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 |
|---|---|---|---|---|---|---|
10,901 | Confused about independent probabilities. If a fair coin is flipped 5 times, P(HHHHH) = 0.03125, but P(H | HHHH) = 0.5 | I see two explainations:
1: (Same as already posted, but specific to fair coin Heads and Tails)
Because there are only two possibilities, H and T, P(H|HHHH) is the same as P(HHHHH) / (P(HHHHH) + P(HHHHT))
P(HHHHH) = .5^5 and P(HHHHT) = .5^5, therefore P(H|HHHH) = .5^5/(.5^5+.5^5) = .5^5/(2*(.5^5)) = 1/2
2:
P(HHHHH) is ... | Confused about independent probabilities. If a fair coin is flipped 5 times, P(HHHHH) = 0.03125, but | I see two explainations:
1: (Same as already posted, but specific to fair coin Heads and Tails)
Because there are only two possibilities, H and T, P(H|HHHH) is the same as P(HHHHH) / (P(HHHHH) + P(HHH | Confused about independent probabilities. If a fair coin is flipped 5 times, P(HHHHH) = 0.03125, but P(H | HHHH) = 0.5
I see two explainations:
1: (Same as already posted, but specific to fair coin Heads and Tails)
Because there are only two possibilities, H and T, P(H|HHHH) is the same as P(HHHHH) / (P(HHHHH) + P(HHHH... | Confused about independent probabilities. If a fair coin is flipped 5 times, P(HHHHH) = 0.03125, but
I see two explainations:
1: (Same as already posted, but specific to fair coin Heads and Tails)
Because there are only two possibilities, H and T, P(H|HHHH) is the same as P(HHHHH) / (P(HHHHH) + P(HHH |
10,902 | Confused about independent probabilities. If a fair coin is flipped 5 times, P(HHHHH) = 0.03125, but P(H | HHHH) = 0.5 | $P(H|\text{anything}) = P(H) = 0.5$ The probability of the toss of a fair coin being "heads" is half, unconditionally, no matter what other events have occurred previously or at the same time.
The $|$ conditional probability notation $P(A|B)$ primarily expresses the probability of $A$. The $B$ gives the condition which... | Confused about independent probabilities. If a fair coin is flipped 5 times, P(HHHHH) = 0.03125, but | $P(H|\text{anything}) = P(H) = 0.5$ The probability of the toss of a fair coin being "heads" is half, unconditionally, no matter what other events have occurred previously or at the same time.
The $|$ | Confused about independent probabilities. If a fair coin is flipped 5 times, P(HHHHH) = 0.03125, but P(H | HHHH) = 0.5
$P(H|\text{anything}) = P(H) = 0.5$ The probability of the toss of a fair coin being "heads" is half, unconditionally, no matter what other events have occurred previously or at the same time.
The $|$ ... | Confused about independent probabilities. If a fair coin is flipped 5 times, P(HHHHH) = 0.03125, but
$P(H|\text{anything}) = P(H) = 0.5$ The probability of the toss of a fair coin being "heads" is half, unconditionally, no matter what other events have occurred previously or at the same time.
The $|$ |
10,903 | Confused about independent probabilities. If a fair coin is flipped 5 times, P(HHHHH) = 0.03125, but P(H | HHHH) = 0.5 | It may help to think of these independent events like the individual steps used in climbing a mountain. Each step takes you only one step up the mountain. Yet, although those steps are the same in distance and effort, each subsequent step also results in you being higher up.
How is it that my last step up the mountain ... | Confused about independent probabilities. If a fair coin is flipped 5 times, P(HHHHH) = 0.03125, but | It may help to think of these independent events like the individual steps used in climbing a mountain. Each step takes you only one step up the mountain. Yet, although those steps are the same in dis | Confused about independent probabilities. If a fair coin is flipped 5 times, P(HHHHH) = 0.03125, but P(H | HHHH) = 0.5
It may help to think of these independent events like the individual steps used in climbing a mountain. Each step takes you only one step up the mountain. Yet, although those steps are the same in dist... | Confused about independent probabilities. If a fair coin is flipped 5 times, P(HHHHH) = 0.03125, but
It may help to think of these independent events like the individual steps used in climbing a mountain. Each step takes you only one step up the mountain. Yet, although those steps are the same in dis |
10,904 | Confused about independent probabilities. If a fair coin is flipped 5 times, P(HHHHH) = 0.03125, but P(H | HHHH) = 0.5 | The observations are independent, so the previous draws don’t affect the next draw. Thus P(H) = P(T) = 0.50 if you saw THTHH beforehand or H beforehand or TTTHHH beforehand. What you actually saw last does not affect the next draw. If the previous event is yet unseen, however, you are not dealing with a conditional pro... | Confused about independent probabilities. If a fair coin is flipped 5 times, P(HHHHH) = 0.03125, but | The observations are independent, so the previous draws don’t affect the next draw. Thus P(H) = P(T) = 0.50 if you saw THTHH beforehand or H beforehand or TTTHHH beforehand. What you actually saw last | Confused about independent probabilities. If a fair coin is flipped 5 times, P(HHHHH) = 0.03125, but P(H | HHHH) = 0.5
The observations are independent, so the previous draws don’t affect the next draw. Thus P(H) = P(T) = 0.50 if you saw THTHH beforehand or H beforehand or TTTHHH beforehand. What you actually saw last ... | Confused about independent probabilities. If a fair coin is flipped 5 times, P(HHHHH) = 0.03125, but
The observations are independent, so the previous draws don’t affect the next draw. Thus P(H) = P(T) = 0.50 if you saw THTHH beforehand or H beforehand or TTTHHH beforehand. What you actually saw last |
10,905 | Which distribution has its maximum uniformly distributed? | Let $F$ be the CDF of $X_i$. We know that the CDF of $Y$ is
$$G(y) = P(Y\leq y)= P(\textrm{all } X_i\leq y)= \prod_i P(X_i\leq y) = F(y)^n$$
Now, it's no loss of generality to take $a=0$, $b=1$, since we can just shift and scale the distribution of $X$ to $[0,\,1]$ and then unshift and unscale the distribution of $Y$.... | Which distribution has its maximum uniformly distributed? | Let $F$ be the CDF of $X_i$. We know that the CDF of $Y$ is
$$G(y) = P(Y\leq y)= P(\textrm{all } X_i\leq y)= \prod_i P(X_i\leq y) = F(y)^n$$
Now, it's no loss of generality to take $a=0$, $b=1$, since | Which distribution has its maximum uniformly distributed?
Let $F$ be the CDF of $X_i$. We know that the CDF of $Y$ is
$$G(y) = P(Y\leq y)= P(\textrm{all } X_i\leq y)= \prod_i P(X_i\leq y) = F(y)^n$$
Now, it's no loss of generality to take $a=0$, $b=1$, since we can just shift and scale the distribution of $X$ to $[0,\,... | Which distribution has its maximum uniformly distributed?
Let $F$ be the CDF of $X_i$. We know that the CDF of $Y$ is
$$G(y) = P(Y\leq y)= P(\textrm{all } X_i\leq y)= \prod_i P(X_i\leq y) = F(y)^n$$
Now, it's no loss of generality to take $a=0$, $b=1$, since |
10,906 | Which distribution has its maximum uniformly distributed? | $F_{X_{(n)}}(x)=[F_X(x)]^n$, so for a standard uniform you need $F_X(x)=x^{1/n}$ for $0<x<1$ (and $0$ to the left and $1$ to the right of that interval), so $f_X(x)=\frac{1}{n}x^{\frac{1}{n}-1}$ on the unit interval and $0$ elsewhere.
It's a special case of the beta. | Which distribution has its maximum uniformly distributed? | $F_{X_{(n)}}(x)=[F_X(x)]^n$, so for a standard uniform you need $F_X(x)=x^{1/n}$ for $0<x<1$ (and $0$ to the left and $1$ to the right of that interval), so $f_X(x)=\frac{1}{n}x^{\frac{1}{n}-1}$ on t | Which distribution has its maximum uniformly distributed?
$F_{X_{(n)}}(x)=[F_X(x)]^n$, so for a standard uniform you need $F_X(x)=x^{1/n}$ for $0<x<1$ (and $0$ to the left and $1$ to the right of that interval), so $f_X(x)=\frac{1}{n}x^{\frac{1}{n}-1}$ on the unit interval and $0$ elsewhere.
It's a special case of the... | Which distribution has its maximum uniformly distributed?
$F_{X_{(n)}}(x)=[F_X(x)]^n$, so for a standard uniform you need $F_X(x)=x^{1/n}$ for $0<x<1$ (and $0$ to the left and $1$ to the right of that interval), so $f_X(x)=\frac{1}{n}x^{\frac{1}{n}-1}$ on t |
10,907 | Are differences between uniformly distributed numbers uniformly distributed? | No it is not uniform
You can count the $36$ equally likely possibilities for the absolute differences
second 1 2 3 4 5 6
first
1 0 1 2 3 4 5
2 1 0 1 2 3 4
3 2 1 0 1 2 3
4 3 2 1 0 1 2
5 ... | Are differences between uniformly distributed numbers uniformly distributed? | No it is not uniform
You can count the $36$ equally likely possibilities for the absolute differences
second 1 2 3 4 5 6
first
1 0 1 2 3 | Are differences between uniformly distributed numbers uniformly distributed?
