellman's Equation in Reinforcement Learning
Here is my proof. It is based on the manipulation of conditional distributions, which makes it easier to follow. Hope this one helps you.
\begin{align}
v_{\pi}(s)&=E{\left[G_t|S_t=s\right]} \nonumber |
4,968 | Deriving Bellman's Equation in Reinforcement Learning | This is the answer for everybody who wonders about the clean, structured math behind it (i.e. if you belong to the group of people that knows what a random variable is and that you must show or assume that a random variable has a density then this is the answer for you ;-)):
First of all we need to have that the Markov... | Deriving Bellman's Equation in Reinforcement Learning | This is the answer for everybody who wonders about the clean, structured math behind it (i.e. if you belong to the group of people that knows what a random variable is and that you must show or assume | Deriving Bellman's Equation in Reinforcement Learning
This is the answer for everybody who wonders about the clean, structured math behind it (i.e. if you belong to the group of people that knows what a random variable is and that you must show or assume that a random variable has a density then this is the answer for ... | Deriving Bellman's Equation in Reinforcement Learning
This is the answer for everybody who wonders about the clean, structured math behind it (i.e. if you belong to the group of people that knows what a random variable is and that you must show or assume |
4,969 | Deriving Bellman's Equation in Reinforcement Learning | Let total sum of discounted rewards after time $t$ be:
$G_t = R_{t+1}+\gamma R_{t+2}+\gamma^2 R_{t+3}+...$
Utility value of starting in state,$s$ at time,$t$ is equivalent to expected sum of
discounted rewards $R$ of executing policy $\pi$ starting from state $s$ onwards.
$U_\pi(S_t=s) = E_\pi[G_t|S_t = s]$
$\\... | Deriving Bellman's Equation in Reinforcement Learning | Let total sum of discounted rewards after time $t$ be:
$G_t = R_{t+1}+\gamma R_{t+2}+\gamma^2 R_{t+3}+...$
Utility value of starting in state,$s$ at time,$t$ is equivalent to expected sum of
disco | Deriving Bellman's Equation in Reinforcement Learning
Let total sum of discounted rewards after time $t$ be:
$G_t = R_{t+1}+\gamma R_{t+2}+\gamma^2 R_{t+3}+...$
Utility value of starting in state,$s$ at time,$t$ is equivalent to expected sum of
discounted rewards $R$ of executing policy $\pi$ starting from state $s... | Deriving Bellman's Equation in Reinforcement Learning
Let total sum of discounted rewards after time $t$ be:
$G_t = R_{t+1}+\gamma R_{t+2}+\gamma^2 R_{t+3}+...$
Utility value of starting in state,$s$ at time,$t$ is equivalent to expected sum of
disco |
4,970 | Deriving Bellman's Equation in Reinforcement Learning | I know there is already an accepted answer, but I wish to provide a probably more concrete derivation. I would also like to mention that although @Jie Shi trick somewhat makes sense, but it makes me feel very uncomfortable:(. We need to consider the time dimension to make this work. And it is important to note that, th... | Deriving Bellman's Equation in Reinforcement Learning | I know there is already an accepted answer, but I wish to provide a probably more concrete derivation. I would also like to mention that although @Jie Shi trick somewhat makes sense, but it makes me f | Deriving Bellman's Equation in Reinforcement Learning
I know there is already an accepted answer, but I wish to provide a probably more concrete derivation. I would also like to mention that although @Jie Shi trick somewhat makes sense, but it makes me feel very uncomfortable:(. We need to consider the time dimension t... | Deriving Bellman's Equation in Reinforcement Learning
I know there is already an accepted answer, but I wish to provide a probably more concrete derivation. I would also like to mention that although @Jie Shi trick somewhat makes sense, but it makes me f |
4,971 | Deriving Bellman's Equation in Reinforcement Learning | This is just a comment/addition to the accepted answer.
I was confused at the line where law of total expectation is being applied. I don't think the main form of law of total expectation can help here. A variant of that is in fact needed here.
If $X,Y,Z$ are random variables and assuming all the expectation exists, t... | Deriving Bellman's Equation in Reinforcement Learning | This is just a comment/addition to the accepted answer.
I was confused at the line where law of total expectation is being applied. I don't think the main form of law of total expectation can help he | Deriving Bellman's Equation in Reinforcement Learning
This is just a comment/addition to the accepted answer.
I was confused at the line where law of total expectation is being applied. I don't think the main form of law of total expectation can help here. A variant of that is in fact needed here.
