idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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13,501 | Is building a multiclass classifier better than several binary ones? | Some methods deal well with multiclass, Random Forests, MLPs for example.
If you don't want to go that way, then it is possible that ECOC may well out perform 1-vs-All for your problem, only testing will tell. | Is building a multiclass classifier better than several binary ones? | Some methods deal well with multiclass, Random Forests, MLPs for example.
If you don't want to go that way, then it is possible that ECOC may well out perform 1-vs-All for your problem, only testing w | Is building a multiclass classifier better than several binary ones?
Some methods deal well with multiclass, Random Forests, MLPs for example.
If you don't want to go that way, then it is possible that ECOC may well out perform 1-vs-All for your problem, only testing will tell. | Is building a multiclass classifier better than several binary ones?
Some methods deal well with multiclass, Random Forests, MLPs for example.
If you don't want to go that way, then it is possible that ECOC may well out perform 1-vs-All for your problem, only testing w |
13,502 | How can I estimate unique occurrence counts from a random sampling of data? | Here is a whole paper about the problem, with a summary of various approaches. It's called Distinct Value Estimation in the literature.
If I had to do this myself, without having read fancy papers, I'd do this. In building language models, one often has to estimate the probability of observing a previously unknown wo... | How can I estimate unique occurrence counts from a random sampling of data? | Here is a whole paper about the problem, with a summary of various approaches. It's called Distinct Value Estimation in the literature.
If I had to do this myself, without having read fancy papers, I | How can I estimate unique occurrence counts from a random sampling of data?
Here is a whole paper about the problem, with a summary of various approaches. It's called Distinct Value Estimation in the literature.
If I had to do this myself, without having read fancy papers, I'd do this. In building language models, on... | How can I estimate unique occurrence counts from a random sampling of data?
Here is a whole paper about the problem, with a summary of various approaches. It's called Distinct Value Estimation in the literature.
If I had to do this myself, without having read fancy papers, I |
13,503 | How can I estimate unique occurrence counts from a random sampling of data? | There is a python package estndv for this task. For example, your sample is [1,1,1,3,5,5,12] and the original large set has 100000 values:
from estndv import ndvEstimator
estimator = ndvEstimator()
ndv = estimator.sample_predict(S=[1,1,1,3,5,5,12], N=100000)
ndv is the estimated number of unique/distinct values for th... | How can I estimate unique occurrence counts from a random sampling of data? | There is a python package estndv for this task. For example, your sample is [1,1,1,3,5,5,12] and the original large set has 100000 values:
from estndv import ndvEstimator
estimator = ndvEstimator()
nd | How can I estimate unique occurrence counts from a random sampling of data?
There is a python package estndv for this task. For example, your sample is [1,1,1,3,5,5,12] and the original large set has 100000 values:
from estndv import ndvEstimator
estimator = ndvEstimator()
ndv = estimator.sample_predict(S=[1,1,1,3,5,5,... | How can I estimate unique occurrence counts from a random sampling of data?
There is a python package estndv for this task. For example, your sample is [1,1,1,3,5,5,12] and the original large set has 100000 values:
from estndv import ndvEstimator
estimator = ndvEstimator()
nd |
13,504 | How can I estimate unique occurrence counts from a random sampling of data? | The simulation strategy
Collect m random samples of size n from the set S. For each of the m samples, compute the number u of unique values and divide by n to normalize. From the simulated distribution of normalized u, compute summary statistics of interest (e.g., mean, variance, interquartile range). Multiply the simu... | How can I estimate unique occurrence counts from a random sampling of data? | The simulation strategy
Collect m random samples of size n from the set S. For each of the m samples, compute the number u of unique values and divide by n to normalize. From the simulated distributio | How can I estimate unique occurrence counts from a random sampling of data?
The simulation strategy
Collect m random samples of size n from the set S. For each of the m samples, compute the number u of unique values and divide by n to normalize. From the simulated distribution of normalized u, compute summary statistic... | How can I estimate unique occurrence counts from a random sampling of data?
The simulation strategy
Collect m random samples of size n from the set S. For each of the m samples, compute the number u of unique values and divide by n to normalize. From the simulated distributio |
13,505 | How can I estimate unique occurrence counts from a random sampling of data? | Here's an implementation for pandas:
import math
import numpy as np
from collections import Counter
def estimate_uniqueness(df, col, r=10000, n=None):
""" Draws a sample of size r from column col from dataframe df and
returns an estimate for the number of unique values given a
population size of n... | How can I estimate unique occurrence counts from a random sampling of data? | Here's an implementation for pandas:
import math
import numpy as np
from collections import Counter
def estimate_uniqueness(df, col, r=10000, n=None):
""" Draws a sample of size r from column col | How can I estimate unique occurrence counts from a random sampling of data?
Here's an implementation for pandas:
import math
import numpy as np
from collections import Counter
def estimate_uniqueness(df, col, r=10000, n=None):
""" Draws a sample of size r from column col from dataframe df and
returns an e... | How can I estimate unique occurrence counts from a random sampling of data?
Here's an implementation for pandas:
import math
import numpy as np
from collections import Counter
def estimate_uniqueness(df, col, r=10000, n=None):
""" Draws a sample of size r from column col |
13,506 | Using RNN (LSTM) for predicting the timeseries vectors (Theano) | I finally found a way and documented it on my blog here.
There is comparison of several frameworks and then also one implementation in Keras. | Using RNN (LSTM) for predicting the timeseries vectors (Theano) | I finally found a way and documented it on my blog here.
There is comparison of several frameworks and then also one implementation in Keras. | Using RNN (LSTM) for predicting the timeseries vectors (Theano)
I finally found a way and documented it on my blog here.
There is comparison of several frameworks and then also one implementation in Keras. | Using RNN (LSTM) for predicting the timeseries vectors (Theano)
I finally found a way and documented it on my blog here.
There is comparison of several frameworks and then also one implementation in Keras. |
13,507 | Using RNN (LSTM) for predicting the timeseries vectors (Theano) | I would suggest the following:
Theano is really powerful but yes the cod can be difficult sometimes to start with
I would suggest you to check out breze: https://github.com/breze-no-salt/breze/blob/master/notebooks/recurrent-networks/RNNs%20for%20Piano%20music.ipynb which is slightly easier to be understood and has a... | Using RNN (LSTM) for predicting the timeseries vectors (Theano) | I would suggest the following:
Theano is really powerful but yes the cod can be difficult sometimes to start with
I would suggest you to check out breze: https://github.com/breze-no-salt/breze/blob/ | Using RNN (LSTM) for predicting the timeseries vectors (Theano)
I would suggest the following:
Theano is really powerful but yes the cod can be difficult sometimes to start with
I would suggest you to check out breze: https://github.com/breze-no-salt/breze/blob/master/notebooks/recurrent-networks/RNNs%20for%20Piano%2... | Using RNN (LSTM) for predicting the timeseries vectors (Theano)
I would suggest the following:
Theano is really powerful but yes the cod can be difficult sometimes to start with
I would suggest you to check out breze: https://github.com/breze-no-salt/breze/blob/ |
13,508 | Using RNN (LSTM) for predicting the timeseries vectors (Theano) | I have tested LSTM predicting some time sequence with Theano. I found that for some smooth curve, it can be predicted properly. However for some zigzag curve . It's hard to predict. The detailed article are as below:
Predict Time Sequence with LSTM
The predicted result can be shown as follow: | Using RNN (LSTM) for predicting the timeseries vectors (Theano) | I have tested LSTM predicting some time sequence with Theano. I found that for some smooth curve, it can be predicted properly. However for some zigzag curve . It's hard to predict. The detailed artic | Using RNN (LSTM) for predicting the timeseries vectors (Theano)
I have tested LSTM predicting some time sequence with Theano. I found that for some smooth curve, it can be predicted properly. However for some zigzag curve . It's hard to predict. The detailed article are as below:
Predict Time Sequence with LSTM
The pre... | Using RNN (LSTM) for predicting the timeseries vectors (Theano)
I have tested LSTM predicting some time sequence with Theano. I found that for some smooth curve, it can be predicted properly. However for some zigzag curve . It's hard to predict. The detailed artic |
13,509 | What is the difference between conditioning on regressors vs. treating them as fixed? | Here I am on thin ice but let me try: I have a feeling (please comment!) that a main difference between statistics and econometrics is that in statistics we tend to consider the regressors as fixed, hence the terminology design matrix which obviously comes from design of experiments, where the supposition is that we ... | What is the difference between conditioning on regressors vs. treating them as fixed? | Here I am on thin ice but let me try: I have a feeling (please comment!) that a main difference between statistics and econometrics is that in statistics we tend to consider the regressors as fixed, | What is the difference between conditioning on regressors vs. treating them as fixed?
Here I am on thin ice but let me try: I have a feeling (please comment!) that a main difference between statistics and econometrics is that in statistics we tend to consider the regressors as fixed, hence the terminology design matr... | What is the difference between conditioning on regressors vs. treating them as fixed?
Here I am on thin ice but let me try: I have a feeling (please comment!) that a main difference between statistics and econometrics is that in statistics we tend to consider the regressors as fixed, |
13,510 | What is the difference between conditioning on regressors vs. treating them as fixed? | +1 to Kjetil b halvorsen. His answers are enlightening and this one is no exception. I do think that there is something additional to be contributed here because the question asks about "treating regressors as fixed" (as in a hypothetical intervention to use Pearl's language) but also touches on "fixing the regressors"... | What is the difference between conditioning on regressors vs. treating them as fixed? | +1 to Kjetil b halvorsen. His answers are enlightening and this one is no exception. I do think that there is something additional to be contributed here because the question asks about "treating regr | What is the difference between conditioning on regressors vs. treating them as fixed?
+1 to Kjetil b halvorsen. His answers are enlightening and this one is no exception. I do think that there is something additional to be contributed here because the question asks about "treating regressors as fixed" (as in a hypothet... | What is the difference between conditioning on regressors vs. treating them as fixed?
+1 to Kjetil b halvorsen. His answers are enlightening and this one is no exception. I do think that there is something additional to be contributed here because the question asks about "treating regr |
13,511 | How and when to use the Bonferroni adjustment | The Bonferroni adjustment will always provide strong control of the family-wise error rate. This means that, whatever the nature and number of the tests, or the relationships between them, if their assumptions are met, it will ensure that the probability of having even one erroneous significant result among all tests i... | How and when to use the Bonferroni adjustment | The Bonferroni adjustment will always provide strong control of the family-wise error rate. This means that, whatever the nature and number of the tests, or the relationships between them, if their as | How and when to use the Bonferroni adjustment
The Bonferroni adjustment will always provide strong control of the family-wise error rate. This means that, whatever the nature and number of the tests, or the relationships between them, if their assumptions are met, it will ensure that the probability of having even one ... | How and when to use the Bonferroni adjustment
The Bonferroni adjustment will always provide strong control of the family-wise error rate. This means that, whatever the nature and number of the tests, or the relationships between them, if their as |
13,512 | How and when to use the Bonferroni adjustment | I was looking at the same issue and found a text in the book:
A copy of the relevant chapter is freely available here:
http://www.utdallas.edu/~herve/Abdi-Bonferroni2007-pretty.pdf
it discusses how the Bonferonni correction can be applied in different circumstances (i.e. independent and non-independent tests) and brief... | How and when to use the Bonferroni adjustment | I was looking at the same issue and found a text in the book:
A copy of the relevant chapter is freely available here:
http://www.utdallas.edu/~herve/Abdi-Bonferroni2007-pretty.pdf
it discusses how th | How and when to use the Bonferroni adjustment
I was looking at the same issue and found a text in the book:
A copy of the relevant chapter is freely available here:
http://www.utdallas.edu/~herve/Abdi-Bonferroni2007-pretty.pdf
it discusses how the Bonferonni correction can be applied in different circumstances (i.e. in... | How and when to use the Bonferroni adjustment
I was looking at the same issue and found a text in the book:
A copy of the relevant chapter is freely available here:
http://www.utdallas.edu/~herve/Abdi-Bonferroni2007-pretty.pdf
it discusses how th |
13,513 | How and when to use the Bonferroni adjustment | You must remember that medical data and scientific data are irreconcilably different in that heteroscedastic medical data is never experimental unlike homoscedastic biological data. Recall also that many discussions on role of power testing and Bonferroni type corrections involve only speculations on the nature of unkn... | How and when to use the Bonferroni adjustment | You must remember that medical data and scientific data are irreconcilably different in that heteroscedastic medical data is never experimental unlike homoscedastic biological data. Recall also that m | How and when to use the Bonferroni adjustment
You must remember that medical data and scientific data are irreconcilably different in that heteroscedastic medical data is never experimental unlike homoscedastic biological data. Recall also that many discussions on role of power testing and Bonferroni type corrections i... | How and when to use the Bonferroni adjustment
You must remember that medical data and scientific data are irreconcilably different in that heteroscedastic medical data is never experimental unlike homoscedastic biological data. Recall also that m |
13,514 | Does BIC try to find a true model? | The Information Criterion by Schwarz (1978) was designed with the feature that it asymptotically chooses the model with the higher posterior odds, i.e. the model with the higher likelihood given the data under equal priors. So roughly
$$
\frac{p(M_1|y)}{p(M_2|y)} > 1 \overset{A}{\sim} SIC(M_1) < SIC(M_2)
$$
where $\ove... | Does BIC try to find a true model? | The Information Criterion by Schwarz (1978) was designed with the feature that it asymptotically chooses the model with the higher posterior odds, i.e. the model with the higher likelihood given the d | Does BIC try to find a true model?