No it is not uniform
You can count the $36$ equally likely possibilities for the absolute differences
second 1 2 3 4 5 6
first
1 0 1 2 3 4 5
2 1 0 1 2 3 4
3 ... | Are differences between uniformly distributed numbers uniformly distributed?
No it is not uniform
You can count the $36$ equally likely possibilities for the absolute differences
second 1 2 3 4 5 6
first
1 0 1 2 3 |
10,908 | Are differences between uniformly distributed numbers uniformly distributed? | Using only the most basic axioms about probabilities and real numbers, one can prove a much stronger statement:
The difference of any two independent, identically distributed nonconstant random values $X-Y$ never has a discrete uniform distribution.
(An analogous statement for continuous variables is proven at Unifor... | Are differences between uniformly distributed numbers uniformly distributed? | Using only the most basic axioms about probabilities and real numbers, one can prove a much stronger statement:
The difference of any two independent, identically distributed nonconstant random value | Are differences between uniformly distributed numbers uniformly distributed?
Using only the most basic axioms about probabilities and real numbers, one can prove a much stronger statement:
The difference of any two independent, identically distributed nonconstant random values $X-Y$ never has a discrete uniform distri... | Are differences between uniformly distributed numbers uniformly distributed?
Using only the most basic axioms about probabilities and real numbers, one can prove a much stronger statement:
The difference of any two independent, identically distributed nonconstant random value |
10,909 | Are differences between uniformly distributed numbers uniformly distributed? | On an intuitive level, a random event can only be uniformly distributed if all of its outcomes are equally likely.
Is that so for the random event in question -- absolute difference between two dice rolls?
It suffices in this case to look at the extremes -- what are the biggest and smallest values this difference could... | Are differences between uniformly distributed numbers uniformly distributed? | On an intuitive level, a random event can only be uniformly distributed if all of its outcomes are equally likely.
Is that so for the random event in question -- absolute difference between two dice r | Are differences between uniformly distributed numbers uniformly distributed?
On an intuitive level, a random event can only be uniformly distributed if all of its outcomes are equally likely.
Is that so for the random event in question -- absolute difference between two dice rolls?
It suffices in this case to look at t... | Are differences between uniformly distributed numbers uniformly distributed?
On an intuitive level, a random event can only be uniformly distributed if all of its outcomes are equally likely.
Is that so for the random event in question -- absolute difference between two dice r |
10,910 | Are differences between uniformly distributed numbers uniformly distributed? | As presented by Henry, differences of uniformly distributed distributions are not uniformly distributed.
To illustrate this with simulated data, we can use a very simple R script:
barplot(table(sample(x=1:6, size=10000, replace=T)))
We see that this produces indeed a uniform distribution. Let's now have a look at the... | Are differences between uniformly distributed numbers uniformly distributed? | As presented by Henry, differences of uniformly distributed distributions are not uniformly distributed.
To illustrate this with simulated data, we can use a very simple R script:
barplot(table(sample | Are differences between uniformly distributed numbers uniformly distributed?
As presented by Henry, differences of uniformly distributed distributions are not uniformly distributed.
To illustrate this with simulated data, we can use a very simple R script:
barplot(table(sample(x=1:6, size=10000, replace=T)))
We see t... | Are differences between uniformly distributed numbers uniformly distributed?
As presented by Henry, differences of uniformly distributed distributions are not uniformly distributed.
To illustrate this with simulated data, we can use a very simple R script:
barplot(table(sample |
10,911 | Are differences between uniformly distributed numbers uniformly distributed? | Others have worked the calculations, I will give you an answer that seems more intuitive to me. You want to study the sum of two unifrom r.v. (Z = X + (-Y)), the overall distribution is the (discrete) convolution product :
$$ P(Z=z) = \sum^{\infty}_{k=-\infty} P(X=k) P(-Y = z-k) $$
This sum is rather intuitive : the pr... | Are differences between uniformly distributed numbers uniformly distributed? | Others have worked the calculations, I will give you an answer that seems more intuitive to me. You want to study the sum of two unifrom r.v. (Z = X + (-Y)), the overall distribution is the (discrete) | Are differences between uniformly distributed numbers uniformly distributed?
Others have worked the calculations, I will give you an answer that seems more intuitive to me. You want to study the sum of two unifrom r.v. (Z = X + (-Y)), the overall distribution is the (discrete) convolution product :
$$ P(Z=z) = \sum^{\i... | Are differences between uniformly distributed numbers uniformly distributed?
Others have worked the calculations, I will give you an answer that seems more intuitive to me. You want to study the sum of two unifrom r.v. (Z = X + (-Y)), the overall distribution is the (discrete) |
10,912 | Are differences between uniformly distributed numbers uniformly distributed? | If $x$ and $y$ are two consecutive dice rolls, you can visualize $|x-y| = k$ (for $k = 0, 1, 2, 3, 4, 5$) as follows where each color corresponds to a different value of $k$:
As you can easily see, the number of points for each color is not the same; therefore, the differences are not uniformly distributed. | Are differences between uniformly distributed numbers uniformly distributed? | If $x$ and $y$ are two consecutive dice rolls, you can visualize $|x-y| = k$ (for $k = 0, 1, 2, 3, 4, 5$) as follows where each color corresponds to a different value of $k$:
As you can easily see, t | Are differences between uniformly distributed numbers uniformly distributed?
If $x$ and $y$ are two consecutive dice rolls, you can visualize $|x-y| = k$ (for $k = 0, 1, 2, 3, 4, 5$) as follows where each color corresponds to a different value of $k$:
As you can easily see, the number of points for each color is not t... | Are differences between uniformly distributed numbers uniformly distributed?
If $x$ and $y$ are two consecutive dice rolls, you can visualize $|x-y| = k$ (for $k = 0, 1, 2, 3, 4, 5$) as follows where each color corresponds to a different value of $k$:
As you can easily see, t |
10,913 | Are differences between uniformly distributed numbers uniformly distributed? | Let $D_t$ denote the difference and $X$ the value of the roll, then
$P(D_t = 5) = P(X_t = 6, X_{t-1} = 1) < P((X_t, X_{t-1}) \in \{(6, 3), (5, 2)\}) < P(D_t = 3)$
So the function $P(D_t = d)$ is not constant in $d$. This means that the distribution is not uniform. | Are differences between uniformly distributed numbers uniformly distributed? | Let $D_t$ denote the difference and $X$ the value of the roll, then
$P(D_t = 5) = P(X_t = 6, X_{t-1} = 1) < P((X_t, X_{t-1}) \in \{(6, 3), (5, 2)\}) < P(D_t = 3)$
So the function $P(D_t = d)$ is not c | Are differences between uniformly distributed numbers uniformly distributed?
Let $D_t$ denote the difference and $X$ the value of the roll, then
$P(D_t = 5) = P(X_t = 6, X_{t-1} = 1) < P((X_t, X_{t-1}) \in \{(6, 3), (5, 2)\}) < P(D_t = 3)$
So the function $P(D_t = d)$ is not constant in $d$. This means that the distrib... | Are differences between uniformly distributed numbers uniformly distributed?
Let $D_t$ denote the difference and $X$ the value of the roll, then
$P(D_t = 5) = P(X_t = 6, X_{t-1} = 1) < P((X_t, X_{t-1}) \in \{(6, 3), (5, 2)\}) < P(D_t = 3)$
So the function $P(D_t = d)$ is not c |
10,914 | How do I make my neural network better at predicting sine waves? | You're using a feed-forward network; the other answers are correct that FFNNs are not great at extrapolation beyond the range of the training data.
However, since the data has a periodic quality, the problem may be amenable to modeling with an LSTM. LSTMs are a variety of neural network cell that operate on sequences, ... | How do I make my neural network better at predicting sine waves? | You're using a feed-forward network; the other answers are correct that FFNNs are not great at extrapolation beyond the range of the training data.
However, since the data has a periodic quality, the | How do I make my neural network better at predicting sine waves?
You're using a feed-forward network; the other answers are correct that FFNNs are not great at extrapolation beyond the range of the training data.
However, since the data has a periodic quality, the problem may be amenable to modeling with an LSTM. LSTMs... | How do I make my neural network better at predicting sine waves?
You're using a feed-forward network; the other answers are correct that FFNNs are not great at extrapolation beyond the range of the training data.
However, since the data has a periodic quality, the |
10,915 | How do I make my neural network better at predicting sine waves? | If what you want to do is learn simple periodic functions like this, then you could look into using Gaussian Processes. GPs allow you to enforce your domain knowledge to an extent by specifying an appropriate covariance function; in this example, since you know the data is periodic, you can choose a periodic kernel, th... | How do I make my neural network better at predicting sine waves? | If what you want to do is learn simple periodic functions like this, then you could look into using Gaussian Processes. GPs allow you to enforce your domain knowledge to an extent by specifying an app | How do I make my neural network better at predicting sine waves?