If $X,Y,Z$ are rando... | Deriving Bellman's Equation in Reinforcement Learning
This is just a comment/addition to the accepted answer.
I was confused at the line where law of total expectation is being applied. I don't think the main form of law of total expectation can help he |
4,972 | Deriving Bellman's Equation in Reinforcement Learning | even though the correct answer has already been given and some time has passed, I thought the following step by step guide might be useful:
By linearity of the Expected Value we can split $E[R_{t+1} + \gamma E[G_{t+1}|S_{t}=s]]$
into $E[R_{t+1}|S_t=s]$ and $\gamma E[G_{t+1}|S_{t}=s]$.
I will outline the steps only for... | Deriving Bellman's Equation in Reinforcement Learning | even though the correct answer has already been given and some time has passed, I thought the following step by step guide might be useful:
By linearity of the Expected Value we can split $E[R_{t+1} + | Deriving Bellman's Equation in Reinforcement Learning
even though the correct answer has already been given and some time has passed, I thought the following step by step guide might be useful:
By linearity of the Expected Value we can split $E[R_{t+1} + \gamma E[G_{t+1}|S_{t}=s]]$
into $E[R_{t+1}|S_t=s]$ and $\gamma ... | Deriving Bellman's Equation in Reinforcement Learning
even though the correct answer has already been given and some time has passed, I thought the following step by step guide might be useful:
By linearity of the Expected Value we can split $E[R_{t+1} + |
4,973 | Deriving Bellman's Equation in Reinforcement Learning | What's with the following approach?
$$\begin{align}
v_\pi(s) & = \mathbb{E}_\pi\left[G_t \mid S_t = s\right] \\
& = \mathbb{E}_\pi\left[R_{t+1} + \gamma G_{t+1} \mid S_t = s\right] \\
& = \sum_a \pi(a \mid s) \sum_{s'} \sum_r p(s', r \mid s, a) \cdot \,\\
& \qquad \mathbb{E}_\pi\left[R_{t+1} + \gamma G_{t+1} \m... | Deriving Bellman's Equation in Reinforcement Learning | What's with the following approach?
$$\begin{align}
v_\pi(s) & = \mathbb{E}_\pi\left[G_t \mid S_t = s\right] \\
& = \mathbb{E}_\pi\left[R_{t+1} + \gamma G_{t+1} \mid S_t = s\right] \\
& = \sum_a | Deriving Bellman's Equation in Reinforcement Learning
What's with the following approach?
$$\begin{align}
v_\pi(s) & = \mathbb{E}_\pi\left[G_t \mid S_t = s\right] \\
& = \mathbb{E}_\pi\left[R_{t+1} + \gamma G_{t+1} \mid S_t = s\right] \\
& = \sum_a \pi(a \mid s) \sum_{s'} \sum_r p(s', r \mid s, a) \cdot \,\\
& ... | Deriving Bellman's Equation in Reinforcement Learning
What's with the following approach?
$$\begin{align}
v_\pi(s) & = \mathbb{E}_\pi\left[G_t \mid S_t = s\right] \\
& = \mathbb{E}_\pi\left[R_{t+1} + \gamma G_{t+1} \mid S_t = s\right] \\
& = \sum_a |
4,974 | Deriving Bellman's Equation in Reinforcement Learning | $\mathbb{E}_\pi(\cdot)$ usually denotes the expectation assuming the agent follows policy $\pi$. In this case $\pi(a|s)$ seems non-deterministic, i.e. returns the probability that the agent takes action $a$ when in state $s$.
It looks like $r$, lower-case, is replacing $R_{t+1}$, a random variable. The second expectat... | Deriving Bellman's Equation in Reinforcement Learning | $\mathbb{E}_\pi(\cdot)$ usually denotes the expectation assuming the agent follows policy $\pi$. In this case $\pi(a|s)$ seems non-deterministic, i.e. returns the probability that the agent takes acti | Deriving Bellman's Equation in Reinforcement Learning
$\mathbb{E}_\pi(\cdot)$ usually denotes the expectation assuming the agent follows policy $\pi$. In this case $\pi(a|s)$ seems non-deterministic, i.e. returns the probability that the agent takes action $a$ when in state $s$.