The Information Criterion by Schwarz (1978) was designed with the feature that it asymptotically chooses the model with the higher posterior odds, i.e. the model with the higher likelihood given the data under equal priors. So roughly
$$
\frac{p(M_1|y)}{p(M_2|y)} > 1 \overset{A}{\sim}... | Does BIC try to find a true model?
The Information Criterion by Schwarz (1978) was designed with the feature that it asymptotically chooses the model with the higher posterior odds, i.e. the model with the higher likelihood given the d |
13,515 | Intuition for moments about the mean of a distribution? | There is a good reason for these definitions, which becomes clearer when you look at the general form for moments of standardised random variables. To answer this question, first consider the general form of the $k$th standardised central moment:$^\dagger$
$$\phi_k = \mathbb{E} \Bigg[ \Bigg( \frac{X - \mathbb{E}[X]}{\... | Intuition for moments about the mean of a distribution? | There is a good reason for these definitions, which becomes clearer when you look at the general form for moments of standardised random variables. To answer this question, first consider the general | Intuition for moments about the mean of a distribution?
There is a good reason for these definitions, which becomes clearer when you look at the general form for moments of standardised random variables. To answer this question, first consider the general form of the $k$th standardised central moment:$^\dagger$
$$\phi... | Intuition for moments about the mean of a distribution?
There is a good reason for these definitions, which becomes clearer when you look at the general form for moments of standardised random variables. To answer this question, first consider the general |
13,516 | Intuition for moments about the mean of a distribution? | Similar question What's so 'moment' about 'moments' of a probability distribution? I gave a physical answer to that which addressed moments.
"Angular acceleration is the derivative of angular velocity, which is the derivative of angle with respect to time, i.e., $ \dfrac{d\omega}{dt}=\alpha,\,\dfrac{d\theta}{dt}=\omega... | Intuition for moments about the mean of a distribution? | Similar question What's so 'moment' about 'moments' of a probability distribution? I gave a physical answer to that which addressed moments.
"Angular acceleration is the derivative of angular velocity | Intuition for moments about the mean of a distribution?
Similar question What's so 'moment' about 'moments' of a probability distribution? I gave a physical answer to that which addressed moments.
"Angular acceleration is the derivative of angular velocity, which is the derivative of angle with respect to time, i.e., $... | Intuition for moments about the mean of a distribution?
Similar question What's so 'moment' about 'moments' of a probability distribution? I gave a physical answer to that which addressed moments.
"Angular acceleration is the derivative of angular velocity |
13,517 | Root finding for stochastic function | You might find the following references useful:
Pasupathy, R.and Kim, S. (2011) The stochastic root-finding problem: Overview, solutions, and open questions. ACM Transactions on Modeling and Computer Simulation, 21(3). [DOI] [preprint]
Waeber, R. (2013) Probabilistic Bisection Search for Stochastic Root-Finding.
Ph.D d... | Root finding for stochastic function | You might find the following references useful:
Pasupathy, R.and Kim, S. (2011) The stochastic root-finding problem: Overview, solutions, and open questions. ACM Transactions on Modeling and Computer | Root finding for stochastic function
You might find the following references useful:
Pasupathy, R.and Kim, S. (2011) The stochastic root-finding problem: Overview, solutions, and open questions. ACM Transactions on Modeling and Computer Simulation, 21(3). [DOI] [preprint]
Waeber, R. (2013) Probabilistic Bisection Searc... | Root finding for stochastic function
You might find the following references useful:
Pasupathy, R.and Kim, S. (2011) The stochastic root-finding problem: Overview, solutions, and open questions. ACM Transactions on Modeling and Computer |
13,518 | Law of total variance as Pythagorean theorem | I assume that you are comfortable with regarding the right-angled triangle as meaning that $E[Y\mid X]$ and $Y - E[Y\mid X]$ are uncorrelated random variables.
For uncorrelated random variables $A$ and $B$,
$$\operatorname{var}(A+B) = \operatorname{var}(A) + \operatorname{var}(B),\tag{1}$$
and so if we set $A = Y - E[Y... | Law of total variance as Pythagorean theorem | I assume that you are comfortable with regarding the right-angled triangle as meaning that $E[Y\mid X]$ and $Y - E[Y\mid X]$ are uncorrelated random variables.
For uncorrelated random variables $A$ an | Law of total variance as Pythagorean theorem
I assume that you are comfortable with regarding the right-angled triangle as meaning that $E[Y\mid X]$ and $Y - E[Y\mid X]$ are uncorrelated random variables.
For uncorrelated random variables $A$ and $B$,
$$\operatorname{var}(A+B) = \operatorname{var}(A) + \operatorname{va... | Law of total variance as Pythagorean theorem
I assume that you are comfortable with regarding the right-angled triangle as meaning that $E[Y\mid X]$ and $Y - E[Y\mid X]$ are uncorrelated random variables.
For uncorrelated random variables $A$ an |
13,519 | Law of total variance as Pythagorean theorem | Statement:
The Pythagorean theorem says, for any elements $T_1$ and $T_2$ of an inner-product space with finite norms such that $\langle T_1,T_2\rangle = 0$,
$$
||T_1+T_2||^2 = ||T_1||^2 + ||T_2||^2 \tag{1}.
$$
Or in other words, for orthogonal vectors, the squared length of the sum is the sum of the squared lengths.
O... | Law of total variance as Pythagorean theorem | Statement:
The Pythagorean theorem says, for any elements $T_1$ and $T_2$ of an inner-product space with finite norms such that $\langle T_1,T_2\rangle = 0$,
$$
||T_1+T_2||^2 = ||T_1||^2 + ||T_2||^2 \ | Law of total variance as Pythagorean theorem
Statement:
The Pythagorean theorem says, for any elements $T_1$ and $T_2$ of an inner-product space with finite norms such that $\langle T_1,T_2\rangle = 0$,
$$
||T_1+T_2||^2 = ||T_1||^2 + ||T_2||^2 \tag{1}.
$$
Or in other words, for orthogonal vectors, the squared length of... | Law of total variance as Pythagorean theorem
Statement:
The Pythagorean theorem says, for any elements $T_1$ and $T_2$ of an inner-product space with finite norms such that $\langle T_1,T_2\rangle = 0$,
$$
||T_1+T_2||^2 = ||T_1||^2 + ||T_2||^2 \ |
13,520 | Clustering 1D data | The K-means algorithm and the EM algorithm are going to be pretty similar for 1D clustering.
In K-means you start with a guess where the means are and assign each point to the cluster with the closest mean, then you recompute the means (and variances) based on current assignments of points, then update the assigment of... | Clustering 1D data | The K-means algorithm and the EM algorithm are going to be pretty similar for 1D clustering.
In K-means you start with a guess where the means are and assign each point to the cluster with the closest | Clustering 1D data
The K-means algorithm and the EM algorithm are going to be pretty similar for 1D clustering.
In K-means you start with a guess where the means are and assign each point to the cluster with the closest mean, then you recompute the means (and variances) based on current assignments of points, then upda... | Clustering 1D data
The K-means algorithm and the EM algorithm are going to be pretty similar for 1D clustering.
In K-means you start with a guess where the means are and assign each point to the cluster with the closest |
13,521 | Clustering 1D data | EM is better than k-means in terms of results.
K-means, however, has a faster run-time.
They will produce similar results if the standard deviation/covariance matrices are approximately equal. If you suspect this is true, use k-means.
DBSCAN is used when the data is non-gaussian. If you are using 1-dimensional data, ... | Clustering 1D data | EM is better than k-means in terms of results.
K-means, however, has a faster run-time.
They will produce similar results if the standard deviation/covariance matrices are approximately equal. If you | Clustering 1D data
EM is better than k-means in terms of results.
K-means, however, has a faster run-time.
They will produce similar results if the standard deviation/covariance matrices are approximately equal. If you suspect this is true, use k-means.
DBSCAN is used when the data is non-gaussian. If you are using 1... | Clustering 1D data
EM is better than k-means in terms of results.
K-means, however, has a faster run-time.
They will produce similar results if the standard deviation/covariance matrices are approximately equal. If you |
13,522 | Clustering 1D data | Another simple way is to basically use sorting of the 1D array: i.e. iterate over each point and get the values which are at a minimum distance from it in both the positive and the negative directions. For example:
data = [1,2,3,4,5,6,7,8,9,10,12]
k = 5
for a in data:
print {'group': sorted(k, key=lambda n: abs(n-a)... | Clustering 1D data | Another simple way is to basically use sorting of the 1D array: i.e. iterate over each point and get the values which are at a minimum distance from it in both the positive and the negative directions | Clustering 1D data
Another simple way is to basically use sorting of the 1D array: i.e. iterate over each point and get the values which are at a minimum distance from it in both the positive and the negative directions. For example:
data = [1,2,3,4,5,6,7,8,9,10,12]
k = 5
for a in data:
print {'group': sorted(k, key... | Clustering 1D data
Another simple way is to basically use sorting of the 1D array: i.e. iterate over each point and get the values which are at a minimum distance from it in both the positive and the negative directions |
13,523 | Clustering 1D data | If there is only one variable, no need for clustering. You can easily group your observations based on the variable's distribution.
Or am I missing some points here? | Clustering 1D data | If there is only one variable, no need for clustering. You can easily group your observations based on the variable's distribution.
Or am I missing some points here? | Clustering 1D data
If there is only one variable, no need for clustering. You can easily group your observations based on the variable's distribution.
Or am I missing some points here? | Clustering 1D data
If there is only one variable, no need for clustering. You can easily group your observations based on the variable's distribution.
Or am I missing some points here? |
13,524 | Input format for response in binomial glm in R | There's no statistical reason to prefer one to the other, besides conceptual clarity. Although the reported deviance values are different, these differences are completely due to the saturated model. So any comparison using relative deviance between models is unaffected, since the saturated model log-likelihood cancels... | Input format for response in binomial glm in R | There's no statistical reason to prefer one to the other, besides conceptual clarity. Although the reported deviance values are different, these differences are completely due to the saturated model. | Input format for response in binomial glm in R
There's no statistical reason to prefer one to the other, besides conceptual clarity. Although the reported deviance values are different, these differences are completely due to the saturated model. So any comparison using relative deviance between models is unaffected, s... | Input format for response in binomial glm in R
There's no statistical reason to prefer one to the other, besides conceptual clarity. Although the reported deviance values are different, these differences are completely due to the saturated model. |
13,525 | Linear regression or ordinal logistic regression to predict wine rating (from 0 and 10) | An ordered logit model is more appropriate as you have a dependent variable which is a ranking, 7 is better than 4 for instance. So there is a clear order.
This allows you to obtain a probability for each bin.
There are few assumptions that you need to take into account. You can have a look here.
One of the assumption... | Linear regression or ordinal logistic regression to predict wine rating (from 0 and 10) | An ordered logit model is more appropriate as you have a dependent variable which is a ranking, 7 is better than 4 for instance. So there is a clear order.
This allows you to obtain a probability for | Linear regression or ordinal logistic regression to predict wine rating (from 0 and 10)
An ordered logit model is more appropriate as you have a dependent variable which is a ranking, 7 is better than 4 for instance. So there is a clear order.
This allows you to obtain a probability for each bin.
There are few assumpti... | Linear regression or ordinal logistic regression to predict wine rating (from 0 and 10)
An ordered logit model is more appropriate as you have a dependent variable which is a ranking, 7 is better than 4 for instance. So there is a clear order.
This allows you to obtain a probability for |
13,526 | Linear regression or ordinal logistic regression to predict wine rating (from 0 and 10) | I would like to provide another view to the problem: In real world, it is less likely to encounter the this question, because what to do is depending on business needs.