If what you want to do is learn simple periodic functions like this, then you could look into using Gaussian Processes. GPs allow you to enforce your domain knowledge to an extent by specifying an appropriate covariance function; in this example, since yo... | How do I make my neural network better at predicting sine waves?
If what you want to do is learn simple periodic functions like this, then you could look into using Gaussian Processes. GPs allow you to enforce your domain knowledge to an extent by specifying an app |
10,916 | How do I make my neural network better at predicting sine waves? | Machine learning algorithms - including neural networks - can learn to approximate arbitrary functions, but only in the interval where there is enough density of training data.
Statistics-based machine learning algorithms work best when they are performing interpolation - predicting values that are close to or in-betwe... | How do I make my neural network better at predicting sine waves? | Machine learning algorithms - including neural networks - can learn to approximate arbitrary functions, but only in the interval where there is enough density of training data.
Statistics-based machin | How do I make my neural network better at predicting sine waves?
Machine learning algorithms - including neural networks - can learn to approximate arbitrary functions, but only in the interval where there is enough density of training data.
Statistics-based machine learning algorithms work best when they are performin... | How do I make my neural network better at predicting sine waves?
Machine learning algorithms - including neural networks - can learn to approximate arbitrary functions, but only in the interval where there is enough density of training data.
Statistics-based machin |
10,917 | How do I make my neural network better at predicting sine waves? | In some cases, @Neil Slater's suggested approach of transforming your features with a periodic function will work very well, and might be the best solution. The difficulty here is that you may need to choose the period/wavelength manually (see this question).
If you want the periodicity to be embedded more deeply into ... | How do I make my neural network better at predicting sine waves? | In some cases, @Neil Slater's suggested approach of transforming your features with a periodic function will work very well, and might be the best solution. The difficulty here is that you may need to | How do I make my neural network better at predicting sine waves?
In some cases, @Neil Slater's suggested approach of transforming your features with a periodic function will work very well, and might be the best solution. The difficulty here is that you may need to choose the period/wavelength manually (see this questi... | How do I make my neural network better at predicting sine waves?
In some cases, @Neil Slater's suggested approach of transforming your features with a periodic function will work very well, and might be the best solution. The difficulty here is that you may need to |
10,918 | How do I make my neural network better at predicting sine waves? | You took a wrong approach, nothing can be done with this approach to fix the issue.
There are several different ways to address the problem. I'll suggest the most obvious one through feature engineering. Instead of plugging time as a linear feature, put it as remainder of modulus T=1. For instance, t=0.2, 1.2 and 2.2 w... | How do I make my neural network better at predicting sine waves? | You took a wrong approach, nothing can be done with this approach to fix the issue.
There are several different ways to address the problem. I'll suggest the most obvious one through feature engineeri | How do I make my neural network better at predicting sine waves?
You took a wrong approach, nothing can be done with this approach to fix the issue.
There are several different ways to address the problem. I'll suggest the most obvious one through feature engineering. Instead of plugging time as a linear feature, put i... | How do I make my neural network better at predicting sine waves?
You took a wrong approach, nothing can be done with this approach to fix the issue.
There are several different ways to address the problem. I'll suggest the most obvious one through feature engineeri |
10,919 | How do I make my neural network better at predicting sine waves? | You can train the neural network on the autoregressive principle, i.e. based on N previous values. The value of the argument is not required. Forecasting is done in the same way based on previous values, including those predicted. This works fine:
from sklearn.neural_network import MLPRegressor
import numpy as np
step... | How do I make my neural network better at predicting sine waves? | You can train the neural network on the autoregressive principle, i.e. based on N previous values. The value of the argument is not required. Forecasting is done in the same way based on previous valu | How do I make my neural network better at predicting sine waves?
You can train the neural network on the autoregressive principle, i.e. based on N previous values. The value of the argument is not required. Forecasting is done in the same way based on previous values, including those predicted. This works fine:
from sk... | How do I make my neural network better at predicting sine waves?
You can train the neural network on the autoregressive principle, i.e. based on N previous values. The value of the argument is not required. Forecasting is done in the same way based on previous valu |
10,920 | How to project a new vector onto PCA space? | Well, @Srikant already gave you the right answer since the rotation (or loadings) matrix contains eigenvectors arranged column-wise, so that you just have to multiply (using %*%) your vector or matrix of new data with e.g. prcomp(X)$rotation. Be careful, however, with any extra centering or scaling parameters that were... | How to project a new vector onto PCA space? | Well, @Srikant already gave you the right answer since the rotation (or loadings) matrix contains eigenvectors arranged column-wise, so that you just have to multiply (using %*%) your vector or matrix | How to project a new vector onto PCA space?
Well, @Srikant already gave you the right answer since the rotation (or loadings) matrix contains eigenvectors arranged column-wise, so that you just have to multiply (using %*%) your vector or matrix of new data with e.g. prcomp(X)$rotation. Be careful, however, with any ext... | How to project a new vector onto PCA space?
Well, @Srikant already gave you the right answer since the rotation (or loadings) matrix contains eigenvectors arranged column-wise, so that you just have to multiply (using %*%) your vector or matrix |
10,921 | How to project a new vector onto PCA space? | Just to add to @chl's fantastic answer (+1), you can use a more lightweight solution:
# perform principal components analysis
pca <- prcomp(data)
# project new data onto the PCA space
scale(newdata, pca$center, pca$scale) %*% pca$rotation
This is very useful if you do not want to save the entire pca object for proj... | How to project a new vector onto PCA space? | Just to add to @chl's fantastic answer (+1), you can use a more lightweight solution:
# perform principal components analysis
pca <- prcomp(data)
# project new data onto the PCA space
scale(newdata, | How to project a new vector onto PCA space?
Just to add to @chl's fantastic answer (+1), you can use a more lightweight solution:
# perform principal components analysis
pca <- prcomp(data)
# project new data onto the PCA space
scale(newdata, pca$center, pca$scale) %*% pca$rotation
This is very useful if you do not... | How to project a new vector onto PCA space?
Just to add to @chl's fantastic answer (+1), you can use a more lightweight solution:
# perform principal components analysis
pca <- prcomp(data)
# project new data onto the PCA space
scale(newdata, |
10,922 | How to project a new vector onto PCA space? | In SVD, if A is an m x n matrix, the top k rows of the right singular matrix V, is a k-dimension representation of the original columns of A where k <= n
A = UΣVt
=> At = VΣtUt = VΣUt
=> AtU = VΣUtU = VΣ -----------(because U is orthogonal)
=> AtUΣ-1=VΣΣ-1=V
So $V = A^tUΣ$-1
The rows of At or the columns of A map to ... | How to project a new vector onto PCA space? | In SVD, if A is an m x n matrix, the top k rows of the right singular matrix V, is a k-dimension representation of the original columns of A where k <= n
A = UΣVt
=> At = VΣtUt = VΣUt
=> AtU = VΣUtU | How to project a new vector onto PCA space?
In SVD, if A is an m x n matrix, the top k rows of the right singular matrix V, is a k-dimension representation of the original columns of A where k <= n
A = UΣVt
=> At = VΣtUt = VΣUt
=> AtU = VΣUtU = VΣ -----------(because U is orthogonal)
=> AtUΣ-1=VΣΣ-1=V
So $V = A^tUΣ$-... | How to project a new vector onto PCA space?
In SVD, if A is an m x n matrix, the top k rows of the right singular matrix V, is a k-dimension representation of the original columns of A where k <= n
A = UΣVt
=> At = VΣtUt = VΣUt
=> AtU = VΣUtU |
10,923 | How to project a new vector onto PCA space? | I believe that the eigenvectors (i.e., the principal components) should be arranged as columns. | How to project a new vector onto PCA space? | I believe that the eigenvectors (i.e., the principal components) should be arranged as columns. | How to project a new vector onto PCA space?
I believe that the eigenvectors (i.e., the principal components) should be arranged as columns. | How to project a new vector onto PCA space?
I believe that the eigenvectors (i.e., the principal components) should be arranged as columns. |
10,924 | Can a confounding factor hide a possible causal relationship? (as opposed to find a spurious one) | Yes
Rephrasing the opposite of a confounder: It is definitely possible that an unobserved variable yields the impression that there is no relationship, when there is one.
Confounding usually refers to a situation where an unobserved variable yields the illusion that there exists a relationship between two variables wh... | Can a confounding factor hide a possible causal relationship? (as opposed to find a spurious one) | Yes
Rephrasing the opposite of a confounder: It is definitely possible that an unobserved variable yields the impression that there is no relationship, when there is one.
Confounding usually refers t | Can a confounding factor hide a possible causal relationship? (as opposed to find a spurious one)
Yes
Rephrasing the opposite of a confounder: It is definitely possible that an unobserved variable yields the impression that there is no relationship, when there is one.