It looks like $r$, lower-case, is repla... | Deriving Bellman's Equation in Reinforcement Learning
$\mathbb{E}_\pi(\cdot)$ usually denotes the expectation assuming the agent follows policy $\pi$. In this case $\pi(a|s)$ seems non-deterministic, i.e. returns the probability that the agent takes acti |
4,975 | Deriving Bellman's Equation in Reinforcement Learning | Here is an approach that uses the results of exercises in the book (assuming you are using the 2nd edition of the book). In exercise 3.12 you should have derived the equation $$v_\pi(s) = \sum_a \pi(a \mid s) q_\pi(s,a)$$ and in exercise 3.13 you should have derived the equation $$q_\pi(s,a) = \sum_{s',r} p(s',r\mid s,... | Deriving Bellman's Equation in Reinforcement Learning | Here is an approach that uses the results of exercises in the book (assuming you are using the 2nd edition of the book). In exercise 3.12 you should have derived the equation $$v_\pi(s) = \sum_a \pi(a | Deriving Bellman's Equation in Reinforcement Learning
Here is an approach that uses the results of exercises in the book (assuming you are using the 2nd edition of the book). In exercise 3.12 you should have derived the equation $$v_\pi(s) = \sum_a \pi(a \mid s) q_\pi(s,a)$$ and in exercise 3.13 you should have derived... | Deriving Bellman's Equation in Reinforcement Learning
Here is an approach that uses the results of exercises in the book (assuming you are using the 2nd edition of the book). In exercise 3.12 you should have derived the equation $$v_\pi(s) = \sum_a \pi(a |
4,976 | Deriving Bellman's Equation in Reinforcement Learning | I wasn't satisfied with any of the above solutions, so I'll give it a try. I find the solution proposed by riceissa the most elegant one, but he only proved the last step. I want to add the missing pieces. So let's go ...
Proof of $v_\pi(s) = \sum_a\pi(a|s)q_\pi(s,a)$:
\begin{eqnarray*}
v_\pi(s) &=& \mathbb{E}_\pi[G_t|... | Deriving Bellman's Equation in Reinforcement Learning | I wasn't satisfied with any of the above solutions, so I'll give it a try. I find the solution proposed by riceissa the most elegant one, but he only proved the last step. I want to add the missing pi | Deriving Bellman's Equation in Reinforcement Learning
I wasn't satisfied with any of the above solutions, so I'll give it a try. I find the solution proposed by riceissa the most elegant one, but he only proved the last step. I want to add the missing pieces. So let's go ...
Proof of $v_\pi(s) = \sum_a\pi(a|s)q_\pi(s,a... | Deriving Bellman's Equation in Reinforcement Learning
I wasn't satisfied with any of the above solutions, so I'll give it a try. I find the solution proposed by riceissa the most elegant one, but he only proved the last step. I want to add the missing pi |
4,977 | How does rectilinear activation function solve the vanishing gradient problem in neural networks? | Here is a paper that explains the issue. I'm quoting some part of it to make the issue clear.
The rectifier activation function allows a network to easily obtain sparse representations. For example, after uniform initialization of the weights, around
50%
of hidden units continuous output values are real zeros, ... | How does rectilinear activation function solve the vanishing gradient problem in neural networks? | Here is a paper that explains the issue. I'm quoting some part of it to make the issue clear.
The rectifier activation function allows a network to easily obtain sparse representations. For example, | How does rectilinear activation function solve the vanishing gradient problem in neural networks?
Here is a paper that explains the issue. I'm quoting some part of it to make the issue clear.
The rectifier activation function allows a network to easily obtain sparse representations. For example, after uniform initial... | How does rectilinear activation function solve the vanishing gradient problem in neural networks?
Here is a paper that explains the issue. I'm quoting some part of it to make the issue clear.
The rectifier activation function allows a network to easily obtain sparse representations. For example, |
4,978 | How does rectilinear activation function solve the vanishing gradient problem in neural networks? | Here is a heuristic explanation:
Each gradient update in backprop consists of a number of multiplied factors.
The further you get towards the start of the network, the more of these factors are multiplied together to get the gradient update.
Many of these factors are derivatives of the activation function of the neur... | How does rectilinear activation function solve the vanishing gradient problem in neural networks? | Here is a heuristic explanation:
Each gradient update in backprop consists of a number of multiplied factors.
The further you get towards the start of the network, the more of these factors are mult | How does rectilinear activation function solve the vanishing gradient problem in neural networks?
Here is a heuristic explanation:
Each gradient update in backprop consists of a number of multiplied factors.
The further you get towards the start of the network, the more of these factors are multiplied together to get... | How does rectilinear activation function solve the vanishing gradient problem in neural networks?
Here is a heuristic explanation:
Each gradient update in backprop consists of a number of multiplied factors.