The essential question in real world is what to do after getting the prediction?
Suppose business wants to trash "low quality" wine. Then, we need som... | Linear regression or ordinal logistic regression to predict wine rating (from 0 and 10) | I would like to provide another view to the problem: In real world, it is less likely to encounter the this question, because what to do is depending on business needs.
The essential question in real | Linear regression or ordinal logistic regression to predict wine rating (from 0 and 10)
I would like to provide another view to the problem: In real world, it is less likely to encounter the this question, because what to do is depending on business needs.
The essential question in real world is what to do after gettin... | Linear regression or ordinal logistic regression to predict wine rating (from 0 and 10)
I would like to provide another view to the problem: In real world, it is less likely to encounter the this question, because what to do is depending on business needs.
The essential question in real |
13,527 | Linear regression or ordinal logistic regression to predict wine rating (from 0 and 10) | Although an ordered logit model (as detailed by @adrian1121) would be most appropriate in terms of model assumptions, I think multiple linear regression has some advantages as well.
Ease of interpretation. Linear models are easier to interpret than ordered logit models.
Stakeholder comfort. Users of the model may be... | Linear regression or ordinal logistic regression to predict wine rating (from 0 and 10) | Although an ordered logit model (as detailed by @adrian1121) would be most appropriate in terms of model assumptions, I think multiple linear regression has some advantages as well.
Ease of interpret | Linear regression or ordinal logistic regression to predict wine rating (from 0 and 10)
Although an ordered logit model (as detailed by @adrian1121) would be most appropriate in terms of model assumptions, I think multiple linear regression has some advantages as well.
Ease of interpretation. Linear models are easier... | Linear regression or ordinal logistic regression to predict wine rating (from 0 and 10)
Although an ordered logit model (as detailed by @adrian1121) would be most appropriate in terms of model assumptions, I think multiple linear regression has some advantages as well.
Ease of interpret |
13,528 | Linear regression or ordinal logistic regression to predict wine rating (from 0 and 10) | In principle ordered logit model seems appropriate, but 10 (or even 7) categories is quite a lot.
1/ Eventually would it make sense to do some re-coding (e.g., ratings 1-4 would be merged into 1 single modality, say "low rating")?
2/ What is the distribution of the ratings? If pretty well normally distributed, then... | Linear regression or ordinal logistic regression to predict wine rating (from 0 and 10) | In principle ordered logit model seems appropriate, but 10 (or even 7) categories is quite a lot.
1/ Eventually would it make sense to do some re-coding (e.g., ratings 1-4 would be merged into 1 sin | Linear regression or ordinal logistic regression to predict wine rating (from 0 and 10)
In principle ordered logit model seems appropriate, but 10 (or even 7) categories is quite a lot.
1/ Eventually would it make sense to do some re-coding (e.g., ratings 1-4 would be merged into 1 single modality, say "low rating")?... | Linear regression or ordinal logistic regression to predict wine rating (from 0 and 10)
In principle ordered logit model seems appropriate, but 10 (or even 7) categories is quite a lot.
1/ Eventually would it make sense to do some re-coding (e.g., ratings 1-4 would be merged into 1 sin |
13,529 | Linear regression or ordinal logistic regression to predict wine rating (from 0 and 10) | I am not a specialist of logistic regression, but I would say that you want to use multinomial because of your discrete dependent variable.
A linear regression could output coefficients that can be extrapolated out of the possible boundaries of your dependent variable (i.e an increase of independent variable would lea... | Linear regression or ordinal logistic regression to predict wine rating (from 0 and 10) | I am not a specialist of logistic regression, but I would say that you want to use multinomial because of your discrete dependent variable.
A linear regression could output coefficients that can be e | Linear regression or ordinal logistic regression to predict wine rating (from 0 and 10)
I am not a specialist of logistic regression, but I would say that you want to use multinomial because of your discrete dependent variable.
A linear regression could output coefficients that can be extrapolated out of the possible ... | Linear regression or ordinal logistic regression to predict wine rating (from 0 and 10)
I am not a specialist of logistic regression, but I would say that you want to use multinomial because of your discrete dependent variable.
A linear regression could output coefficients that can be e |
13,530 | Linear regression or ordinal logistic regression to predict wine rating (from 0 and 10) | Another possibility is to use a Random Forest. There are two ways to measure the "importance" of a variable under a Random Forest:
Permutation: the importance of input variable $X_j$ is proportional to the average increase in error rate cause by randomly shuffling that variable. Randomly shuffling $X_j$ destroys the r... | Linear regression or ordinal logistic regression to predict wine rating (from 0 and 10) | Another possibility is to use a Random Forest. There are two ways to measure the "importance" of a variable under a Random Forest:
Permutation: the importance of input variable $X_j$ is proportional | Linear regression or ordinal logistic regression to predict wine rating (from 0 and 10)
Another possibility is to use a Random Forest. There are two ways to measure the "importance" of a variable under a Random Forest:
Permutation: the importance of input variable $X_j$ is proportional to the average increase in error... | Linear regression or ordinal logistic regression to predict wine rating (from 0 and 10)
Another possibility is to use a Random Forest. There are two ways to measure the "importance" of a variable under a Random Forest:
Permutation: the importance of input variable $X_j$ is proportional |
13,531 | is scaling data [0,1] necessary when batch normalization is used? | As mentioned, it's best to use [-1, 1] min-max scaling or zero-mean, unit-variance standardization. Scaling your data into [0, 1] will result in slow learning.
To answer your question: Yes, you should still standardize your inputs to a network that uses Batch Normalization. This will ensure that inputs to the first lay... | is scaling data [0,1] necessary when batch normalization is used? | As mentioned, it's best to use [-1, 1] min-max scaling or zero-mean, unit-variance standardization. Scaling your data into [0, 1] will result in slow learning.
To answer your question: Yes, you should | is scaling data [0,1] necessary when batch normalization is used?
As mentioned, it's best to use [-1, 1] min-max scaling or zero-mean, unit-variance standardization. Scaling your data into [0, 1] will result in slow learning.
To answer your question: Yes, you should still standardize your inputs to a network that uses ... | is scaling data [0,1] necessary when batch normalization is used?
As mentioned, it's best to use [-1, 1] min-max scaling or zero-mean, unit-variance standardization. Scaling your data into [0, 1] will result in slow learning.
To answer your question: Yes, you should |
13,532 | is scaling data [0,1] necessary when batch normalization is used? | In this case scaling data would only influence the first layer of your network. Also if you are scaling your input it's better to scale it to [-1, 1], but it's best to scale it to 0 mean and 1 variance (since your weights are probably initialized to expect such distribution).
Not that it's going to make a huge differen... | is scaling data [0,1] necessary when batch normalization is used? | In this case scaling data would only influence the first layer of your network. Also if you are scaling your input it's better to scale it to [-1, 1], but it's best to scale it to 0 mean and 1 varianc | is scaling data [0,1] necessary when batch normalization is used?
In this case scaling data would only influence the first layer of your network. Also if you are scaling your input it's better to scale it to [-1, 1], but it's best to scale it to 0 mean and 1 variance (since your weights are probably initialized to expe... | is scaling data [0,1] necessary when batch normalization is used?
In this case scaling data would only influence the first layer of your network. Also if you are scaling your input it's better to scale it to [-1, 1], but it's best to scale it to 0 mean and 1 varianc |
13,533 | How exactly to compute Deep Q-Learning Loss Function? | After reviewing the equations a few more times. I think the correct loss is the following:
$$\mathcal{L} = (11.1 - 4.3)^2$$
My reasoning is that the q-learning update rule for the general case is only updating the q-value for a specific $state,action$ pair.
$$Q(s,a) = r + \gamma \max_{a*}Q(s',a*)$$
This equation means... | How exactly to compute Deep Q-Learning Loss Function? | After reviewing the equations a few more times. I think the correct loss is the following:
$$\mathcal{L} = (11.1 - 4.3)^2$$
My reasoning is that the q-learning update rule for the general case is onl | How exactly to compute Deep Q-Learning Loss Function?
After reviewing the equations a few more times. I think the correct loss is the following:
$$\mathcal{L} = (11.1 - 4.3)^2$$
My reasoning is that the q-learning update rule for the general case is only updating the q-value for a specific $state,action$ pair.
$$Q(s,a... | How exactly to compute Deep Q-Learning Loss Function?
After reviewing the equations a few more times. I think the correct loss is the following:
$$\mathcal{L} = (11.1 - 4.3)^2$$
My reasoning is that the q-learning update rule for the general case is onl |
13,534 | How exactly to compute Deep Q-Learning Loss Function? | TLDR:
Probably won't matter unless you have a large action space.
If your loss function is MSE, then the calculated loss is half of the term specific loss (if action space = 2). This may matter if your action space is large and may slow down training since the slope of the loss function is reduced by a factor equal to ... | How exactly to compute Deep Q-Learning Loss Function? | TLDR:
Probably won't matter unless you have a large action space.
If your loss function is MSE, then the calculated loss is half of the term specific loss (if action space = 2). This may matter if you | How exactly to compute Deep Q-Learning Loss Function?
TLDR:
Probably won't matter unless you have a large action space.
If your loss function is MSE, then the calculated loss is half of the term specific loss (if action space = 2). This may matter if your action space is large and may slow down training since the slope... | How exactly to compute Deep Q-Learning Loss Function?
TLDR:
Probably won't matter unless you have a large action space.
If your loss function is MSE, then the calculated loss is half of the term specific loss (if action space = 2). This may matter if you |
13,535 | Use of standard error of bootstrap distribution | There are several problems in this question. First, there is the question of whether bootstrapped averages will be sensible estimators even when some of the individual bootstrapped estimators are not computable (lack of convergence, non-existence of solutions). Second, given that the bootstrapped estimators are sensibl... | Use of standard error of bootstrap distribution | There are several problems in this question. First, there is the question of whether bootstrapped averages will be sensible estimators even when some of the individual bootstrapped estimators are not | Use of standard error of bootstrap distribution
There are several problems in this question. First, there is the question of whether bootstrapped averages will be sensible estimators even when some of the individual bootstrapped estimators are not computable (lack of convergence, non-existence of solutions). Second, gi... | Use of standard error of bootstrap distribution
There are several problems in this question. First, there is the question of whether bootstrapped averages will be sensible estimators even when some of the individual bootstrapped estimators are not |
13,536 | How deep is the connection between the softmax function in ML and the Boltzmann distribution in thermodynamics? | To my knowledge there is no deeper reason, apart from the fact that a lot of the people who took ANNs beyond the Perceptron stage were physicists.
Apart from the mentioned benefits, this particular choice has more advantages. As mentioned, it has a single parameter that determines the output behaviour. Which in turn ca... | How deep is the connection between the softmax function in ML and the Boltzmann distribution in ther | To my knowledge there is no deeper reason, apart from the fact that a lot of the people who took ANNs beyond the Perceptron stage were physicists.
Apart from the mentioned benefits, this particular ch | How deep is the connection between the softmax function in ML and the Boltzmann distribution in thermodynamics?
To my knowledge there is no deeper reason, apart from the fact that a lot of the people who took ANNs beyond the Perceptron stage were physicists.
Apart from the mentioned benefits, this particular choice has... | How deep is the connection between the softmax function in ML and the Boltzmann distribution in ther
To my knowledge there is no deeper reason, apart from the fact that a lot of the people who took ANNs beyond the Perceptron stage were physicists.
Apart from the mentioned benefits, this particular ch |
13,537 | How deep is the connection between the softmax function in ML and the Boltzmann distribution in thermodynamics? | the softmax function is also used in discrete choice modelling, it is same as the logit model, if u assume there is a utility function associated with each class, and the utility function equals to the output of neural network + an error term following the Gumbel distribution, the probability of belonging to a class eq... | How deep is the connection between the softmax function in ML and the Boltzmann distribution in ther | the softmax function is also used in discrete choice modelling, it is same as the logit model, if u assume there is a utility function associated with each class, and the utility function equals to th | How deep is the connection between the softmax function in ML and the Boltzmann distribution in thermodynamics?
the softmax function is also used in discrete choice modelling, it is same as the logit model, if u assume there is a utility function associated with each class, and the utility function equals to the output... | How deep is the connection between the softmax function in ML and the Boltzmann distribution in ther
the softmax function is also used in discrete choice modelling, it is same as the logit model, if u assume there is a utility function associated with each class, and the utility function equals to th |
13,538 | How deep is the connection between the softmax function in ML and the Boltzmann distribution in thermodynamics? | Yes. There is a connection, one that is articulated in the following paper:
Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One. Will Grathwohl, Kuan-Chieh Wang, Jörn-Henrik Jacobsen, David Duvenaud, Mohammad Norouzi, Kevin Swersky. ICLR 2020.