Confounding usually refers to a situation where an... | Can a confounding factor hide a possible causal relationship? (as opposed to find a spurious one)
Yes
Rephrasing the opposite of a confounder: It is definitely possible that an unobserved variable yields the impression that there is no relationship, when there is one.
Confounding usually refers t |
10,925 | Can a confounding factor hide a possible causal relationship? (as opposed to find a spurious one) | Following on existing answers, I wanted to give a concrete example. Imagine trying to figure out if the gas pedal affects the speed of a car. You observe how far the gas pedal is pressed and how fast the car is going at various times and see no correlations, so we conclude there's no causal effect between them. However... | Can a confounding factor hide a possible causal relationship? (as opposed to find a spurious one) | Following on existing answers, I wanted to give a concrete example. Imagine trying to figure out if the gas pedal affects the speed of a car. You observe how far the gas pedal is pressed and how fast | Can a confounding factor hide a possible causal relationship? (as opposed to find a spurious one)
Following on existing answers, I wanted to give a concrete example. Imagine trying to figure out if the gas pedal affects the speed of a car. You observe how far the gas pedal is pressed and how fast the car is going at va... | Can a confounding factor hide a possible causal relationship? (as opposed to find a spurious one)
Following on existing answers, I wanted to give a concrete example. Imagine trying to figure out if the gas pedal affects the speed of a car. You observe how far the gas pedal is pressed and how fast |
10,926 | Can a confounding factor hide a possible causal relationship? (as opposed to find a spurious one) | First, I think you are mixing the usage of "correlation" and "causal relationship". They are different things. To discuss the differences, and how to find "causal relationship", we need a lot of efforts.
Here I will only answer if a confounding variable can hide correlation.
Yes, here is an intuitive example (data is... | Can a confounding factor hide a possible causal relationship? (as opposed to find a spurious one) | First, I think you are mixing the usage of "correlation" and "causal relationship". They are different things. To discuss the differences, and how to find "causal relationship", we need a lot of effor | Can a confounding factor hide a possible causal relationship? (as opposed to find a spurious one)
First, I think you are mixing the usage of "correlation" and "causal relationship". They are different things. To discuss the differences, and how to find "causal relationship", we need a lot of efforts.
Here I will only ... | Can a confounding factor hide a possible causal relationship? (as opposed to find a spurious one)
First, I think you are mixing the usage of "correlation" and "causal relationship". They are different things. To discuss the differences, and how to find "causal relationship", we need a lot of effor |
10,927 | Given true positive, false negative rates, can you calculate false positive, true negative? | There is quite a bit of terminological confusion in this area. Personally, I always find it useful to come back to a confusion matrix to think about this. In a classification / screening test, you can have four different situations:
Condition: A Not A
Test says “A” True positive ... | Given true positive, false negative rates, can you calculate false positive, true negative? | There is quite a bit of terminological confusion in this area. Personally, I always find it useful to come back to a confusion matrix to think about this. In a classification / screening test, you can | Given true positive, false negative rates, can you calculate false positive, true negative?
There is quite a bit of terminological confusion in this area. Personally, I always find it useful to come back to a confusion matrix to think about this. In a classification / screening test, you can have four different situati... | Given true positive, false negative rates, can you calculate false positive, true negative?
There is quite a bit of terminological confusion in this area. Personally, I always find it useful to come back to a confusion matrix to think about this. In a classification / screening test, you can |
10,928 | Given true positive, false negative rates, can you calculate false positive, true negative? | EDIT: see the answer of Gaël Laurans, which is more accurate.
If your true positive rate is 0.25 it means that every time you call a positive, you have a probability of 0.75 of being wrong. This is your false positive rate. Similarly, every time you call a negative, you have a probability of 0.25 of being right, which ... | Given true positive, false negative rates, can you calculate false positive, true negative? | EDIT: see the answer of Gaël Laurans, which is more accurate.
If your true positive rate is 0.25 it means that every time you call a positive, you have a probability of 0.75 of being wrong. This is yo | Given true positive, false negative rates, can you calculate false positive, true negative?
EDIT: see the answer of Gaël Laurans, which is more accurate.
If your true positive rate is 0.25 it means that every time you call a positive, you have a probability of 0.75 of being wrong. This is your false positive rate. Simi... | Given true positive, false negative rates, can you calculate false positive, true negative?
EDIT: see the answer of Gaël Laurans, which is more accurate.
If your true positive rate is 0.25 it means that every time you call a positive, you have a probability of 0.75 of being wrong. This is yo |
10,929 | Given true positive, false negative rates, can you calculate false positive, true negative? | None if this makes any sense if "positive" and "negative" do not make sense for the problem at hand. I see many problems where "positive" and "negative" are arbitrary forced choices on an ordinal or continuous variable. FP, TP, sens, spec are only useful for all-or-nothing phenomena. | Given true positive, false negative rates, can you calculate false positive, true negative? | None if this makes any sense if "positive" and "negative" do not make sense for the problem at hand. I see many problems where "positive" and "negative" are arbitrary forced choices on an ordinal or | Given true positive, false negative rates, can you calculate false positive, true negative?
None if this makes any sense if "positive" and "negative" do not make sense for the problem at hand. I see many problems where "positive" and "negative" are arbitrary forced choices on an ordinal or continuous variable. FP, TP... | Given true positive, false negative rates, can you calculate false positive, true negative?
None if this makes any sense if "positive" and "negative" do not make sense for the problem at hand. I see many problems where "positive" and "negative" are arbitrary forced choices on an ordinal or |
10,930 | Given true positive, false negative rates, can you calculate false positive, true negative? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
http://www.statsdirect.com/help/default.htm#clinical_e... | Given true positive, false negative rates, can you calculate false positive, true negative? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| Given true positive, false negative rates, can you calculate false positive, true negative?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
... | Given true positive, false negative rates, can you calculate false positive, true negative?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
|
10,931 | Is the t-test miscalibrated in R? | t.test performs Welch's t-test if the argument var.equal is not explicitly set to TRUE. The distribution of the test statistic (under the null hypothesis) in Welch's t-test is only approximated by a t-distribution and this approximation gets better with increasing sample sizes. Therefore, the result of your simulation ... | Is the t-test miscalibrated in R? | t.test performs Welch's t-test if the argument var.equal is not explicitly set to TRUE. The distribution of the test statistic (under the null hypothesis) in Welch's t-test is only approximated by a t | Is the t-test miscalibrated in R?
t.test performs Welch's t-test if the argument var.equal is not explicitly set to TRUE. The distribution of the test statistic (under the null hypothesis) in Welch's t-test is only approximated by a t-distribution and this approximation gets better with increasing sample sizes. Therefo... | Is the t-test miscalibrated in R?
t.test performs Welch's t-test if the argument var.equal is not explicitly set to TRUE. The distribution of the test statistic (under the null hypothesis) in Welch's t-test is only approximated by a t |
10,932 | Is the t-test miscalibrated in R? | Following up on @statmerkur's correct answer: first, here's what you get with var.equal=TRUE
which is well calibrated.
Second, here's the distribution of estimated degrees of freedom for the Welch t-test
As you can see, the estimated degrees of freedom are typically near 8, but occasionally quite a bit smaller. When ... | Is the t-test miscalibrated in R? | Following up on @statmerkur's correct answer: first, here's what you get with var.equal=TRUE
which is well calibrated.
Second, here's the distribution of estimated degrees of freedom for the Welch t- | Is the t-test miscalibrated in R?
Following up on @statmerkur's correct answer: first, here's what you get with var.equal=TRUE
which is well calibrated.
Second, here's the distribution of estimated degrees of freedom for the Welch t-test
As you can see, the estimated degrees of freedom are typically near 8, but occas... | Is the t-test miscalibrated in R?
Following up on @statmerkur's correct answer: first, here's what you get with var.equal=TRUE
which is well calibrated.
Second, here's the distribution of estimated degrees of freedom for the Welch t- |
10,933 | Mean of a sliding window in R | Function rollapply in package zoo gets you close:
> require(zoo)
> TS <- zoo(c(4, 5, 7, 3, 9, 8))
> rollapply(TS, width = 3, by = 2, FUN = mean, align = "left")
1 3
5.333333 6.333333
It just won't compute the last value for you as it doesn't contain 3 observations. Maybe this will be sufficient for your... | Mean of a sliding window in R | Function rollapply in package zoo gets you close:
> require(zoo)
> TS <- zoo(c(4, 5, 7, 3, 9, 8))
> rollapply(TS, width = 3, by = 2, FUN = mean, align = "left")
1 3
5.333333 6.333333
I | Mean of a sliding window in R
Function rollapply in package zoo gets you close:
> require(zoo)
> TS <- zoo(c(4, 5, 7, 3, 9, 8))
> rollapply(TS, width = 3, by = 2, FUN = mean, align = "left")
1 3
5.333333 6.333333
It just won't compute the last value for you as it doesn't contain 3 observations. Maybe th... | Mean of a sliding window in R
Function rollapply in package zoo gets you close:
> require(zoo)
> TS <- zoo(c(4, 5, 7, 3, 9, 8))
> rollapply(TS, width = 3, by = 2, FUN = mean, align = "left")
1 3
5.333333 6.333333
I |
10,934 | Mean of a sliding window in R | Rollapply works great with a small dataset. However, if you are working with several million rows (genomics) it is quite slow.