The further you get towards the start of the network, the more of these factors are mult |
4,979 | How does rectilinear activation function solve the vanishing gradient problem in neural networks? | This is why it's probably a better idea to use PReLU, ELU, or other leaky ReLU-like activations which don't just die off to 0, but which fall to something like 0.1*x when x gets negative to keep learning. It seemed to me for a long time that ReLUs are history like sigmoid, though for some reason people still publish pa... | How does rectilinear activation function solve the vanishing gradient problem in neural networks? | This is why it's probably a better idea to use PReLU, ELU, or other leaky ReLU-like activations which don't just die off to 0, but which fall to something like 0.1*x when x gets negative to keep learn | How does rectilinear activation function solve the vanishing gradient problem in neural networks?
This is why it's probably a better idea to use PReLU, ELU, or other leaky ReLU-like activations which don't just die off to 0, but which fall to something like 0.1*x when x gets negative to keep learning. It seemed to me f... | How does rectilinear activation function solve the vanishing gradient problem in neural networks?
This is why it's probably a better idea to use PReLU, ELU, or other leaky ReLU-like activations which don't just die off to 0, but which fall to something like 0.1*x when x gets negative to keep learn |
4,980 | How does rectilinear activation function solve the vanishing gradient problem in neural networks? | Let's consider the main recurrence relation that defines the back propagation of the error signal.
let $ {W_i}$ and ${b_i}$ be the weight matrix and bias vector of layer $\text{i}$, and ${f}$ be the activation function.
The activation vector ${h_i}$ of layer ${i}$ is calculated as follows:
${s_i} = {W_i}({h_{i-1}}) + ... | How does rectilinear activation function solve the vanishing gradient problem in neural networks? | Let's consider the main recurrence relation that defines the back propagation of the error signal.
let $ {W_i}$ and ${b_i}$ be the weight matrix and bias vector of layer $\text{i}$, and ${f}$ be the | How does rectilinear activation function solve the vanishing gradient problem in neural networks?
Let's consider the main recurrence relation that defines the back propagation of the error signal.
let $ {W_i}$ and ${b_i}$ be the weight matrix and bias vector of layer $\text{i}$, and ${f}$ be the activation function.
T... | How does rectilinear activation function solve the vanishing gradient problem in neural networks?
Let's consider the main recurrence relation that defines the back propagation of the error signal.
let $ {W_i}$ and ${b_i}$ be the weight matrix and bias vector of layer $\text{i}$, and ${f}$ be the |
4,981 | How does rectilinear activation function solve the vanishing gradient problem in neural networks? | Essentially, ReLUs only lead to vanishing gradients for inputs smaller than zero, while for other inputs they allow the gradient to pass through (look at plot of derivative of ReLU). This is unlike Sigmoid and Tanh, with can lead to gradient saturation for small and large values.
From Original ReLU paper:
Because of t... | How does rectilinear activation function solve the vanishing gradient problem in neural networks? | Essentially, ReLUs only lead to vanishing gradients for inputs smaller than zero, while for other inputs they allow the gradient to pass through (look at plot of derivative of ReLU). This is unlike Si | How does rectilinear activation function solve the vanishing gradient problem in neural networks?
Essentially, ReLUs only lead to vanishing gradients for inputs smaller than zero, while for other inputs they allow the gradient to pass through (look at plot of derivative of ReLU). This is unlike Sigmoid and Tanh, with c... | How does rectilinear activation function solve the vanishing gradient problem in neural networks?
Essentially, ReLUs only lead to vanishing gradients for inputs smaller than zero, while for other inputs they allow the gradient to pass through (look at plot of derivative of ReLU). This is unlike Si |
4,982 | Hierarchical clustering with mixed type data - what distance/similarity to use? | One way is to use Gower similarity coefficient which is a composite measure$^1$; it takes quantitative (such as rating scale), binary (such as present/absent) and nominal (such as worker/teacher/clerk) variables. Later Podani$^2$ added an option to take ordinal variables as well.
The coefficient is easily understood ev... | Hierarchical clustering with mixed type data - what distance/similarity to use? | One way is to use Gower similarity coefficient which is a composite measure$^1$; it takes quantitative (such as rating scale), binary (such as present/absent) and nominal (such as worker/teacher/clerk | Hierarchical clustering with mixed type data - what distance/similarity to use?