In particular, we can think of neural netw... | How deep is the connection between the softmax function in ML and the Boltzmann distribution in ther | Yes. There is a connection, one that is articulated in the following paper:
Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One. Will Grathwohl, Kuan-Chieh Wang, Jörn- | How deep is the connection between the softmax function in ML and the Boltzmann distribution in thermodynamics?
Yes. There is a connection, one that is articulated in the following paper:
Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One. Will Grathwohl, Kuan-Chieh Wang, Jörn-Henrik J... | How deep is the connection between the softmax function in ML and the Boltzmann distribution in ther
Yes. There is a connection, one that is articulated in the following paper:
Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One. Will Grathwohl, Kuan-Chieh Wang, Jörn- |
13,539 | How deep is the connection between the softmax function in ML and the Boltzmann distribution in thermodynamics? | Here is an academic paper published in the Journal of Statistical Physics by various physicists at MIT: https://dspace.mit.edu/handle/1721.1/135715.
The paper discusses the relation of the softmax function to statistical physics. The authors claim that the relation between the Boltzmann distribution from thermodynamics... | How deep is the connection between the softmax function in ML and the Boltzmann distribution in ther | Here is an academic paper published in the Journal of Statistical Physics by various physicists at MIT: https://dspace.mit.edu/handle/1721.1/135715.
The paper discusses the relation of the softmax fun | How deep is the connection between the softmax function in ML and the Boltzmann distribution in thermodynamics?
Here is an academic paper published in the Journal of Statistical Physics by various physicists at MIT: https://dspace.mit.edu/handle/1721.1/135715.
The paper discusses the relation of the softmax function to... | How deep is the connection between the softmax function in ML and the Boltzmann distribution in ther
Here is an academic paper published in the Journal of Statistical Physics by various physicists at MIT: https://dspace.mit.edu/handle/1721.1/135715.
The paper discusses the relation of the softmax fun |
13,540 | R: glm function with family = "binomial" and "weight" specification | Your example is merely causing rounding error in R. Large weights don't perform well in glm. It's true that scaling w by virtually any smaller number, like 100, leads to same estimates as the unscaled w.
If you want more reliable behavior with the weights arguments, try using the svyglm function from the survey packag... | R: glm function with family = "binomial" and "weight" specification | Your example is merely causing rounding error in R. Large weights don't perform well in glm. It's true that scaling w by virtually any smaller number, like 100, leads to same estimates as the unscaled | R: glm function with family = "binomial" and "weight" specification
Your example is merely causing rounding error in R. Large weights don't perform well in glm. It's true that scaling w by virtually any smaller number, like 100, leads to same estimates as the unscaled w.
If you want more reliable behavior with the wei... | R: glm function with family = "binomial" and "weight" specification
Your example is merely causing rounding error in R. Large weights don't perform well in glm. It's true that scaling w by virtually any smaller number, like 100, leads to same estimates as the unscaled |
13,541 | R: glm function with family = "binomial" and "weight" specification | I think it comes down to the initial values that is used in glm.fit from the family$initialize which makes the method divergere. As far as I know, glm.fit solve the problem by forming a QR-decomposition of $\sqrt{W}X$ where $X$ is the design matrix and $\sqrt{W}$ is a diagonal with square roots of the entries as descri... | R: glm function with family = "binomial" and "weight" specification | I think it comes down to the initial values that is used in glm.fit from the family$initialize which makes the method divergere. As far as I know, glm.fit solve the problem by forming a QR-decompositi | R: glm function with family = "binomial" and "weight" specification
I think it comes down to the initial values that is used in glm.fit from the family$initialize which makes the method divergere. As far as I know, glm.fit solve the problem by forming a QR-decomposition of $\sqrt{W}X$ where $X$ is the design matrix and... | R: glm function with family = "binomial" and "weight" specification
I think it comes down to the initial values that is used in glm.fit from the family$initialize which makes the method divergere. As far as I know, glm.fit solve the problem by forming a QR-decompositi |
13,542 | Difference between Randomization test and Permutation test | There is quite a bit of overlap and the most common form of the permutation test is a form of a randomization test.
Some purists consider the true permutation test to be based on every possible permutation of the data. But in practice we sample from the set of all possible permutations and so that is a randomization... | Difference between Randomization test and Permutation test | There is quite a bit of overlap and the most common form of the permutation test is a form of a randomization test.
Some purists consider the true permutation test to be based on every possible perm | Difference between Randomization test and Permutation test
There is quite a bit of overlap and the most common form of the permutation test is a form of a randomization test.
Some purists consider the true permutation test to be based on every possible permutation of the data. But in practice we sample from the set ... | Difference between Randomization test and Permutation test
There is quite a bit of overlap and the most common form of the permutation test is a form of a randomization test.
Some purists consider the true permutation test to be based on every possible perm |
13,543 | Definition and Convergence of Iteratively Reweighted Least Squares | As for your first question, one should define "standard", or acknowledge that a "canonical model" has been gradually established. As a comment indicated, it appears at least that the way you use IRWLS is rather standard.
As for your second question, "contraction mapping in probability" could be linked (however informal... | Definition and Convergence of Iteratively Reweighted Least Squares | As for your first question, one should define "standard", or acknowledge that a "canonical model" has been gradually established. As a comment indicated, it appears at least that the way you use IRWLS | Definition and Convergence of Iteratively Reweighted Least Squares
As for your first question, one should define "standard", or acknowledge that a "canonical model" has been gradually established. As a comment indicated, it appears at least that the way you use IRWLS is rather standard.
As for your second question, "co... | Definition and Convergence of Iteratively Reweighted Least Squares
As for your first question, one should define "standard", or acknowledge that a "canonical model" has been gradually established. As a comment indicated, it appears at least that the way you use IRWLS |
13,544 | Definition and Convergence of Iteratively Reweighted Least Squares | Is this the standard IRLS algorithm?
IRLS algorithms can be generally said to find/approach a solution to a minimization problem by using an iterative process that generates a sequence of solutions to a weighted least squares problem.
There is no standard, but your approach seems to fit this general description.
What ... | Definition and Convergence of Iteratively Reweighted Least Squares | Is this the standard IRLS algorithm?
IRLS algorithms can be generally said to find/approach a solution to a minimization problem by using an iterative process that generates a sequence of solutions t | Definition and Convergence of Iteratively Reweighted Least Squares
Is this the standard IRLS algorithm?
IRLS algorithms can be generally said to find/approach a solution to a minimization problem by using an iterative process that generates a sequence of solutions to a weighted least squares problem.
There is no stand... | Definition and Convergence of Iteratively Reweighted Least Squares
Is this the standard IRLS algorithm?
IRLS algorithms can be generally said to find/approach a solution to a minimization problem by using an iterative process that generates a sequence of solutions t |
13,545 | Semi-supervised learning, active learning and deep learning for classification | It seems as if deep learning might be very interesting for you. This is a very recent field of deep connectionist models which are pretrained in an unsupervised way and fine tuned afterwards with supervision. The fine tuning requires a much less samples than the pretraining.
To wet your tongue, I recommend [Semantig Ha... | Semi-supervised learning, active learning and deep learning for classification | It seems as if deep learning might be very interesting for you. This is a very recent field of deep connectionist models which are pretrained in an unsupervised way and fine tuned afterwards with supe | Semi-supervised learning, active learning and deep learning for classification
It seems as if deep learning might be very interesting for you. This is a very recent field of deep connectionist models which are pretrained in an unsupervised way and fine tuned afterwards with supervision. The fine tuning requires a much ... | Semi-supervised learning, active learning and deep learning for classification
It seems as if deep learning might be very interesting for you. This is a very recent field of deep connectionist models which are pretrained in an unsupervised way and fine tuned afterwards with supe |
13,546 | Semi-supervised learning, active learning and deep learning for classification | Isabelle Guyon (and colleagues) organised a challenge on active learning a while back, the proceedings are published here (open access). This has the advantage of being quite practical and you can directly compare the performances of different approaches under an unbiased (in a colloquial sense) protocol (random selec... | Semi-supervised learning, active learning and deep learning for classification | Isabelle Guyon (and colleagues) organised a challenge on active learning a while back, the proceedings are published here (open access). This has the advantage of being quite practical and you can di | Semi-supervised learning, active learning and deep learning for classification
Isabelle Guyon (and colleagues) organised a challenge on active learning a while back, the proceedings are published here (open access). This has the advantage of being quite practical and you can directly compare the performances of differ... | Semi-supervised learning, active learning and deep learning for classification
Isabelle Guyon (and colleagues) organised a challenge on active learning a while back, the proceedings are published here (open access). This has the advantage of being quite practical and you can di |
13,547 | Semi-supervised learning, active learning and deep learning for classification | Here is a nice list of libraries.
http://www.infoworld.com/article/2608742/predictive-analytics/5-ways-to-add-machine-learning-to-java--javascript--and-more.html | Semi-supervised learning, active learning and deep learning for classification | Here is a nice list of libraries.
http://www.infoworld.com/article/2608742/predictive-analytics/5-ways-to-add-machine-learning-to-java--javascript--and-more.html | Semi-supervised learning, active learning and deep learning for classification
Here is a nice list of libraries.
http://www.infoworld.com/article/2608742/predictive-analytics/5-ways-to-add-machine-learning-to-java--javascript--and-more.html | Semi-supervised learning, active learning and deep learning for classification
Here is a nice list of libraries.
http://www.infoworld.com/article/2608742/predictive-analytics/5-ways-to-add-machine-learning-to-java--javascript--and-more.html |
13,548 | Why are Gaussian Processes valid statistical models for time series forecasting? | Some relevant concepts may come along in the question Why does including latitude and longitude in a GAM account for spatial autocorrelation?
If you use Gaussian processing in regression then you include the trend in the model definition $y(t) = f(t,\theta) + \epsilon(t)$ where those errors are $\epsilon(t) \sim \mathc... | Why are Gaussian Processes valid statistical models for time series forecasting? | Some relevant concepts may come along in the question Why does including latitude and longitude in a GAM account for spatial autocorrelation?
If you use Gaussian processing in regression then you incl | Why are Gaussian Processes valid statistical models for time series forecasting?
Some relevant concepts may come along in the question Why does including latitude and longitude in a GAM account for spatial autocorrelation?
If you use Gaussian processing in regression then you include the trend in the model definition $... | Why are Gaussian Processes valid statistical models for time series forecasting?
Some relevant concepts may come along in the question Why does including latitude and longitude in a GAM account for spatial autocorrelation?
If you use Gaussian processing in regression then you incl |
13,549 | Why are Gaussian Processes valid statistical models for time series forecasting? | One of the main assumptions for GP is that data should be stationary. Your data has a clear trend therefore it is not stationary. The correct way to use GP in time series (and in any other type of data) is that first you remove some obvious trends, then apply GP over the residual. | Why are Gaussian Processes valid statistical models for time series forecasting? | One of the main assumptions for GP is that data should be stationary. Your data has a clear trend therefore it is not stationary. The correct way to use GP in time series (and in any other type of dat | Why are Gaussian Processes valid statistical models for time series forecasting?
One of the main assumptions for GP is that data should be stationary. Your data has a clear trend therefore it is not stationary. The correct way to use GP in time series (and in any other type of data) is that first you remove some obviou... | Why are Gaussian Processes valid statistical models for time series forecasting?
One of the main assumptions for GP is that data should be stationary. Your data has a clear trend therefore it is not stationary. The correct way to use GP in time series (and in any other type of dat |
13,550 | Is it better to do exploratory data analysis on the training dataset only? | I'd recommend having a look at "7.10.2 The Wrong and Right Way to Do Cross-validation" in http://statweb.stanford.edu/~tibs/ElemStatLearn/printings/ESLII_print10.pdf.
The authors give an example in which someone does the following:
Screen the predictors: find a subset of “good” predictors that show
fairly strong (univ... | Is it better to do exploratory data analysis on the training dataset only? | I'd recommend having a look at "7.10.2 The Wrong and Right Way to Do Cross-validation" in http://statweb.stanford.edu/~tibs/ElemStatLearn/printings/ESLII_print10.pdf.
The authors give an example in wh | Is it better to do exploratory data analysis on the training dataset only?
I'd recommend having a look at "7.10.2 The Wrong and Right Way to Do Cross-validation" in http://statweb.stanford.edu/~tibs/ElemStatLearn/printings/ESLII_print10.pdf.
The authors give an example in which someone does the following:
Screen the p... | Is it better to do exploratory data analysis on the training dataset only?