The following function is super fast.
data <- c(runif(100000, min=0, max=.1),runif(100000, min=.05, max=.1),runif(10000, min=.05, max=1), runif(100000, min=0, max=.2))
slideFunct <- function(... | Mean of a sliding window in R | Rollapply works great with a small dataset. However, if you are working with several million rows (genomics) it is quite slow.
The following function is super fast.
data <- c(runif(100000, min=0, max | Mean of a sliding window in R
Rollapply works great with a small dataset. However, if you are working with several million rows (genomics) it is quite slow.
The following function is super fast.
data <- c(runif(100000, min=0, max=.1),runif(100000, min=.05, max=.1),runif(10000, min=.05, max=1), runif(100000, min=0, max... | Mean of a sliding window in R
Rollapply works great with a small dataset. However, if you are working with several million rows (genomics) it is quite slow.
The following function is super fast.
data <- c(runif(100000, min=0, max |
10,935 | Mean of a sliding window in R | This simple line of code does the thing:
((c(x,0,0) + c(0,x,0) + c(0,0,x))/3)[3:(length(x)-1)]
if x is the vector in question. | Mean of a sliding window in R | This simple line of code does the thing:
((c(x,0,0) + c(0,x,0) + c(0,0,x))/3)[3:(length(x)-1)]
if x is the vector in question. | Mean of a sliding window in R
This simple line of code does the thing:
((c(x,0,0) + c(0,x,0) + c(0,0,x))/3)[3:(length(x)-1)]
if x is the vector in question. | Mean of a sliding window in R
This simple line of code does the thing:
((c(x,0,0) + c(0,x,0) + c(0,0,x))/3)[3:(length(x)-1)]
if x is the vector in question. |
10,936 | Mean of a sliding window in R | library(zoo)
x=c(4, 5, 7, 3, 9, 8)
rollmean(x,3)
or
library(TTR)
x=c(4, 5, 7, 3, 9, 8)
SMA(x,3) | Mean of a sliding window in R | library(zoo)
x=c(4, 5, 7, 3, 9, 8)
rollmean(x,3)
or
library(TTR)
x=c(4, 5, 7, 3, 9, 8)
SMA(x,3) | Mean of a sliding window in R
library(zoo)
x=c(4, 5, 7, 3, 9, 8)
rollmean(x,3)
or
library(TTR)
x=c(4, 5, 7, 3, 9, 8)
SMA(x,3) | Mean of a sliding window in R
library(zoo)
x=c(4, 5, 7, 3, 9, 8)
rollmean(x,3)
or
library(TTR)
x=c(4, 5, 7, 3, 9, 8)
SMA(x,3) |
10,937 | Mean of a sliding window in R | shabbychef's answer in R:
slideMean<-function(x,windowsize=3,slide=2){
idx1<-seq(1,length(x),by=slide);
idx1+windowsize->idx2;
idx2[idx2>(length(x)+1)]<-length(x)+1;
c(0,cumsum(x))->cx;
return((cx[idx2]-cx[idx1])/windowsize);
}
EDIT: Indices you're looking for are just idx1... this function can be easily modified... | Mean of a sliding window in R | shabbychef's answer in R:
slideMean<-function(x,windowsize=3,slide=2){
idx1<-seq(1,length(x),by=slide);
idx1+windowsize->idx2;
idx2[idx2>(length(x)+1)]<-length(x)+1;
c(0,cumsum(x))->cx;
return((c | Mean of a sliding window in R
shabbychef's answer in R:
slideMean<-function(x,windowsize=3,slide=2){
idx1<-seq(1,length(x),by=slide);
idx1+windowsize->idx2;
idx2[idx2>(length(x)+1)]<-length(x)+1;
c(0,cumsum(x))->cx;
return((cx[idx2]-cx[idx1])/windowsize);
}
EDIT: Indices you're looking for are just idx1... this f... | Mean of a sliding window in R
shabbychef's answer in R:
slideMean<-function(x,windowsize=3,slide=2){
idx1<-seq(1,length(x),by=slide);
idx1+windowsize->idx2;
idx2[idx2>(length(x)+1)]<-length(x)+1;
c(0,cumsum(x))->cx;
return((c |
10,938 | Mean of a sliding window in R | I can do this easily in Matlab and duck while you downvote me:
%given vector x, windowsize, slide
idx1 = 1:slide:numel(x);
idx2 = min(numel(x) + 1,idx1 + windowsize); %sic on +1 here and no -1;
cx = [0;cumsum(x(:))]; %pad out a zero, perform a cumulative sum;
rv = (cx(idx2) - cx(idx1)) / windowsize; %tada! the answe... | Mean of a sliding window in R | I can do this easily in Matlab and duck while you downvote me:
%given vector x, windowsize, slide
idx1 = 1:slide:numel(x);
idx2 = min(numel(x) + 1,idx1 + windowsize); %sic on +1 here and no -1;
cx = | Mean of a sliding window in R
I can do this easily in Matlab and duck while you downvote me:
%given vector x, windowsize, slide
idx1 = 1:slide:numel(x);
idx2 = min(numel(x) + 1,idx1 + windowsize); %sic on +1 here and no -1;
cx = [0;cumsum(x(:))]; %pad out a zero, perform a cumulative sum;
rv = (cx(idx2) - cx(idx1)) ... | Mean of a sliding window in R
I can do this easily in Matlab and duck while you downvote me:
%given vector x, windowsize, slide
idx1 = 1:slide:numel(x);
idx2 = min(numel(x) + 1,idx1 + windowsize); %sic on +1 here and no -1;
cx = |
10,939 | Mean of a sliding window in R | This will get you the window means and the index of the first value of the window:
#The data
x <- c(4, 5, 7, 3, 9, 8)
#Set window size and slide
win.size <- 3
slide <- 2
#Set up the table of results
results <- data.frame(index = numeric(), win.mean = numeric())
#i indexes the first value of the window (the sill?)
i ... | Mean of a sliding window in R | This will get you the window means and the index of the first value of the window:
#The data
x <- c(4, 5, 7, 3, 9, 8)
#Set window size and slide
win.size <- 3
slide <- 2
#Set up the table of results | Mean of a sliding window in R
This will get you the window means and the index of the first value of the window:
#The data
x <- c(4, 5, 7, 3, 9, 8)
#Set window size and slide
win.size <- 3
slide <- 2
#Set up the table of results
results <- data.frame(index = numeric(), win.mean = numeric())
#i indexes the first valu... | Mean of a sliding window in R
This will get you the window means and the index of the first value of the window:
#The data
x <- c(4, 5, 7, 3, 9, 8)
#Set window size and slide
win.size <- 3
slide <- 2
#Set up the table of results |
10,940 | Mean of a sliding window in R | You are doing a convolution operation. The implementation in R uses FFT internally and you are unlikely to beat it with loops and such things.
> vals=c(4, 5, 7, 3, 9, 8, 0)
> convolve(x=vals, y=c(1, 1, 1)/3, type="filter")
[1] 5.33 5.00 6.33 6.67 5.67
If you want to extract every second result.
> tmp <- convolve(x=val... | Mean of a sliding window in R | You are doing a convolution operation. The implementation in R uses FFT internally and you are unlikely to beat it with loops and such things.
> vals=c(4, 5, 7, 3, 9, 8, 0)
> convolve(x=vals, y=c(1, 1 | Mean of a sliding window in R
You are doing a convolution operation. The implementation in R uses FFT internally and you are unlikely to beat it with loops and such things.
> vals=c(4, 5, 7, 3, 9, 8, 0)
> convolve(x=vals, y=c(1, 1, 1)/3, type="filter")
[1] 5.33 5.00 6.33 6.67 5.67
If you want to extract every second r... | Mean of a sliding window in R
You are doing a convolution operation. The implementation in R uses FFT internally and you are unlikely to beat it with loops and such things.
> vals=c(4, 5, 7, 3, 9, 8, 0)
> convolve(x=vals, y=c(1, 1 |
10,941 | Is probability theory the study of non-negative functions that integrate/sum to one? | At a purely formal level, one could call probability theory the study
of measure spaces with total measure one, but that would be like
calling number theory the study of strings of digits which terminate
-- from Terry Tao's Topics in random matrix theory.
I think this is the really fundamental thing. If we've got ... | Is probability theory the study of non-negative functions that integrate/sum to one? | At a purely formal level, one could call probability theory the study
of measure spaces with total measure one, but that would be like
calling number theory the study of strings of digits which te | Is probability theory the study of non-negative functions that integrate/sum to one?
At a purely formal level, one could call probability theory the study
of measure spaces with total measure one, but that would be like
calling number theory the study of strings of digits which terminate
-- from Terry Tao's Topics... | Is probability theory the study of non-negative functions that integrate/sum to one?