One way is to use Gower similarity coefficient which is a composite measure$^1$; it takes quantitative (such as rating scale), binary (such as present/absent) and nominal (such as worker/teacher/clerk) variables. Later Podani$^2$ added an o... | Hierarchical clustering with mixed type data - what distance/similarity to use?
One way is to use Gower similarity coefficient which is a composite measure$^1$; it takes quantitative (such as rating scale), binary (such as present/absent) and nominal (such as worker/teacher/clerk |
4,983 | Hierarchical clustering with mixed type data - what distance/similarity to use? | If you have stumbled upon this question and are wondering what package to download for using Gower metric in R, the cluster package has a function named daisy(), which by default uses Gower's metric whenever mixed types of variables are used. Or you can manually set it to use Gower's metric.
daisy(x, metric = c("eucli... | Hierarchical clustering with mixed type data - what distance/similarity to use? | If you have stumbled upon this question and are wondering what package to download for using Gower metric in R, the cluster package has a function named daisy(), which by default uses Gower's metric | Hierarchical clustering with mixed type data - what distance/similarity to use?
If you have stumbled upon this question and are wondering what package to download for using Gower metric in R, the cluster package has a function named daisy(), which by default uses Gower's metric whenever mixed types of variables are us... | Hierarchical clustering with mixed type data - what distance/similarity to use?
If you have stumbled upon this question and are wondering what package to download for using Gower metric in R, the cluster package has a function named daisy(), which by default uses Gower's metric |
4,984 | What is difference between “in-sample” and “out-of-sample” forecasts? | By the "sample" it is meant the data sample that you are using to fit the model.
First - you have a sample
Second - you fit a model on the sample
Third - you can use the model for forecasting
If you are forecasting for an observation that was part of the data sample - it is in-sample forecast.
If you are forecasting ... | What is difference between “in-sample” and “out-of-sample” forecasts? | By the "sample" it is meant the data sample that you are using to fit the model.
First - you have a sample
Second - you fit a model on the sample
Third - you can use the model for forecasting
If you | What is difference between “in-sample” and “out-of-sample” forecasts?
By the "sample" it is meant the data sample that you are using to fit the model.
First - you have a sample
Second - you fit a model on the sample
Third - you can use the model for forecasting
If you are forecasting for an observation that was part ... | What is difference between “in-sample” and “out-of-sample” forecasts?
By the "sample" it is meant the data sample that you are using to fit the model.
First - you have a sample
Second - you fit a model on the sample
Third - you can use the model for forecasting
If you |
4,985 | What is difference between “in-sample” and “out-of-sample” forecasts? | Suppose in your sample, you have a sequence of 10 data points. This data can be divided into two parts - e.g. first 7 data points for estimating the model parameters and next 3 data points to test the model performance. Using the fitted model, predictions made for the first 7 data points will be called in-sample foreca... | What is difference between “in-sample” and “out-of-sample” forecasts? | Suppose in your sample, you have a sequence of 10 data points. This data can be divided into two parts - e.g. first 7 data points for estimating the model parameters and next 3 data points to test the | What is difference between “in-sample” and “out-of-sample” forecasts?
Suppose in your sample, you have a sequence of 10 data points. This data can be divided into two parts - e.g. first 7 data points for estimating the model parameters and next 3 data points to test the model performance. Using the fitted model, predic... | What is difference between “in-sample” and “out-of-sample” forecasts?
Suppose in your sample, you have a sequence of 10 data points. This data can be divided into two parts - e.g. first 7 data points for estimating the model parameters and next 3 data points to test the |
4,986 | What is difference between “in-sample” and “out-of-sample” forecasts? | The below diagram will help you understand the IN TIME and OUT OF TIME | What is difference between “in-sample” and “out-of-sample” forecasts? | The below diagram will help you understand the IN TIME and OUT OF TIME | What is difference between “in-sample” and “out-of-sample” forecasts?
The below diagram will help you understand the IN TIME and OUT OF TIME | What is difference between “in-sample” and “out-of-sample” forecasts?
The below diagram will help you understand the IN TIME and OUT OF TIME |
4,987 | What is difference between “in-sample” and “out-of-sample” forecasts? | In-sample forecast is the process of formally evaluating the predictive capabilities of the models developed using observed data to see how effective the algorithms are in reproducing data. It is kind of similar to a training set in a machine learning algorithm and the out-of-sample is similar to the test set. | What is difference between “in-sample” and “out-of-sample” forecasts? | In-sample forecast is the process of formally evaluating the predictive capabilities of the models developed using observed data to see how effective the algorithms are in reproducing data. It is kind | What is difference between “in-sample” and “out-of-sample” forecasts?