I'd recommend having a look at "7.10.2 The Wrong and Right Way to Do Cross-validation" in http://statweb.stanford.edu/~tibs/ElemStatLearn/printings/ESLII_print10.pdf.
The authors give an example in wh |
13,551 | Is it better to do exploratory data analysis on the training dataset only? | So you want to identify independent variables that have an effect on your dependent variable?
Then, both of your approaches are actually not really recommendable.
After having defined your research question, you should develop your theory. That is to say, that using the literature, you should identify variables which ... | Is it better to do exploratory data analysis on the training dataset only? | So you want to identify independent variables that have an effect on your dependent variable?
Then, both of your approaches are actually not really recommendable.
After having defined your research q | Is it better to do exploratory data analysis on the training dataset only?
So you want to identify independent variables that have an effect on your dependent variable?
Then, both of your approaches are actually not really recommendable.
After having defined your research question, you should develop your theory. That... | Is it better to do exploratory data analysis on the training dataset only?
So you want to identify independent variables that have an effect on your dependent variable?
Then, both of your approaches are actually not really recommendable.
After having defined your research q |
13,552 | Is it better to do exploratory data analysis on the training dataset only? | Applying EDA on test data is wrong.
Training is the process of looking into the correct answers to create the best model. This process it not just limited to running code on training data. Using information from EDA to decide which model to use, to tweak parameters, and so forth is part of the training process and henc... | Is it better to do exploratory data analysis on the training dataset only? | Applying EDA on test data is wrong.
Training is the process of looking into the correct answers to create the best model. This process it not just limited to running code on training data. Using infor | Is it better to do exploratory data analysis on the training dataset only?
Applying EDA on test data is wrong.
Training is the process of looking into the correct answers to create the best model. This process it not just limited to running code on training data. Using information from EDA to decide which model to use,... | Is it better to do exploratory data analysis on the training dataset only?
Applying EDA on test data is wrong.
Training is the process of looking into the correct answers to create the best model. This process it not just limited to running code on training data. Using infor |
13,553 | Is it better to do exploratory data analysis on the training dataset only? | After the paragraph of this answer. Hastie further explains p.245:
"Here is the correct way to carry out cross-validation in this example:
Divide the samples into K cross-validation folds (groups) at random.
For each fold k = 1, 2, . . . , K
(a) Find a subset of “good” predictors that show fairly strong
(univaria... | Is it better to do exploratory data analysis on the training dataset only? | After the paragraph of this answer. Hastie further explains p.245:
"Here is the correct way to carry out cross-validation in this example:
Divide the samples into K cross-validation folds (groups) a | Is it better to do exploratory data analysis on the training dataset only?
After the paragraph of this answer. Hastie further explains p.245:
"Here is the correct way to carry out cross-validation in this example:
Divide the samples into K cross-validation folds (groups) at random.
For each fold k = 1, 2, . . . , K
... | Is it better to do exploratory data analysis on the training dataset only?
After the paragraph of this answer. Hastie further explains p.245:
"Here is the correct way to carry out cross-validation in this example:
Divide the samples into K cross-validation folds (groups) a |
13,554 | Is it better to do exploratory data analysis on the training dataset only? | You do EDA on the entire data set. For instance, if you're using leave-one-out cross validation, how would you do EDA only on a training data set? In this case every observation is training and holdout at least once.
So, no, you form your understanding of the data on the entire sample. If you're in the industrial set u... | Is it better to do exploratory data analysis on the training dataset only? | You do EDA on the entire data set. For instance, if you're using leave-one-out cross validation, how would you do EDA only on a training data set? In this case every observation is training and holdou | Is it better to do exploratory data analysis on the training dataset only?
You do EDA on the entire data set. For instance, if you're using leave-one-out cross validation, how would you do EDA only on a training data set? In this case every observation is training and holdout at least once.
So, no, you form your unders... | Is it better to do exploratory data analysis on the training dataset only?
You do EDA on the entire data set. For instance, if you're using leave-one-out cross validation, how would you do EDA only on a training data set? In this case every observation is training and holdou |
13,555 | Is there any required amount of variance captured by PCA in order to do later analyses? | Regarding your particular questions:
Is there any required value of how much variance should be captured by PCA to be valid?
No, there is not (to my best of knowledge). I firmly believe that there is no single value you can use; no magic threshold of the captured variance percentage. The Cangelosi and Goriely's arti... | Is there any required amount of variance captured by PCA in order to do later analyses? | Regarding your particular questions:
Is there any required value of how much variance should be captured by PCA to be valid?
No, there is not (to my best of knowledge). I firmly believe that there | Is there any required amount of variance captured by PCA in order to do later analyses?
Regarding your particular questions:
Is there any required value of how much variance should be captured by PCA to be valid?
No, there is not (to my best of knowledge). I firmly believe that there is no single value you can use; ... | Is there any required amount of variance captured by PCA in order to do later analyses?
Regarding your particular questions:
Is there any required value of how much variance should be captured by PCA to be valid?
No, there is not (to my best of knowledge). I firmly believe that there |
13,556 | Why do we use term “population” instead of “Data-generating process”? | There are certainly already many contexts where statisticians do refer to a process rather than a population when discussing statistical analysis (e.g., when discussing a time-series process, stochastic process, etc.). Formally, a stochastic process is a set of random variables with a common domain, indexed over some ... | Why do we use term “population” instead of “Data-generating process”? | There are certainly already many contexts where statisticians do refer to a process rather than a population when discussing statistical analysis (e.g., when discussing a time-series process, stochast | Why do we use term “population” instead of “Data-generating process”?
There are certainly already many contexts where statisticians do refer to a process rather than a population when discussing statistical analysis (e.g., when discussing a time-series process, stochastic process, etc.). Formally, a stochastic process... | Why do we use term “population” instead of “Data-generating process”?
There are certainly already many contexts where statisticians do refer to a process rather than a population when discussing statistical analysis (e.g., when discussing a time-series process, stochast |
13,557 | What kinds of statistical problems are likely to benefit from quantum computing? | About quantum computing
Quantum computing makes use of superposition and entanglement.
Superposition means that the state of a system is a collection of multiple states that are superposed. Intuitively you can see this as quantum computing being based on wave mechanics and the state of the system is a wave. For waves ... | What kinds of statistical problems are likely to benefit from quantum computing? | About quantum computing
Quantum computing makes use of superposition and entanglement.
Superposition means that the state of a system is a collection of multiple states that are superposed. Intuitive | What kinds of statistical problems are likely to benefit from quantum computing?
About quantum computing
Quantum computing makes use of superposition and entanglement.
Superposition means that the state of a system is a collection of multiple states that are superposed. Intuitively you can see this as quantum computin... | What kinds of statistical problems are likely to benefit from quantum computing?
About quantum computing
Quantum computing makes use of superposition and entanglement.
Superposition means that the state of a system is a collection of multiple states that are superposed. Intuitive |
13,558 | What kinds of statistical problems are likely to benefit from quantum computing? | Brute force methods are most likely to benefit because of what quantum computing is. Why? One possible physical explanation of the path of a pitched baseball is that all possible quantum paths are automatically explored and the least energy expenditure path, i.e., the path of least resistance available, is chosen, and ... | What kinds of statistical problems are likely to benefit from quantum computing? | Brute force methods are most likely to benefit because of what quantum computing is. Why? One possible physical explanation of the path of a pitched baseball is that all possible quantum paths are aut | What kinds of statistical problems are likely to benefit from quantum computing?
Brute force methods are most likely to benefit because of what quantum computing is. Why? One possible physical explanation of the path of a pitched baseball is that all possible quantum paths are automatically explored and the least energ... | What kinds of statistical problems are likely to benefit from quantum computing?
Brute force methods are most likely to benefit because of what quantum computing is. Why? One possible physical explanation of the path of a pitched baseball is that all possible quantum paths are aut |
13,559 | What kinds of statistical problems are likely to benefit from quantum computing? | I liked the answer above on baseball. But I would be cautious about what quantum computing might do well.
It seems like it might do very well at things like cracking cryptographic schemes and the like: being able to superimpose all solutions and then collapse onto the actual one might go quite fast.
But in the 1980s -... | What kinds of statistical problems are likely to benefit from quantum computing? | I liked the answer above on baseball. But I would be cautious about what quantum computing might do well.
It seems like it might do very well at things like cracking cryptographic schemes and the lik | What kinds of statistical problems are likely to benefit from quantum computing?
I liked the answer above on baseball. But I would be cautious about what quantum computing might do well.
It seems like it might do very well at things like cracking cryptographic schemes and the like: being able to superimpose all soluti... | What kinds of statistical problems are likely to benefit from quantum computing?
I liked the answer above on baseball. But I would be cautious about what quantum computing might do well.
It seems like it might do very well at things like cracking cryptographic schemes and the lik |
13,560 | What kinds of statistical problems are likely to benefit from quantum computing? | What kinds of statistical problems are likely to benefit from quantum computing?
On page 645 of "Physical Chemistry: Concepts and Theory" Kenneth S. Schmitz explains:
Quantum effects become important when the de Broglie wavelength becomes comparable to, or is greater than, the dimensions of the particle. When this oc... | What kinds of statistical problems are likely to benefit from quantum computing? | What kinds of statistical problems are likely to benefit from quantum computing?
On page 645 of "Physical Chemistry: Concepts and Theory" Kenneth S. Schmitz explains:
Quantum effects become importan | What kinds of statistical problems are likely to benefit from quantum computing?
What kinds of statistical problems are likely to benefit from quantum computing?
On page 645 of "Physical Chemistry: Concepts and Theory" Kenneth S. Schmitz explains:
Quantum effects become important when the de Broglie wavelength become... | What kinds of statistical problems are likely to benefit from quantum computing?
What kinds of statistical problems are likely to benefit from quantum computing?
On page 645 of "Physical Chemistry: Concepts and Theory" Kenneth S. Schmitz explains:
Quantum effects become importan |
13,561 | Extreme learning machine: what's it all about? | Your intuition about the use of ELM for high dimensional problems is correct, I have some results on this, which I am preparing for publication. For many practical problems, the data are not very non-linear and the ELM does fairly well, but there will always be datasets where the curse of dimensionality means that the... | Extreme learning machine: what's it all about? | Your intuition about the use of ELM for high dimensional problems is correct, I have some results on this, which I am preparing for publication. For many practical problems, the data are not very non | Extreme learning machine: what's it all about?
Your intuition about the use of ELM for high dimensional problems is correct, I have some results on this, which I am preparing for publication. For many practical problems, the data are not very non-linear and the ELM does fairly well, but there will always be datasets w... | Extreme learning machine: what's it all about?
Your intuition about the use of ELM for high dimensional problems is correct, I have some results on this, which I am preparing for publication. For many practical problems, the data are not very non |
13,562 | Extreme learning machine: what's it all about? | The ELM "learns" from the data by analytically solving for the output weights. Thus the larger the data that is fed into the network will produce better results. However this also requires more numbers of hidden nodes. If the ELM is trained with little or no error, when given a new set of input, it is unable to produce... | Extreme learning machine: what's it all about? | The ELM "learns" from the data by analytically solving for the output weights. Thus the larger the data that is fed into the network will produce better results. However this also requires more number | Extreme learning machine: what's it all about?
The ELM "learns" from the data by analytically solving for the output weights. Thus the larger the data that is fed into the network will produce better results. However this also requires more numbers of hidden nodes. If the ELM is trained with little or no error, when gi... | Extreme learning machine: what's it all about?
The ELM "learns" from the data by analytically solving for the output weights. Thus the larger the data that is fed into the network will produce better results. However this also requires more number |
13,563 | Choosing between loss functions for binary classification | The state-of-the-art reference on the matter is [1].
Essentially, it shows that all the loss functions you specify will converge to the Bayes classifier, with fast rates.
Choosing between these for finite samples can be driven by several different arguments:
If you want to recover event probabilities (and not only c... | Choosing between loss functions for binary classification | The state-of-the-art reference on the matter is [1].
Essentially, it shows that all the loss functions you specify will converge to the Bayes classifier, with fast rates.
Choosing between these for | Choosing between loss functions for binary classification
The state-of-the-art reference on the matter is [1].
Essentially, it shows that all the loss functions you specify will converge to the Bayes classifier, with fast rates.
Choosing between these for finite samples can be driven by several different arguments:
... | Choosing between loss functions for binary classification
The state-of-the-art reference on the matter is [1].
Essentially, it shows that all the loss functions you specify will converge to the Bayes classifier, with fast rates.
Choosing between these for |
13,564 | Is there a Bayesian interpretation of linear regression with simultaneous L1 and L2 regularization (aka elastic net)? | Ben's comment is likely sufficient, but I provide some more references one of which is from before the paper Ben referenced.