At a purely formal level, one could call probability theory the study
of measure spaces with total measure one, but that would be like
calling number theory the study of strings of digits which te |
10,942 | Is probability theory the study of non-negative functions that integrate/sum to one? | No; the Cantor distribution is just such a counterexample. It's a random variable, but it has no density. It has a distribution function, however. I would say, therefore, that probability theory is the study of càdlàg functions, inclusive of the Cantor DF, that have left limits of 0 and right limits of 1.
EDIT: This ab... | Is probability theory the study of non-negative functions that integrate/sum to one? | No; the Cantor distribution is just such a counterexample. It's a random variable, but it has no density. It has a distribution function, however. I would say, therefore, that probability theory is th | Is probability theory the study of non-negative functions that integrate/sum to one?
No; the Cantor distribution is just such a counterexample. It's a random variable, but it has no density. It has a distribution function, however. I would say, therefore, that probability theory is the study of càdlàg functions, inclus... | Is probability theory the study of non-negative functions that integrate/sum to one?
No; the Cantor distribution is just such a counterexample. It's a random variable, but it has no density. It has a distribution function, however. I would say, therefore, that probability theory is th |
10,943 | Is probability theory the study of non-negative functions that integrate/sum to one? | I'm sure you'll get good answers, but will give you a slightly different perspective here.
You may have heard mathematicians saying that physics is pretty much mathematics, or just an application of mathematics to the most basic laws of nature. Some mathematicians (many?) actually do believe that this the case. I've he... | Is probability theory the study of non-negative functions that integrate/sum to one? | I'm sure you'll get good answers, but will give you a slightly different perspective here.
You may have heard mathematicians saying that physics is pretty much mathematics, or just an application of m | Is probability theory the study of non-negative functions that integrate/sum to one?
I'm sure you'll get good answers, but will give you a slightly different perspective here.
You may have heard mathematicians saying that physics is pretty much mathematics, or just an application of mathematics to the most basic laws o... | Is probability theory the study of non-negative functions that integrate/sum to one?
I'm sure you'll get good answers, but will give you a slightly different perspective here.
You may have heard mathematicians saying that physics is pretty much mathematics, or just an application of m |
10,944 | Is probability theory the study of non-negative functions that integrate/sum to one? | Well, partially true, it lacks a second condition. Negative probabilities do not make sense. Hence, these functions have to satisfy two conditions:
Continuous distributions:
$$ \int_{\mathcal{D}}f(x) dx = 1 \quad \text{and} \quad f(x)>0 \; \forall x \in \mathcal{D}$$
Discrete distributions:
$$ \sum_{x \in \mathcal{D}}... | Is probability theory the study of non-negative functions that integrate/sum to one? | Well, partially true, it lacks a second condition. Negative probabilities do not make sense. Hence, these functions have to satisfy two conditions:
Continuous distributions:
$$ \int_{\mathcal{D}}f(x) | Is probability theory the study of non-negative functions that integrate/sum to one?
Well, partially true, it lacks a second condition. Negative probabilities do not make sense. Hence, these functions have to satisfy two conditions:
Continuous distributions:
$$ \int_{\mathcal{D}}f(x) dx = 1 \quad \text{and} \quad f(x)... | Is probability theory the study of non-negative functions that integrate/sum to one?
Well, partially true, it lacks a second condition. Negative probabilities do not make sense. Hence, these functions have to satisfy two conditions:
Continuous distributions:
$$ \int_{\mathcal{D}}f(x) |
10,945 | Is probability theory the study of non-negative functions that integrate/sum to one? | I would say no, that's not what probability theory fundamentally is, but I would say it for different reasons than the other answers.
Fundamentally, I would say, probability theory is the study of two things:
Stochastic processes, and
Bayesian inference.
Stochastic processes includes things like rolling dice, drawin... | Is probability theory the study of non-negative functions that integrate/sum to one? | I would say no, that's not what probability theory fundamentally is, but I would say it for different reasons than the other answers.
Fundamentally, I would say, probability theory is the study of two | Is probability theory the study of non-negative functions that integrate/sum to one?
I would say no, that's not what probability theory fundamentally is, but I would say it for different reasons than the other answers.
Fundamentally, I would say, probability theory is the study of two things:
Stochastic processes, an... | Is probability theory the study of non-negative functions that integrate/sum to one?
I would say no, that's not what probability theory fundamentally is, but I would say it for different reasons than the other answers.
Fundamentally, I would say, probability theory is the study of two |
10,946 | Is ArXiv popular in the statistics community? | Yes, Arxiv is popular in the statistics and the data science community.
As the world of stats and data science evolves everyday, it is important for statisticians and data scientists to keep themselves adept with the latest happenings, techniques and algorithms.
It might not be as popular as it is in the physics commun... | Is ArXiv popular in the statistics community? | Yes, Arxiv is popular in the statistics and the data science community.
As the world of stats and data science evolves everyday, it is important for statisticians and data scientists to keep themselve | Is ArXiv popular in the statistics community?
Yes, Arxiv is popular in the statistics and the data science community.
As the world of stats and data science evolves everyday, it is important for statisticians and data scientists to keep themselves adept with the latest happenings, techniques and algorithms.
It might no... | Is ArXiv popular in the statistics community?
Yes, Arxiv is popular in the statistics and the data science community.
As the world of stats and data science evolves everyday, it is important for statisticians and data scientists to keep themselve |
10,947 | Is ArXiv popular in the statistics community? | I shall give a definitive, evidence based answer. The answer is YES.
Look at Google Scholar metrics for probability and statistics, top 10 sources by h5-index:
Publication h5-index h5-median
1. Journal of Econometrics 62 93
2. The Annals of Statistics ... | Is ArXiv popular in the statistics community? | I shall give a definitive, evidence based answer. The answer is YES.
Look at Google Scholar metrics for probability and statistics, top 10 sources by h5-index:
Publication | Is ArXiv popular in the statistics community?
I shall give a definitive, evidence based answer. The answer is YES.
Look at Google Scholar metrics for probability and statistics, top 10 sources by h5-index:
Publication h5-index h5-median
1. Journal of Econometrics ... | Is ArXiv popular in the statistics community?
I shall give a definitive, evidence based answer. The answer is YES.
Look at Google Scholar metrics for probability and statistics, top 10 sources by h5-index:
Publication |
10,948 | Is ArXiv popular in the statistics community? | It is not a matter of personal opinion so let's look at some figures on terms appearing on arXiv pages (some random Google queries with few domain-specific terms):
cross validation site:arxiv.org returns
About 17,800 results
monte carlo site:arxiv.org returns
About 187,000 results
sampling site:arxiv.org returns
A... | Is ArXiv popular in the statistics community? | It is not a matter of personal opinion so let's look at some figures on terms appearing on arXiv pages (some random Google queries with few domain-specific terms):
cross validation site:arxiv.org retu | Is ArXiv popular in the statistics community?
It is not a matter of personal opinion so let's look at some figures on terms appearing on arXiv pages (some random Google queries with few domain-specific terms):
cross validation site:arxiv.org returns
About 17,800 results
monte carlo site:arxiv.org returns
About 187,0... | Is ArXiv popular in the statistics community?
It is not a matter of personal opinion so let's look at some figures on terms appearing on arXiv pages (some random Google queries with few domain-specific terms):
cross validation site:arxiv.org retu |
10,949 | Is ArXiv popular in the statistics community? | All journals published by the Institute of Mathematical Statistics (IMS) -- and that includes The Annals of Statistics (one of the very top statistics journals), The Annals of Applied Statistics, etc. -- explicitly encourage authors to put preprints on arXiv and, moreover, take care of putting postprints on arXiv too. ... | Is ArXiv popular in the statistics community? | All journals published by the Institute of Mathematical Statistics (IMS) -- and that includes The Annals of Statistics (one of the very top statistics journals), The Annals of Applied Statistics, etc. | Is ArXiv popular in the statistics community?
All journals published by the Institute of Mathematical Statistics (IMS) -- and that includes The Annals of Statistics (one of the very top statistics journals), The Annals of Applied Statistics, etc. -- explicitly encourage authors to put preprints on arXiv and, moreover, ... | Is ArXiv popular in the statistics community?
All journals published by the Institute of Mathematical Statistics (IMS) -- and that includes The Annals of Statistics (one of the very top statistics journals), The Annals of Applied Statistics, etc. |
10,950 | AIC or p-value: which one to choose for model selection? | AIC is a goodness of fit measure that favours smaller residual error in the model, but penalises for including further predictors and helps avoiding overfitting. In your second set of models model 1 (the one with the lowest AIC) may perform best when used for prediction outside your dataset. A possible explanation why ... | AIC or p-value: which one to choose for model selection? | AIC is a goodness of fit measure that favours smaller residual error in the model, but penalises for including further predictors and helps avoiding overfitting. In your second set of models model 1 ( | AIC or p-value: which one to choose for model selection?