In-sample forecast is the process of formally evaluating the predictive capabilities of the models developed using observed data to see how effective the algorithms are in reproducing data. It is kind of similar to a training set in a machine learnin... | What is difference between “in-sample” and “out-of-sample” forecasts?
In-sample forecast is the process of formally evaluating the predictive capabilities of the models developed using observed data to see how effective the algorithms are in reproducing data. It is kind |
4,988 | What is difference between “in-sample” and “out-of-sample” forecasts? | I consider the in-sample is used to construct a model. And out-of-sample means to exam the model which uses im-sample data. It just likes the data analysis training and test. | What is difference between “in-sample” and “out-of-sample” forecasts? | I consider the in-sample is used to construct a model. And out-of-sample means to exam the model which uses im-sample data. It just likes the data analysis training and test. | What is difference between “in-sample” and “out-of-sample” forecasts?
I consider the in-sample is used to construct a model. And out-of-sample means to exam the model which uses im-sample data. It just likes the data analysis training and test. | What is difference between “in-sample” and “out-of-sample” forecasts?
I consider the in-sample is used to construct a model. And out-of-sample means to exam the model which uses im-sample data. It just likes the data analysis training and test. |
4,989 | What is a latent space? | Latent space refers to an abstract multi-dimensional space containing feature values that we cannot interpret directly, but which encodes a meaningful internal representation of externally observed events.
Just as we, humans, have an understanding of a broad range of topics and the events belonging to those topics, lat... | What is a latent space? | Latent space refers to an abstract multi-dimensional space containing feature values that we cannot interpret directly, but which encodes a meaningful internal representation of externally observed ev | What is a latent space?
Latent space refers to an abstract multi-dimensional space containing feature values that we cannot interpret directly, but which encodes a meaningful internal representation of externally observed events.
Just as we, humans, have an understanding of a broad range of topics and the events belong... | What is a latent space?
Latent space refers to an abstract multi-dimensional space containing feature values that we cannot interpret directly, but which encodes a meaningful internal representation of externally observed ev |
4,990 | What is a latent space? | Latent space is a vector space spanned by the latent variables. Latent variables are variables which are not directly observable, but which are $-$ up to the level of noise $-$ sufficient to describe the data. I.e. the observable variables can be derived (computed) from the latent ones.
Let me use this image, adapted f... | What is a latent space? | Latent space is a vector space spanned by the latent variables. Latent variables are variables which are not directly observable, but which are $-$ up to the level of noise $-$ sufficient to describe | What is a latent space?
Latent space is a vector space spanned by the latent variables. Latent variables are variables which are not directly observable, but which are $-$ up to the level of noise $-$ sufficient to describe the data. I.e. the observable variables can be derived (computed) from the latent ones.
Let me u... | What is a latent space?
Latent space is a vector space spanned by the latent variables. Latent variables are variables which are not directly observable, but which are $-$ up to the level of noise $-$ sufficient to describe |
4,991 | What is a latent space? | This article would give you a great understanding about latent space,as a short review :
The latent space is simply a representation of compressed data in
which similar data points are closer together in space.
Latent space is useful for learning data features and for finding
simpler representations of data for analy... | What is a latent space? | This article would give you a great understanding about latent space,as a short review :
The latent space is simply a representation of compressed data in
which similar data points are closer togethe | What is a latent space?
This article would give you a great understanding about latent space,as a short review :
The latent space is simply a representation of compressed data in
which similar data points are closer together in space.
Latent space is useful for learning data features and for finding
simpler represent... | What is a latent space?
This article would give you a great understanding about latent space,as a short review :
The latent space is simply a representation of compressed data in
which similar data points are closer togethe |
4,992 | Danger of setting all initial weights to zero in Backpropagation [duplicate] | edit see alfa's comment below. I'm not an expert on neural nets, so I'll defer to him.
My understanding is different from the other answers that have been posted here.
I'm pretty sure that backpropagation involves adding to the existing weights, not multiplying. The amount that you add is specified by the delta rule.... | Danger of setting all initial weights to zero in Backpropagation [duplicate] | edit see alfa's comment below. I'm not an expert on neural nets, so I'll defer to him.
My understanding is different from the other answers that have been posted here.
I'm pretty sure that backpropag | Danger of setting all initial weights to zero in Backpropagation [duplicate]
edit see alfa's comment below. I'm not an expert on neural nets, so I'll defer to him.
My understanding is different from the other answers that have been posted here.