A Bayesian elastic net representation was proposed by Kyung et. al. in their Section 3.1. Although the prior for the regression coefficient $\beta$ was correct, the authors incorrectly wrote down... | Is there a Bayesian interpretation of linear regression with simultaneous L1 and L2 regularization ( | Ben's comment is likely sufficient, but I provide some more references one of which is from before the paper Ben referenced.
A Bayesian elastic net representation was proposed by Kyung et. al. in thei | Is there a Bayesian interpretation of linear regression with simultaneous L1 and L2 regularization (aka elastic net)?
Ben's comment is likely sufficient, but I provide some more references one of which is from before the paper Ben referenced.
A Bayesian elastic net representation was proposed by Kyung et. al. in their ... | Is there a Bayesian interpretation of linear regression with simultaneous L1 and L2 regularization (
Ben's comment is likely sufficient, but I provide some more references one of which is from before the paper Ben referenced.
A Bayesian elastic net representation was proposed by Kyung et. al. in thei |
13,565 | Effect size to Wilcoxon signed rank test? | If you don't have ties, I would report the proportion of after values that are less than the corresponding before values.
If you do have ties, you could report the proportion of after values that are less than before out of the total number of non-tied pairs, or report all three proportions (<, =, >) and perhaps the ... | Effect size to Wilcoxon signed rank test? | If you don't have ties, I would report the proportion of after values that are less than the corresponding before values.
If you do have ties, you could report the proportion of after values that ar | Effect size to Wilcoxon signed rank test?
If you don't have ties, I would report the proportion of after values that are less than the corresponding before values.
If you do have ties, you could report the proportion of after values that are less than before out of the total number of non-tied pairs, or report all th... | Effect size to Wilcoxon signed rank test?
If you don't have ties, I would report the proportion of after values that are less than the corresponding before values.
If you do have ties, you could report the proportion of after values that ar |
13,566 | Effect size to Wilcoxon signed rank test? | Without knowing what kind of data were being assessed it's very hard to give good advice here. And really, that's all you can get. There's just no such thing as a best measure of effect size for questions like this... maybe ever.
The effect sizes mentioned in the question are all standardized effect sizes. But it's ent... | Effect size to Wilcoxon signed rank test? | Without knowing what kind of data were being assessed it's very hard to give good advice here. And really, that's all you can get. There's just no such thing as a best measure of effect size for quest | Effect size to Wilcoxon signed rank test?
Without knowing what kind of data were being assessed it's very hard to give good advice here. And really, that's all you can get. There's just no such thing as a best measure of effect size for questions like this... maybe ever.
The effect sizes mentioned in the question are a... | Effect size to Wilcoxon signed rank test?
Without knowing what kind of data were being assessed it's very hard to give good advice here. And really, that's all you can get. There's just no such thing as a best measure of effect size for quest |
13,567 | Drawing n intervals uniformly randomly, probability that at least one interval overlaps with all others | This post answers the question and outlines partial progress toward proving it correct.
For $n=1$, the answer trivially is $1$. For all larger $n$, it is (surprisingly) always $2/3$.
To see why, first observe that the question can be generalized to any continuous distribution $F$ (in place of the uniform distribution)... | Drawing n intervals uniformly randomly, probability that at least one interval overlaps with all oth | This post answers the question and outlines partial progress toward proving it correct.
For $n=1$, the answer trivially is $1$. For all larger $n$, it is (surprisingly) always $2/3$.
To see why, firs | Drawing n intervals uniformly randomly, probability that at least one interval overlaps with all others
This post answers the question and outlines partial progress toward proving it correct.
For $n=1$, the answer trivially is $1$. For all larger $n$, it is (surprisingly) always $2/3$.
To see why, first observe that t... | Drawing n intervals uniformly randomly, probability that at least one interval overlaps with all oth
This post answers the question and outlines partial progress toward proving it correct.
For $n=1$, the answer trivially is $1$. For all larger $n$, it is (surprisingly) always $2/3$.
To see why, firs |
13,568 | Tutorials for feature engineering | I would say experience -- basic ideas are:
to fit how classifiers work; giving a geometry problem to a tree, oversized dimension to a kNN and interval data to an SVM are not a good ideas
remove as much nonlinearities as possible; expecting that some classifier will do Fourier analysis inside is rather naive (even if, ... | Tutorials for feature engineering | I would say experience -- basic ideas are:
to fit how classifiers work; giving a geometry problem to a tree, oversized dimension to a kNN and interval data to an SVM are not a good ideas
remove as mu | Tutorials for feature engineering
I would say experience -- basic ideas are:
to fit how classifiers work; giving a geometry problem to a tree, oversized dimension to a kNN and interval data to an SVM are not a good ideas
remove as much nonlinearities as possible; expecting that some classifier will do Fourier analysis... | Tutorials for feature engineering
I would say experience -- basic ideas are:
to fit how classifiers work; giving a geometry problem to a tree, oversized dimension to a kNN and interval data to an SVM are not a good ideas
remove as mu |
13,569 | Tutorials for feature engineering | There is a book from O'Reilly called "Feature Engineering for Machine Learning" by Zheng et al.
I read the book and it covers different types of data (e.g categorical, text...) and describes different aspects of feature engineering that go with it. This includes things like normalization of data, feature selection, tf-... | Tutorials for feature engineering | There is a book from O'Reilly called "Feature Engineering for Machine Learning" by Zheng et al.
I read the book and it covers different types of data (e.g categorical, text...) and describes different | Tutorials for feature engineering
There is a book from O'Reilly called "Feature Engineering for Machine Learning" by Zheng et al.
I read the book and it covers different types of data (e.g categorical, text...) and describes different aspects of feature engineering that go with it. This includes things like normalizati... | Tutorials for feature engineering
There is a book from O'Reilly called "Feature Engineering for Machine Learning" by Zheng et al.
I read the book and it covers different types of data (e.g categorical, text...) and describes different |
13,570 | Train vs Test Error Gap and its relationship to Overfitting : Reconciling conflicting advice | I do not think this is conflicting advice. What we are really interested in is good out-of-sample performance, not in reducing the gap between training and test set performance. If the test set performance is representative of out-of-sample performance (i.e. the test set is large enough, uncontaminated and is a represe... | Train vs Test Error Gap and its relationship to Overfitting : Reconciling conflicting advice | I do not think this is conflicting advice. What we are really interested in is good out-of-sample performance, not in reducing the gap between training and test set performance. If the test set perfor | Train vs Test Error Gap and its relationship to Overfitting : Reconciling conflicting advice
I do not think this is conflicting advice. What we are really interested in is good out-of-sample performance, not in reducing the gap between training and test set performance. If the test set performance is representative of ... | Train vs Test Error Gap and its relationship to Overfitting : Reconciling conflicting advice
I do not think this is conflicting advice. What we are really interested in is good out-of-sample performance, not in reducing the gap between training and test set performance. If the test set perfor |
13,571 | How do I interpret the covariance matrix from a curve fit? | As a clarification, the variable pcov from scipy.optimize.curve_fit is the
estimated covariance of the parameter estimate, that is loosely speaking, given the data and a model, how much information is there in the data to determine the value of a parameter in the given model. So it does not really tell you if the chos... | How do I interpret the covariance matrix from a curve fit? | As a clarification, the variable pcov from scipy.optimize.curve_fit is the
estimated covariance of the parameter estimate, that is loosely speaking, given the data and a model, how much information i | How do I interpret the covariance matrix from a curve fit?
As a clarification, the variable pcov from scipy.optimize.curve_fit is the
estimated covariance of the parameter estimate, that is loosely speaking, given the data and a model, how much information is there in the data to determine the value of a parameter in ... | How do I interpret the covariance matrix from a curve fit?
As a clarification, the variable pcov from scipy.optimize.curve_fit is the
estimated covariance of the parameter estimate, that is loosely speaking, given the data and a model, how much information i |
13,572 | When would we use tantiles and the medial, rather than quantiles and the median? | This is really a comment, but too long for a comment. It is trying to clarify the definition of "tantile" (in the $p=0.5$ case which is analogous to the median). Let $X$ be a (for simplicity) absolutely continuous random variable with density function $f(x)$. We assume that the expectation $\mu= \mathbb E X$ does exist... | When would we use tantiles and the medial, rather than quantiles and the median? | This is really a comment, but too long for a comment. It is trying to clarify the definition of "tantile" (in the $p=0.5$ case which is analogous to the median). Let $X$ be a (for simplicity) absolute | When would we use tantiles and the medial, rather than quantiles and the median?
This is really a comment, but too long for a comment. It is trying to clarify the definition of "tantile" (in the $p=0.5$ case which is analogous to the median). Let $X$ be a (for simplicity) absolutely continuous random variable with dens... | When would we use tantiles and the medial, rather than quantiles and the median?
This is really a comment, but too long for a comment. It is trying to clarify the definition of "tantile" (in the $p=0.5$ case which is analogous to the median). Let $X$ be a (for simplicity) absolute |
13,573 | When would we use tantiles and the medial, rather than quantiles and the median? | If you draw a Lorenz curve of sorted cumulative incomes, you might get something like this (copied from Wikipedia). Real Lorenz curves are not as symmetric, and those for wealth are more extreme than those for income.
To find the median income, you might split the horizontal axis in half, as with the thick red line b... | When would we use tantiles and the medial, rather than quantiles and the median? | If you draw a Lorenz curve of sorted cumulative incomes, you might get something like this (copied from Wikipedia). Real Lorenz curves are not as symmetric, and those for wealth are more extreme than | When would we use tantiles and the medial, rather than quantiles and the median?
If you draw a Lorenz curve of sorted cumulative incomes, you might get something like this (copied from Wikipedia). Real Lorenz curves are not as symmetric, and those for wealth are more extreme than those for income.
To find the median ... | When would we use tantiles and the medial, rather than quantiles and the median?
If you draw a Lorenz curve of sorted cumulative incomes, you might get something like this (copied from Wikipedia). Real Lorenz curves are not as symmetric, and those for wealth are more extreme than |
13,574 | RNN vs Kalman filter : learning the underlying dynamics? | Yes indeed they are related because both are used to predict $y_{n}$ and $s_{n}$ at time step n based on some current observation $x_{n}$ and state $s_{n-1}$ i.e. they both represent a function $F$ such that $$F(x_{n}, s_{n-1}) = (y_{n}, s_{n})$$
The advantage of the RNN over Kalman filter is that the RNN architecture ... | RNN vs Kalman filter : learning the underlying dynamics? | Yes indeed they are related because both are used to predict $y_{n}$ and $s_{n}$ at time step n based on some current observation $x_{n}$ and state $s_{n-1}$ i.e. they both represent a function $F$ su | RNN vs Kalman filter : learning the underlying dynamics?
Yes indeed they are related because both are used to predict $y_{n}$ and $s_{n}$ at time step n based on some current observation $x_{n}$ and state $s_{n-1}$ i.e. they both represent a function $F$ such that $$F(x_{n}, s_{n-1}) = (y_{n}, s_{n})$$
The advantage of... | RNN vs Kalman filter : learning the underlying dynamics?
Yes indeed they are related because both are used to predict $y_{n}$ and $s_{n}$ at time step n based on some current observation $x_{n}$ and state $s_{n-1}$ i.e. they both represent a function $F$ su |
13,575 | RNN vs Kalman filter : learning the underlying dynamics? | As you say, the difference is the activation functions.
The usual purpose of a Kalman filter is used to model an intrinsically linear process, where the observations are subject to additive noise. You can get away with using a Kalman filter if there are slow deviation from linearity, but not if the process is strongly ... | RNN vs Kalman filter : learning the underlying dynamics? | As you say, the difference is the activation functions.
The usual purpose of a Kalman filter is used to model an intrinsically linear process, where the observations are subject to additive noise. You | RNN vs Kalman filter : learning the underlying dynamics?
As you say, the difference is the activation functions.
The usual purpose of a Kalman filter is used to model an intrinsically linear process, where the observations are subject to additive noise. You can get away with using a Kalman filter if there are slow devi... | RNN vs Kalman filter : learning the underlying dynamics?
As you say, the difference is the activation functions.
The usual purpose of a Kalman filter is used to model an intrinsically linear process, where the observations are subject to additive noise. You |
13,576 | RNN vs Kalman filter : learning the underlying dynamics? | They replace the kalman gain calculations by a RNN on this paper if you're still interested. | RNN vs Kalman filter : learning the underlying dynamics? | They replace the kalman gain calculations by a RNN on this paper if you're still interested. | RNN vs Kalman filter : learning the underlying dynamics?