AIC is a goodness of fit measure that favours smaller residual error in the model, but penalises for including further predictors and helps avoiding overfitting. In your second set of models model 1 (the one with the lowest AIC) may perform best when used for pre... | AIC or p-value: which one to choose for model selection?
AIC is a goodness of fit measure that favours smaller residual error in the model, but penalises for including further predictors and helps avoiding overfitting. In your second set of models model 1 ( |
10,951 | AIC or p-value: which one to choose for model selection? | Looking at individual p-values can be misleading. If you have variables that are collinear (have high correlation), you will get big p-values. This does not mean the variables are useless.
As a quick rule of thumb, selecting your model with the AIC criteria is better than looking at p-values.
One reason one might not s... | AIC or p-value: which one to choose for model selection? | Looking at individual p-values can be misleading. If you have variables that are collinear (have high correlation), you will get big p-values. This does not mean the variables are useless.
As a quick | AIC or p-value: which one to choose for model selection?
Looking at individual p-values can be misleading. If you have variables that are collinear (have high correlation), you will get big p-values. This does not mean the variables are useless.
As a quick rule of thumb, selecting your model with the AIC criteria is be... | AIC or p-value: which one to choose for model selection?
Looking at individual p-values can be misleading. If you have variables that are collinear (have high correlation), you will get big p-values. This does not mean the variables are useless.
As a quick |
10,952 | AIC or p-value: which one to choose for model selection? | AIC is motivated by the estimation of the generalization error (like Mallow's CP, BIC,...).
If you want the model for predictions, better use one of these criteria.
If you want your model for explaining a phenomenon, use p-values.
Also, see here. | AIC or p-value: which one to choose for model selection? | AIC is motivated by the estimation of the generalization error (like Mallow's CP, BIC,...).
If you want the model for predictions, better use one of these criteria.
If you want your model for explain | AIC or p-value: which one to choose for model selection?
AIC is motivated by the estimation of the generalization error (like Mallow's CP, BIC,...).
If you want the model for predictions, better use one of these criteria.
If you want your model for explaining a phenomenon, use p-values.
Also, see here. | AIC or p-value: which one to choose for model selection?
AIC is motivated by the estimation of the generalization error (like Mallow's CP, BIC,...).
If you want the model for predictions, better use one of these criteria.
If you want your model for explain |
10,953 | Given big enough sample size, a test will always show significant result unless the true effect size is exactly zero. Why? | As a simple example, suppose that I am estimating your height using some statistical mumbo jumbo.
You've always stated to others that you are 177 cm (about 5 ft 10 in).
If I were to test this hypothesis (that your height is equal to 177 cm, $h = 177$), and I could reduce the error in my measurement enough, then I could... | Given big enough sample size, a test will always show significant result unless the true effect size | As a simple example, suppose that I am estimating your height using some statistical mumbo jumbo.
You've always stated to others that you are 177 cm (about 5 ft 10 in).
If I were to test this hypothes | Given big enough sample size, a test will always show significant result unless the true effect size is exactly zero. Why?
As a simple example, suppose that I am estimating your height using some statistical mumbo jumbo.
You've always stated to others that you are 177 cm (about 5 ft 10 in).
If I were to test this hypot... | Given big enough sample size, a test will always show significant result unless the true effect size
As a simple example, suppose that I am estimating your height using some statistical mumbo jumbo.
You've always stated to others that you are 177 cm (about 5 ft 10 in).
If I were to test this hypothes |
10,954 | Given big enough sample size, a test will always show significant result unless the true effect size is exactly zero. Why? | As @Kodiologist points out, this is really about what happens for large sample sizes. For small sample sizes there's no reason why you can't have false positives or false negatives.
I think the $z$-test makes the asymptotic case clearest. Suppose we have $X_1, \dots, X_n \stackrel{\text{iid}}\sim \mathcal N(\mu, 1)$ a... | Given big enough sample size, a test will always show significant result unless the true effect size | As @Kodiologist points out, this is really about what happens for large sample sizes. For small sample sizes there's no reason why you can't have false positives or false negatives.
I think the $z$-t | Given big enough sample size, a test will always show significant result unless the true effect size is exactly zero. Why?
As @Kodiologist points out, this is really about what happens for large sample sizes. For small sample sizes there's no reason why you can't have false positives or false negatives.
I think the $z... | Given big enough sample size, a test will always show significant result unless the true effect size
As @Kodiologist points out, this is really about what happens for large sample sizes. For small sample sizes there's no reason why you can't have false positives or false negatives.
I think the $z$-t |
10,955 | Given big enough sample size, a test will always show significant result unless the true effect size is exactly zero. Why? | Arguably what they said is wrong, if for no other reason than their use of "this always happens".
I don't know if this is the crux of the confusion you're having, but I'll post it because I think many do and will get confused by this:
"$X$ happens if $n$ is large enough" does NOT mean "If $n > n_0$, then $X$."
Rather, ... | Given big enough sample size, a test will always show significant result unless the true effect size | Arguably what they said is wrong, if for no other reason than their use of "this always happens".
I don't know if this is the crux of the confusion you're having, but I'll post it because I think many | Given big enough sample size, a test will always show significant result unless the true effect size is exactly zero. Why?
Arguably what they said is wrong, if for no other reason than their use of "this always happens".
I don't know if this is the crux of the confusion you're having, but I'll post it because I think m... | Given big enough sample size, a test will always show significant result unless the true effect size
Arguably what they said is wrong, if for no other reason than their use of "this always happens".
I don't know if this is the crux of the confusion you're having, but I'll post it because I think many |
10,956 | Given big enough sample size, a test will always show significant result unless the true effect size is exactly zero. Why? | My favorite example is number of fingers by gender. The vast majority of people have 10 fingers. Some have lost fingers due to accidents. Some have extra fingers.
I don't know if men have more fingers than women (on average). All the easily available evidence suggests that men and women both have 10 fingers.
Howeve... | Given big enough sample size, a test will always show significant result unless the true effect size | My favorite example is number of fingers by gender. The vast majority of people have 10 fingers. Some have lost fingers due to accidents. Some have extra fingers.
I don't know if men have more fing | Given big enough sample size, a test will always show significant result unless the true effect size is exactly zero. Why?
My favorite example is number of fingers by gender. The vast majority of people have 10 fingers. Some have lost fingers due to accidents. Some have extra fingers.
I don't know if men have more f... | Given big enough sample size, a test will always show significant result unless the true effect size
My favorite example is number of fingers by gender. The vast majority of people have 10 fingers. Some have lost fingers due to accidents. Some have extra fingers.
I don't know if men have more fing |
10,957 | Maximum number of independent variables that can be entered into a multiple regression equation | You need to think about what you mean by a "limit".
There are limits, such as when you have more predictors than cases, you run into issues in parameter estimation (see the little R simulation at the bottom of this answer).
However, I imagine you are talking more about soft limits related to statistical power and good ... | Maximum number of independent variables that can be entered into a multiple regression equation | You need to think about what you mean by a "limit".
There are limits, such as when you have more predictors than cases, you run into issues in parameter estimation (see the little R simulation at the | Maximum number of independent variables that can be entered into a multiple regression equation
You need to think about what you mean by a "limit".
There are limits, such as when you have more predictors than cases, you run into issues in parameter estimation (see the little R simulation at the bottom of this answer).
... | Maximum number of independent variables that can be entered into a multiple regression equation
You need to think about what you mean by a "limit".