I'm pretty sure that backpropagation involves adding to the existing weigh... | Danger of setting all initial weights to zero in Backpropagation [duplicate]
edit see alfa's comment below. I'm not an expert on neural nets, so I'll defer to him.
My understanding is different from the other answers that have been posted here.
I'm pretty sure that backpropag |
4,993 | Danger of setting all initial weights to zero in Backpropagation [duplicate] | It's a bad idea because of 2 reasons:
If you have sigmoid activation, or anything where $g(0) \neq 0$ then it will cause weights to move "together", limiting the power of back-propagation to search the entire space to find the optimal weights which lower the loss/cost.
If you have $\tanh$ or ReLu activation, or anyth... | Danger of setting all initial weights to zero in Backpropagation [duplicate] | It's a bad idea because of 2 reasons:
If you have sigmoid activation, or anything where $g(0) \neq 0$ then it will cause weights to move "together", limiting the power of back-propagation to search t | Danger of setting all initial weights to zero in Backpropagation [duplicate]
It's a bad idea because of 2 reasons:
If you have sigmoid activation, or anything where $g(0) \neq 0$ then it will cause weights to move "together", limiting the power of back-propagation to search the entire space to find the optimal weights... | Danger of setting all initial weights to zero in Backpropagation [duplicate]
It's a bad idea because of 2 reasons:
If you have sigmoid activation, or anything where $g(0) \neq 0$ then it will cause weights to move "together", limiting the power of back-propagation to search t |
4,994 | Danger of setting all initial weights to zero in Backpropagation [duplicate] | If you thought of the weights as priors, as in a Bayesian network, then you've ruled out any possibility that those inputs could possibly affect the system. Another explanation is that backpropagation identifies the set of weights that minimizes the weighted squared difference between the target and observed values (E)... | Danger of setting all initial weights to zero in Backpropagation [duplicate] | If you thought of the weights as priors, as in a Bayesian network, then you've ruled out any possibility that those inputs could possibly affect the system. Another explanation is that backpropagation | Danger of setting all initial weights to zero in Backpropagation [duplicate]
If you thought of the weights as priors, as in a Bayesian network, then you've ruled out any possibility that those inputs could possibly affect the system. Another explanation is that backpropagation identifies the set of weights that minimiz... | Danger of setting all initial weights to zero in Backpropagation [duplicate]
If you thought of the weights as priors, as in a Bayesian network, then you've ruled out any possibility that those inputs could possibly affect the system. Another explanation is that backpropagation |
4,995 | Danger of setting all initial weights to zero in Backpropagation [duplicate] | In each iteration of your backpropagation algorithm, you will update the weights by multiplying the existing weight by a delta determined by backpropagation. If the initial weight value is 0, multiplying it by any value for delta won't change the weight which means each iteration has no effect on the weights you're try... | Danger of setting all initial weights to zero in Backpropagation [duplicate] | In each iteration of your backpropagation algorithm, you will update the weights by multiplying the existing weight by a delta determined by backpropagation. If the initial weight value is 0, multiply | Danger of setting all initial weights to zero in Backpropagation [duplicate]
In each iteration of your backpropagation algorithm, you will update the weights by multiplying the existing weight by a delta determined by backpropagation. If the initial weight value is 0, multiplying it by any value for delta won't change ... | Danger of setting all initial weights to zero in Backpropagation [duplicate]
In each iteration of your backpropagation algorithm, you will update the weights by multiplying the existing weight by a delta determined by backpropagation. If the initial weight value is 0, multiply |
4,996 | Danger of setting all initial weights to zero in Backpropagation [duplicate] | It seems to me that one reason why it's bad to initialize weights to the same values (not just zero) is because then for any particular hidden layer all the nodes in this layer would have exactly the same inputs and would therefore stay the same as each other. | Danger of setting all initial weights to zero in Backpropagation [duplicate] | It seems to me that one reason why it's bad to initialize weights to the same values (not just zero) is because then for any particular hidden layer all the nodes in this layer would have exactly the | Danger of setting all initial weights to zero in Backpropagation [duplicate]
It seems to me that one reason why it's bad to initialize weights to the same values (not just zero) is because then for any particular hidden layer all the nodes in this layer would have exactly the same inputs and would therefore stay the sa... | Danger of setting all initial weights to zero in Backpropagation [duplicate]
It seems to me that one reason why it's bad to initialize weights to the same values (not just zero) is because then for any particular hidden layer all the nodes in this layer would have exactly the |
4,997 | Danger of setting all initial weights to zero in Backpropagation [duplicate] | The answer to this is not entirely "Local Minima/Maxima".