They replace the kalman gain calculations by a RNN on this paper if you're still interested. | RNN vs Kalman filter : learning the underlying dynamics?
They replace the kalman gain calculations by a RNN on this paper if you're still interested. |
13,577 | RNN vs Kalman filter : learning the underlying dynamics? | I'll substitute linear Gaussian state space model for Kalman filter here.
Similarities
they both model time series
they both have a hidden/latent "state" or "layer" process for which there is no data
the observed dependent sequence depends/conditions on the above process
the hidden/latent state/layer can depend on ind... | RNN vs Kalman filter : learning the underlying dynamics? | I'll substitute linear Gaussian state space model for Kalman filter here.
Similarities
they both model time series
they both have a hidden/latent "state" or "layer" process for which there is no data | RNN vs Kalman filter : learning the underlying dynamics?
I'll substitute linear Gaussian state space model for Kalman filter here.
Similarities
they both model time series
they both have a hidden/latent "state" or "layer" process for which there is no data
the observed dependent sequence depends/conditions on the abov... | RNN vs Kalman filter : learning the underlying dynamics?
I'll substitute linear Gaussian state space model for Kalman filter here.
Similarities
they both model time series
they both have a hidden/latent "state" or "layer" process for which there is no data |
13,578 | confidence intervals' coverage with regularized estimates | There is a recent paper which address precisely your question (if you want to perform regression on your data, as I understand) and, luckily, provides expressions which are easy to calculate (Confidence Intervals and Hypothesis Testing for High-Dimensional Regression).
Also, you may be interested in the recent work by ... | confidence intervals' coverage with regularized estimates | There is a recent paper which address precisely your question (if you want to perform regression on your data, as I understand) and, luckily, provides expressions which are easy to calculate (Confiden | confidence intervals' coverage with regularized estimates
There is a recent paper which address precisely your question (if you want to perform regression on your data, as I understand) and, luckily, provides expressions which are easy to calculate (Confidence Intervals and Hypothesis Testing for High-Dimensional Regre... | confidence intervals' coverage with regularized estimates
There is a recent paper which address precisely your question (if you want to perform regression on your data, as I understand) and, luckily, provides expressions which are easy to calculate (Confiden |
13,579 | confidence intervals' coverage with regularized estimates | http://cran.r-project.org/web/packages/hdi/index.html
Is this what you're looking for?
Description
Computes confidence intervals for the l1-norm of groups of regression parameters in a hierarchical
clustering tree. | confidence intervals' coverage with regularized estimates | http://cran.r-project.org/web/packages/hdi/index.html
Is this what you're looking for?
Description
Computes confidence intervals for the l1-norm of groups of regression parameters in a hierarchical
cl | confidence intervals' coverage with regularized estimates
http://cran.r-project.org/web/packages/hdi/index.html
Is this what you're looking for?
Description
Computes confidence intervals for the l1-norm of groups of regression parameters in a hierarchical
clustering tree. | confidence intervals' coverage with regularized estimates
http://cran.r-project.org/web/packages/hdi/index.html
Is this what you're looking for?
Description
Computes confidence intervals for the l1-norm of groups of regression parameters in a hierarchical
cl |
13,580 | How can we simulate from a geometric mixture? | Well, of course there's the acceptance-rejection algorithm, which I would implement for your example as:
(Initialization) For each $i$, find $A_i = \sup_x \{\Pi_{j=1}^k f_j(x)^{\alpha_j}/f_i(x)\} $. Edit reflecting Xi'an's comment below: Select the distribution $f_i$ which corresponds to the smallest $A_i$.
Generate... | How can we simulate from a geometric mixture? | Well, of course there's the acceptance-rejection algorithm, which I would implement for your example as:
(Initialization) For each $i$, find $A_i = \sup_x \{\Pi_{j=1}^k f_j(x)^{\alpha_j}/f_i(x)\} $. | How can we simulate from a geometric mixture?
Well, of course there's the acceptance-rejection algorithm, which I would implement for your example as:
(Initialization) For each $i$, find $A_i = \sup_x \{\Pi_{j=1}^k f_j(x)^{\alpha_j}/f_i(x)\} $. Edit reflecting Xi'an's comment below: Select the distribution $f_i$ whi... | How can we simulate from a geometric mixture?
Well, of course there's the acceptance-rejection algorithm, which I would implement for your example as:
(Initialization) For each $i$, find $A_i = \sup_x \{\Pi_{j=1}^k f_j(x)^{\alpha_j}/f_i(x)\} $. |
13,581 | Does Stein's Paradox still hold when using the $l_1$ norm instead of the $l_2$ norm? | Stein's paradox holds for all loss functions, and even worse- admissibility w.r.t. to a particular loss function probably implies inadmissibility w.r.t to any other loss.
For a formal treatment see Section 8.8 (Shrinkage Estimators) in [1].
[1] van der Vaart, A. W. Asymptotic Statistics. Cambridge, UK ; New York, NY, U... | Does Stein's Paradox still hold when using the $l_1$ norm instead of the $l_2$ norm? | Stein's paradox holds for all loss functions, and even worse- admissibility w.r.t. to a particular loss function probably implies inadmissibility w.r.t to any other loss.
For a formal treatment see Se | Does Stein's Paradox still hold when using the $l_1$ norm instead of the $l_2$ norm?
Stein's paradox holds for all loss functions, and even worse- admissibility w.r.t. to a particular loss function probably implies inadmissibility w.r.t to any other loss.
For a formal treatment see Section 8.8 (Shrinkage Estimators) in... | Does Stein's Paradox still hold when using the $l_1$ norm instead of the $l_2$ norm?
Stein's paradox holds for all loss functions, and even worse- admissibility w.r.t. to a particular loss function probably implies inadmissibility w.r.t to any other loss.
For a formal treatment see Se |
13,582 | Reporting variance of the repeated k-fold cross-validation | 1 and 3 seem to me as invalid since they do not take into account the dependencies between repeated runs. In other words, repeated k-fold runs are more similar to each other than real repetitions of the experiment with independent data.
2 does not take into account the dependencies between folds within the same run.
I ... | Reporting variance of the repeated k-fold cross-validation | 1 and 3 seem to me as invalid since they do not take into account the dependencies between repeated runs. In other words, repeated k-fold runs are more similar to each other than real repetitions of t | Reporting variance of the repeated k-fold cross-validation
1 and 3 seem to me as invalid since they do not take into account the dependencies between repeated runs. In other words, repeated k-fold runs are more similar to each other than real repetitions of the experiment with independent data.
2 does not take into acc... | Reporting variance of the repeated k-fold cross-validation
1 and 3 seem to me as invalid since they do not take into account the dependencies between repeated runs. In other words, repeated k-fold runs are more similar to each other than real repetitions of t |
13,583 | Reporting variance of the repeated k-fold cross-validation | I might be wrong (and I am open to change my mind!) but to my understanding, when we say that CV reduces variance we cannot actually see it by looking at the variance across the folds.
The thing is, CV is just a techinque that improves the estimation of the performance of a (one!) model (since in the k-folds we train t... | Reporting variance of the repeated k-fold cross-validation | I might be wrong (and I am open to change my mind!) but to my understanding, when we say that CV reduces variance we cannot actually see it by looking at the variance across the folds.
The thing is, C | Reporting variance of the repeated k-fold cross-validation
I might be wrong (and I am open to change my mind!) but to my understanding, when we say that CV reduces variance we cannot actually see it by looking at the variance across the folds.
The thing is, CV is just a techinque that improves the estimation of the per... | Reporting variance of the repeated k-fold cross-validation
I might be wrong (and I am open to change my mind!) but to my understanding, when we say that CV reduces variance we cannot actually see it by looking at the variance across the folds.
The thing is, C |
13,584 | Getting started with bayesian structural models using MCMC | You might be interested in TensorFlow Probability. It has a Python API, and has been chosen to replace Theano as the PyMC3 backend at some point in the future. Tensorflow Probability can also be used for MCMC directly, and it has dedicated functionality for Bayesian structural time series modelling. There is a nice blo... | Getting started with bayesian structural models using MCMC | You might be interested in TensorFlow Probability. It has a Python API, and has been chosen to replace Theano as the PyMC3 backend at some point in the future. Tensorflow Probability can also be used | Getting started with bayesian structural models using MCMC
You might be interested in TensorFlow Probability. It has a Python API, and has been chosen to replace Theano as the PyMC3 backend at some point in the future. Tensorflow Probability can also be used for MCMC directly, and it has dedicated functionality for Bay... | Getting started with bayesian structural models using MCMC
You might be interested in TensorFlow Probability. It has a Python API, and has been chosen to replace Theano as the PyMC3 backend at some point in the future. Tensorflow Probability can also be used |
13,585 | Howlers caused by using stepwise regression | There is more than one question being asked. The most narrow one is asking for an example of when stepwise regression has caused harm because it was perfomed stepwise. This is of course true, but can only be established unequivocally when the data used for stepwise regression is also published, and someone reanalyses i... | Howlers caused by using stepwise regression | There is more than one question being asked. The most narrow one is asking for an example of when stepwise regression has caused harm because it was perfomed stepwise. This is of course true, but can | Howlers caused by using stepwise regression
There is more than one question being asked. The most narrow one is asking for an example of when stepwise regression has caused harm because it was perfomed stepwise. This is of course true, but can only be established unequivocally when the data used for stepwise regression... | Howlers caused by using stepwise regression
There is more than one question being asked. The most narrow one is asking for an example of when stepwise regression has caused harm because it was perfomed stepwise. This is of course true, but can |
13,586 | Can we see shape of normal curve somewhere in nature? | I wouldn't think any pattern of erosion or deposition on Earth would fit because skewing factors including gravity and Coriolis are always involved (rivers meander more as they age, for example, and valley floors are sort of the average of rivers). Maybe the cross section of a stalagmite, assuming the drip remained in... | Can we see shape of normal curve somewhere in nature? | I wouldn't think any pattern of erosion or deposition on Earth would fit because skewing factors including gravity and Coriolis are always involved (rivers meander more as they age, for example, and v | Can we see shape of normal curve somewhere in nature?
I wouldn't think any pattern of erosion or deposition on Earth would fit because skewing factors including gravity and Coriolis are always involved (rivers meander more as they age, for example, and valley floors are sort of the average of rivers). Maybe the cross ... | Can we see shape of normal curve somewhere in nature?
I wouldn't think any pattern of erosion or deposition on Earth would fit because skewing factors including gravity and Coriolis are always involved (rivers meander more as they age, for example, and v |
13,587 | Can we see shape of normal curve somewhere in nature? | I thought a lot about my question and probably I found something. U-shape of many valleys imitates "reversed" normal curve. Are there any reasons why this should not be gaussian (note that water makes the valleys smooth)?
Here is an example. | Can we see shape of normal curve somewhere in nature? | I thought a lot about my question and probably I found something. U-shape of many valleys imitates "reversed" normal curve. Are there any reasons why this should not be gaussian (note that water makes | Can we see shape of normal curve somewhere in nature?
I thought a lot about my question and probably I found something. U-shape of many valleys imitates "reversed" normal curve. Are there any reasons why this should not be gaussian (note that water makes the valleys smooth)?
Here is an example. | Can we see shape of normal curve somewhere in nature?
I thought a lot about my question and probably I found something. U-shape of many valleys imitates "reversed" normal curve. Are there any reasons why this should not be gaussian (note that water makes |
13,588 | Can adaptive MCMC be trusted? | How do we know that adaptation is not messing up with ergodicity at a
given finite time, and that a sampler is sampling from the correct
distribution? If it makes sense at all, how much burn-in should one do
to ensure that early adaptation is not biasing the chains?
Ergodicity and bias are about asymptotic prope... | Can adaptive MCMC be trusted? | How do we know that adaptation is not messing up with ergodicity at a
given finite time, and that a sampler is sampling from the correct
distribution? If it makes sense at all, how much burn-in sh | Can adaptive MCMC be trusted?
How do we know that adaptation is not messing up with ergodicity at a
given finite time, and that a sampler is sampling from the correct
distribution? If it makes sense at all, how much burn-in should one do
to ensure that early adaptation is not biasing the chains?
Ergodicity and b... | Can adaptive MCMC be trusted?