When you have more than 1 Hidden Layer and every weight are 0's, no matter how big/small a change in Weight_i will not cause a change in the Output.
This is because delta Weight_i will be absorbed by the next Hidden Layer.
When there is no change in the Output, ... | Danger of setting all initial weights to zero in Backpropagation [duplicate] | The answer to this is not entirely "Local Minima/Maxima".
When you have more than 1 Hidden Layer and every weight are 0's, no matter how big/small a change in Weight_i will not cause a change in the O | Danger of setting all initial weights to zero in Backpropagation [duplicate]
The answer to this is not entirely "Local Minima/Maxima".
When you have more than 1 Hidden Layer and every weight are 0's, no matter how big/small a change in Weight_i will not cause a change in the Output.
This is because delta Weight_i will ... | Danger of setting all initial weights to zero in Backpropagation [duplicate]
The answer to this is not entirely "Local Minima/Maxima".
When you have more than 1 Hidden Layer and every weight are 0's, no matter how big/small a change in Weight_i will not cause a change in the O |
4,998 | Danger of setting all initial weights to zero in Backpropagation [duplicate] | A few reasonable arguments have been provided as to why you should not initialise your network with all weights set to zero.
However, I would like to point out that zero initialisation can work — if done correctly!
To start things of, it is not just zero initialisation that is problematic.
As a matter of fact, when ini... | Danger of setting all initial weights to zero in Backpropagation [duplicate] | A few reasonable arguments have been provided as to why you should not initialise your network with all weights set to zero.
However, I would like to point out that zero initialisation can work — if d | Danger of setting all initial weights to zero in Backpropagation [duplicate]
A few reasonable arguments have been provided as to why you should not initialise your network with all weights set to zero.
However, I would like to point out that zero initialisation can work — if done correctly!
To start things of, it is no... | Danger of setting all initial weights to zero in Backpropagation [duplicate]
A few reasonable arguments have been provided as to why you should not initialise your network with all weights set to zero.
However, I would like to point out that zero initialisation can work — if d |
4,999 | Danger of setting all initial weights to zero in Backpropagation [duplicate] | Main problem with initialization of all weights to zero mathematically leads to either the neuron values are zero (for multi layers) or the delta would be zero. In one of the comments by @alfa in the above answers already a hint is provided, it is mentioned that the product of weights and delta needs to be zero. Thi... | Danger of setting all initial weights to zero in Backpropagation [duplicate] | Main problem with initialization of all weights to zero mathematically leads to either the neuron values are zero (for multi layers) or the delta would be zero. In one of the comments by @alfa in the | Danger of setting all initial weights to zero in Backpropagation [duplicate]
Main problem with initialization of all weights to zero mathematically leads to either the neuron values are zero (for multi layers) or the delta would be zero. In one of the comments by @alfa in the above answers already a hint is provided, ... | Danger of setting all initial weights to zero in Backpropagation [duplicate]
Main problem with initialization of all weights to zero mathematically leads to either the neuron values are zero (for multi layers) or the delta would be zero. In one of the comments by @alfa in the |
5,000 | Cumming (2008) claims that distribution of p-values obtained in replications depends only on the original p-value. How can it be true? | Summary: The trick appears to be a Bayesian approach which assumes a uniform (Jeffreys) prior for the hidden parameter ($z_\mu$ in appendix B of the paper, $\theta$ here).
I believe there may be a Bayesian-style approach to get the equations given in the paper's appendix B.
As I understand it, the experiment boils dow... | Cumming (2008) claims that distribution of p-values obtained in replications depends only on the ori | Summary: The trick appears to be a Bayesian approach which assumes a uniform (Jeffreys) prior for the hidden parameter ($z_\mu$ in appendix B of the paper, $\theta$ here).
I believe there may be a Ba | Cumming (2008) claims that distribution of p-values obtained in replications depends only on the original p-value. How can it be true?
Summary: The trick appears to be a Bayesian approach which assumes a uniform (Jeffreys) prior for the hidden parameter ($z_\mu$ in appendix B of the paper, $\theta$ here).
I believe th... | Cumming (2008) claims that distribution of p-values obtained in replications depends only on the ori
Summary: The trick appears to be a Bayesian approach which assumes a uniform (Jeffreys) prior for the hidden parameter ($z_\mu$ in appendix B of the paper, $\theta$ here).
I believe there may be a Ba |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.