How do we know that adaptation is not messing up with ergodicity at a
given finite time, and that a sampler is sampling from the correct
distribution? If it makes sense at all, how much burn-in sh |
13,589 | Fisher information in a hierarchical model | There is no closed-form analytic expression for the Fisher information for the hierarchical model you give. In practice, Fisher information can only be computed analytically for exponential family distributions. For exponential families, the log-likelihood is linear in the sufficient statistics, and the sufficient stat... | Fisher information in a hierarchical model | There is no closed-form analytic expression for the Fisher information for the hierarchical model you give. In practice, Fisher information can only be computed analytically for exponential family dis | Fisher information in a hierarchical model
There is no closed-form analytic expression for the Fisher information for the hierarchical model you give. In practice, Fisher information can only be computed analytically for exponential family distributions. For exponential families, the log-likelihood is linear in the suf... | Fisher information in a hierarchical model
There is no closed-form analytic expression for the Fisher information for the hierarchical model you give. In practice, Fisher information can only be computed analytically for exponential family dis |
13,590 | Fisher information in a hierarchical model | The two of the Normal and Laplace are from the exponential family. If you can write the distribution in the exponential form then the fisher information matrix is the second gradient of the log-normalizer of the exponential family. | Fisher information in a hierarchical model | The two of the Normal and Laplace are from the exponential family. If you can write the distribution in the exponential form then the fisher information matrix is the second gradient of the log-normal | Fisher information in a hierarchical model
The two of the Normal and Laplace are from the exponential family. If you can write the distribution in the exponential form then the fisher information matrix is the second gradient of the log-normalizer of the exponential family. | Fisher information in a hierarchical model
The two of the Normal and Laplace are from the exponential family. If you can write the distribution in the exponential form then the fisher information matrix is the second gradient of the log-normal |
13,591 | Anscombe-like datasets with the same box and whiskers plot (mean/std/median/MAD/min/max) | To be concrete, I'm considering the problem of creating two datasets each of which suggests a relationship but the relationship of each is different, and yet also have approximately the same:
mean x
mean y
SD x
SD y
median x
median y
minimum x
minimum y
maximum x
maximum y
median absolute deviation from the median of ... | Anscombe-like datasets with the same box and whiskers plot (mean/std/median/MAD/min/max) | To be concrete, I'm considering the problem of creating two datasets each of which suggests a relationship but the relationship of each is different, and yet also have approximately the same:
mean x
| Anscombe-like datasets with the same box and whiskers plot (mean/std/median/MAD/min/max)
To be concrete, I'm considering the problem of creating two datasets each of which suggests a relationship but the relationship of each is different, and yet also have approximately the same:
mean x
mean y
SD x
SD y
median x
media... | Anscombe-like datasets with the same box and whiskers plot (mean/std/median/MAD/min/max)
To be concrete, I'm considering the problem of creating two datasets each of which suggests a relationship but the relationship of each is different, and yet also have approximately the same:
mean x
|
13,592 | Clustering algorithms that operate on sparse data matricies [closed] | I don't use R. It is often very slow and has next to no indexing support.
But software recommendations are considered off-topic anyway.
Note that plenty of algorithms don't care how you store your data. If you prefer to have a sparse matrix, that should be your choice, not the algorithms choice.
People that use too muc... | Clustering algorithms that operate on sparse data matricies [closed] | I don't use R. It is often very slow and has next to no indexing support.
But software recommendations are considered off-topic anyway.
Note that plenty of algorithms don't care how you store your dat | Clustering algorithms that operate on sparse data matricies [closed]
I don't use R. It is often very slow and has next to no indexing support.
But software recommendations are considered off-topic anyway.
Note that plenty of algorithms don't care how you store your data. If you prefer to have a sparse matrix, that shou... | Clustering algorithms that operate on sparse data matricies [closed]
I don't use R. It is often very slow and has next to no indexing support.
But software recommendations are considered off-topic anyway.
Note that plenty of algorithms don't care how you store your dat |
13,593 | Simulating time-series given power and cross spectral densities | Since your signals are stationary, a simple approach would be to use white noise as a basis and filter it to fit your PSDs. A way to calculate these filter coefficients is to use linear prediction.
It seems there is a python function for it, try it out:
from scikits.talkbox import lpc
If you'd like (I have only used t... | Simulating time-series given power and cross spectral densities | Since your signals are stationary, a simple approach would be to use white noise as a basis and filter it to fit your PSDs. A way to calculate these filter coefficients is to use linear prediction.
It | Simulating time-series given power and cross spectral densities
Since your signals are stationary, a simple approach would be to use white noise as a basis and filter it to fit your PSDs. A way to calculate these filter coefficients is to use linear prediction.
It seems there is a python function for it, try it out:
fr... | Simulating time-series given power and cross spectral densities
Since your signals are stationary, a simple approach would be to use white noise as a basis and filter it to fit your PSDs. A way to calculate these filter coefficients is to use linear prediction.
It |
13,594 | Simulating time-series given power and cross spectral densities | A bit late to the party, as usual, but I see some recentish activity so I'll my two yen.
First, I can't fault the OPs attempt - it looks right to me. The discrepancies could be due to issues with finite samples, for example positive bias of signal power estimation.
However, I think that there are simpler ways to gener... | Simulating time-series given power and cross spectral densities | A bit late to the party, as usual, but I see some recentish activity so I'll my two yen.
First, I can't fault the OPs attempt - it looks right to me. The discrepancies could be due to issues with fin | Simulating time-series given power and cross spectral densities
A bit late to the party, as usual, but I see some recentish activity so I'll my two yen.
First, I can't fault the OPs attempt - it looks right to me. The discrepancies could be due to issues with finite samples, for example positive bias of signal power e... | Simulating time-series given power and cross spectral densities
A bit late to the party, as usual, but I see some recentish activity so I'll my two yen.
First, I can't fault the OPs attempt - it looks right to me. The discrepancies could be due to issues with fin |
13,595 | How can we bound the probability that a random variable is maximal? | You can use the multivariate Chebyshev's inequality.
Two variables case
For a single situation, $X_1$ vs $X_2$, I arrive at the same situation as Jochen's comment on Nov 4 2016
1) If $\mu_1 < \mu_2$ then $ P(X_1>X_2) \leq (\sigma_1^2 + \sigma_2^2)/(\mu_1-\mu_2)^2 $
(and I wonder as well about your derivation)
Derivati... | How can we bound the probability that a random variable is maximal? | You can use the multivariate Chebyshev's inequality.
Two variables case
For a single situation, $X_1$ vs $X_2$, I arrive at the same situation as Jochen's comment on Nov 4 2016
1) If $\mu_1 < \mu_2$ t | How can we bound the probability that a random variable is maximal?
You can use the multivariate Chebyshev's inequality.
Two variables case
For a single situation, $X_1$ vs $X_2$, I arrive at the same situation as Jochen's comment on Nov 4 2016
1) If $\mu_1 < \mu_2$ then $ P(X_1>X_2) \leq (\sigma_1^2 + \sigma_2^2)/(\mu... | How can we bound the probability that a random variable is maximal?
You can use the multivariate Chebyshev's inequality.
Two variables case
For a single situation, $X_1$ vs $X_2$, I arrive at the same situation as Jochen's comment on Nov 4 2016
1) If $\mu_1 < \mu_2$ t |
13,596 | How can we bound the probability that a random variable is maximal? | I have found a theorem that might help you and will try to adjust it for your needs. Assume you have:
$$exp(t \cdot \mathbf{E}(\underset{1 \leq i \leq n}{max}X_{i}))$$
Then by Jensen's inequality (since exp(.) is a convex function), we get:
$$exp(t \cdot \mathbf{E}(\underset{1 \leq i \leq n}{max}X_{i}))
\leq \mathbf{E... | How can we bound the probability that a random variable is maximal? | I have found a theorem that might help you and will try to adjust it for your needs. Assume you have:
$$exp(t \cdot \mathbf{E}(\underset{1 \leq i \leq n}{max}X_{i}))$$
Then by Jensen's inequality (sin | How can we bound the probability that a random variable is maximal?
I have found a theorem that might help you and will try to adjust it for your needs. Assume you have:
$$exp(t \cdot \mathbf{E}(\underset{1 \leq i \leq n}{max}X_{i}))$$
Then by Jensen's inequality (since exp(.) is a convex function), we get:
$$exp(t \cd... | How can we bound the probability that a random variable is maximal?
I have found a theorem that might help you and will try to adjust it for your needs. Assume you have:
$$exp(t \cdot \mathbf{E}(\underset{1 \leq i \leq n}{max}X_{i}))$$
Then by Jensen's inequality (sin |
13,597 | R's lmer cheat sheet | What's the difference between (~1 +....) and (1 | ...) and (0 | ...) etc.?
Say you have variable V1 predicted by categorical variable V2, which is treated as a random effect, and continuous variable V3, which is treated as a linear fixed effect. Using lmer syntax, simplest model (M1) is:
V1 ~ (1|V2) + V3
This model w... | R's lmer cheat sheet | What's the difference between (~1 +....) and (1 | ...) and (0 | ...) etc.?
Say you have variable V1 predicted by categorical variable V2, which is treated as a random effect, and continuous variable | R's lmer cheat sheet
What's the difference between (~1 +....) and (1 | ...) and (0 | ...) etc.?
Say you have variable V1 predicted by categorical variable V2, which is treated as a random effect, and continuous variable V3, which is treated as a linear fixed effect. Using lmer syntax, simplest model (M1) is:
V1 ~ (1|V... | R's lmer cheat sheet
What's the difference between (~1 +....) and (1 | ...) and (0 | ...) etc.?
Say you have variable V1 predicted by categorical variable V2, which is treated as a random effect, and continuous variable |
13,598 | R's lmer cheat sheet | The general trick is, as mentioned in another answer, is that the formula follows the form dependent ~ independent | grouping. The groupingis generally a random factor, you can include fixed factors without any grouping and you can have additional random factors without any fixed factor (an intercept-only model). A + ... | R's lmer cheat sheet | The general trick is, as mentioned in another answer, is that the formula follows the form dependent ~ independent | grouping. The groupingis generally a random factor, you can include fixed factors w | R's lmer cheat sheet
The general trick is, as mentioned in another answer, is that the formula follows the form dependent ~ independent | grouping. The groupingis generally a random factor, you can include fixed factors without any grouping and you can have additional random factors without any fixed factor (an interce... | R's lmer cheat sheet
The general trick is, as mentioned in another answer, is that the formula follows the form dependent ~ independent | grouping. The groupingis generally a random factor, you can include fixed factors w |
13,599 | R's lmer cheat sheet | The | symbol indicates a grouping factor in mixed methods.
As per Pinheiro & Bates:
...The formula also designates a response and, when available, a primary covariate. It is given as
response ~ primary | grouping
where response is an expression for the response, primary is an expression for the primary covariate, and... | R's lmer cheat sheet | The | symbol indicates a grouping factor in mixed methods.
As per Pinheiro & Bates:
...The formula also designates a response and, when available, a primary covariate. It is given as
response ~ prima | R's lmer cheat sheet
The | symbol indicates a grouping factor in mixed methods.
As per Pinheiro & Bates:
...The formula also designates a response and, when available, a primary covariate. It is given as
response ~ primary | grouping
where response is an expression for the response, primary is an expression for the p... | R's lmer cheat sheet
The | symbol indicates a grouping factor in mixed methods.
As per Pinheiro & Bates:
...The formula also designates a response and, when available, a primary covariate. It is given as
response ~ prima |
13,600 | Roll a die until it lands on any number other than 4. What is the probability the result is > 4? | Just solve it using algebra:
\begin{aligned}
P(W) &= \tfrac 2 6 + \tfrac 1 6 \cdot P(W) \\[7pt]
\tfrac 5 6 \cdot P(W) &= \tfrac 2 6 \\[7pt]
P(W) &= \tfrac 2 5.
\end{aligned} | Roll a die until it lands on any number other than 4. What is the probability the result is > 4? | Just solve it using algebra:
\begin{aligned}
P(W) &= \tfrac 2 6 + \tfrac 1 6 \cdot P(W) \\[7pt]
\tfrac 5 6 \cdot P(W) &= \tfrac 2 6 \\[7pt]
P(W) &= \tfrac 2 5.
\end{aligned} | Roll a die until it lands on any number other than 4. What is the probability the result is > 4?
Just solve it using algebra:
\begin{aligned}
P(W) &= \tfrac 2 6 + \tfrac 1 6 \cdot P(W) \\[7pt]
\tfrac 5 6 \cdot P(W) &= \tfrac 2 6 \\[7pt]
P(W) &= \tfrac 2 5.
\end{aligned} | Roll a die until it lands on any number other than 4. What is the probability the result is > 4?
Just solve it using algebra:
\begin{aligned}
P(W) &= \tfrac 2 6 + \tfrac 1 6 \cdot P(W) \\[7pt]
\tfrac 5 6 \cdot P(W) &= \tfrac 2 6 \\[7pt]
P(W) &= \tfrac 2 5.
\end{aligned} |
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