There are limits, such as when you have more predictors than cases, you run into issues in parameter estimation (see the little R simulation at the |
10,958 | Maximum number of independent variables that can be entered into a multiple regression equation | I often look at this from the standpoint of whether a model fitted with a certain number of parameters is likely to yield predictions out-of-sample that are as accurate as predictions made on the original model development sample. Calibration curves, mean squared errors of X*Beta, and indexes of predictive discriminat... | Maximum number of independent variables that can be entered into a multiple regression equation | I often look at this from the standpoint of whether a model fitted with a certain number of parameters is likely to yield predictions out-of-sample that are as accurate as predictions made on the orig | Maximum number of independent variables that can be entered into a multiple regression equation
I often look at this from the standpoint of whether a model fitted with a certain number of parameters is likely to yield predictions out-of-sample that are as accurate as predictions made on the original model development s... | Maximum number of independent variables that can be entered into a multiple regression equation
I often look at this from the standpoint of whether a model fitted with a certain number of parameters is likely to yield predictions out-of-sample that are as accurate as predictions made on the orig |
10,959 | Maximum number of independent variables that can be entered into a multiple regression equation | I would rephrase the question as follows: I have $n$ observations, and $p$ candidate predictors. Assume that the true model is a linear combination of $m$ variables among the $p$ candidate predictors. Is there an upper bound to $m$ (your limit), such that I can still identify this model? Intuitively, if $m$ is too larg... | Maximum number of independent variables that can be entered into a multiple regression equation | I would rephrase the question as follows: I have $n$ observations, and $p$ candidate predictors. Assume that the true model is a linear combination of $m$ variables among the $p$ candidate predictors. | Maximum number of independent variables that can be entered into a multiple regression equation
I would rephrase the question as follows: I have $n$ observations, and $p$ candidate predictors. Assume that the true model is a linear combination of $m$ variables among the $p$ candidate predictors. Is there an upper bound... | Maximum number of independent variables that can be entered into a multiple regression equation
I would rephrase the question as follows: I have $n$ observations, and $p$ candidate predictors. Assume that the true model is a linear combination of $m$ variables among the $p$ candidate predictors. |
10,960 | Maximum number of independent variables that can be entered into a multiple regression equation | In principle, there is no limit per se to how many predictors you can have. You can estimate 2 billion "betas" in principle. But what happens in practice is that without sufficient data, or sufficient prior information, it will not prove a very fruitful exercise. No particular parameters will be determined very well... | Maximum number of independent variables that can be entered into a multiple regression equation | In principle, there is no limit per se to how many predictors you can have. You can estimate 2 billion "betas" in principle. But what happens in practice is that without sufficient data, or sufficie | Maximum number of independent variables that can be entered into a multiple regression equation
In principle, there is no limit per se to how many predictors you can have. You can estimate 2 billion "betas" in principle. But what happens in practice is that without sufficient data, or sufficient prior information, it... | Maximum number of independent variables that can be entered into a multiple regression equation
In principle, there is no limit per se to how many predictors you can have. You can estimate 2 billion "betas" in principle. But what happens in practice is that without sufficient data, or sufficie |
10,961 | Why does mean tend be more stable in different samples than median? | The median is maximally robust to outliers, but highly susceptible to noise. If you introduce a small amount of noise to each point, it will enter the median undampened as long as the noise is small enough to not change the relative order of the points. For the mean it's the other way around. Noise is averaged out, but... | Why does mean tend be more stable in different samples than median? | The median is maximally robust to outliers, but highly susceptible to noise. If you introduce a small amount of noise to each point, it will enter the median undampened as long as the noise is small e | Why does mean tend be more stable in different samples than median?
The median is maximally robust to outliers, but highly susceptible to noise. If you introduce a small amount of noise to each point, it will enter the median undampened as long as the noise is small enough to not change the relative order of the points... | Why does mean tend be more stable in different samples than median?
The median is maximally robust to outliers, but highly susceptible to noise. If you introduce a small amount of noise to each point, it will enter the median undampened as long as the noise is small e |
10,962 | Why does mean tend be more stable in different samples than median? | As @whuber and others have said, the statement is not true in general. And if you’re willing to be more intuitive — I can’t keep up with the deep math geeks around here — you might look at other ways mean and median are stable or not. For these examples, assume an odd number of points so I can keep my descriptions cons... | Why does mean tend be more stable in different samples than median? | As @whuber and others have said, the statement is not true in general. And if you’re willing to be more intuitive — I can’t keep up with the deep math geeks around here — you might look at other ways | Why does mean tend be more stable in different samples than median?
As @whuber and others have said, the statement is not true in general. And if you’re willing to be more intuitive — I can’t keep up with the deep math geeks around here — you might look at other ways mean and median are stable or not. For these example... | Why does mean tend be more stable in different samples than median?
As @whuber and others have said, the statement is not true in general. And if you’re willing to be more intuitive — I can’t keep up with the deep math geeks around here — you might look at other ways |
10,963 | Why does mean tend be more stable in different samples than median? | Suppose you have $n$ data points from some underlying continuous distribution with mean $\mu$ and variance $\sigma^2 < \infty$. Let $f$ be the density function for this distribution and let $m$ be its median. To simplify this result further, let $\tilde{f}$ be the corresponding standardised density function, given by... | Why does mean tend be more stable in different samples than median? | Suppose you have $n$ data points from some underlying continuous distribution with mean $\mu$ and variance $\sigma^2 < \infty$. Let $f$ be the density function for this distribution and let $m$ be it | Why does mean tend be more stable in different samples than median?
Suppose you have $n$ data points from some underlying continuous distribution with mean $\mu$ and variance $\sigma^2 < \infty$. Let $f$ be the density function for this distribution and let $m$ be its median. To simplify this result further, let $\ti... | Why does mean tend be more stable in different samples than median?
Suppose you have $n$ data points from some underlying continuous distribution with mean $\mu$ and variance $\sigma^2 < \infty$. Let $f$ be the density function for this distribution and let $m$ be it |
10,964 | Why does mean tend be more stable in different samples than median? | Comment: Just to echo back your simulation, using a distribution for which SDs of means and medians have the opposite result:
Specifically, nums are now from a Laplace distribution (also called 'double exponential'), which can be simulated as the difference of two exponential distribution with the same rate (here the d... | Why does mean tend be more stable in different samples than median? | Comment: Just to echo back your simulation, using a distribution for which SDs of means and medians have the opposite result:
Specifically, nums are now from a Laplace distribution (also called 'doubl | Why does mean tend be more stable in different samples than median?
Comment: Just to echo back your simulation, using a distribution for which SDs of means and medians have the opposite result:
Specifically, nums are now from a Laplace distribution (also called 'double exponential'), which can be simulated as the diffe... | Why does mean tend be more stable in different samples than median?
Comment: Just to echo back your simulation, using a distribution for which SDs of means and medians have the opposite result:
Specifically, nums are now from a Laplace distribution (also called 'doubl |
10,965 | What can one conclude about the data when arithmetic mean is very close to geometric mean? | The arithmetic mean is related to the geometric mean through the Arithmetic-Mean-Geometric-Mean (AMGM) inequality which states that:
$$\frac{x_1+x_2+\cdots+x_n} n \geq \sqrt[n]{x_1 x_2\cdots x_n},$$
where equality is achieved iff $x_1=x_2=\cdots=x_n$. So probably your data points are all very close to each other. | What can one conclude about the data when arithmetic mean is very close to geometric mean? | The arithmetic mean is related to the geometric mean through the Arithmetic-Mean-Geometric-Mean (AMGM) inequality which states that:
$$\frac{x_1+x_2+\cdots+x_n} n \geq \sqrt[n]{x_1 x_2\cdots x_n},$$
w | What can one conclude about the data when arithmetic mean is very close to geometric mean?
The arithmetic mean is related to the geometric mean through the Arithmetic-Mean-Geometric-Mean (AMGM) inequality which states that:
$$\frac{x_1+x_2+\cdots+x_n} n \geq \sqrt[n]{x_1 x_2\cdots x_n},$$
where equality is achieved iff... | What can one conclude about the data when arithmetic mean is very close to geometric mean?
The arithmetic mean is related to the geometric mean through the Arithmetic-Mean-Geometric-Mean (AMGM) inequality which states that:
$$\frac{x_1+x_2+\cdots+x_n} n \geq \sqrt[n]{x_1 x_2\cdots x_n},$$
w |
10,966 | What can one conclude about the data when arithmetic mean is very close to geometric mean? | Elaborating on the answer of @Alex R, one way to see the AMGM inequality is as a Jensen's inequality effect. By Jensen's inequality:
$$ \log\left( \frac{1}{n} \sum_i x_i \right) \geq \frac{1}{n} \sum_i \log x_i $$
Then take the exponential of both sides:
$$ \frac{1}{n} \sum_i x_i \geq \exp\left( \frac{1}{n} \sum_i \... | What can one conclude about the data when arithmetic mean is very close to geometric mean? | Elaborating on the answer of @Alex R, one way to see the AMGM inequality is as a Jensen's inequality effect. By Jensen's inequality:
$$ \log\left( \frac{1}{n} \sum_i x_i \right) \geq \frac{1}{n} \su | What can one conclude about the data when arithmetic mean is very close to geometric mean?
Elaborating on the answer of @Alex R, one way to see the AMGM inequality is as a Jensen's inequality effect. By Jensen's inequality:
$$ \log\left( \frac{1}{n} \sum_i x_i \right) \geq \frac{1}{n} \sum_i \log x_i $$
Then take the... | What can one conclude about the data when arithmetic mean is very close to geometric mean?
Elaborating on the answer of @Alex R, one way to see the AMGM inequality is as a Jensen's inequality effect. By Jensen's inequality:
$$ \log\left( \frac{1}{n} \sum_i x_i \right) \geq \frac{1}{n} \su |
10,967 | What can one conclude about the data when arithmetic mean is very close to geometric mean? | Let's investigate the range of $x_1\le x_2 \le \cdots \le x_n$ given that their arithmetic mean (AM) is a small multiple $1+\delta$ of their geometric mean (GM) (with $\delta \ge 0$). In the question, $\delta\approx 0.001$ but we don't know $n$.
Since the ratio of these means does not change when the units of measurem... | What can one conclude about the data when arithmetic mean is very close to geometric mean? | Let's investigate the range of $x_1\le x_2 \le \cdots \le x_n$ given that their arithmetic mean (AM) is a small multiple $1+\delta$ of their geometric mean (GM) (with $\delta \ge 0$). In the question | What can one conclude about the data when arithmetic mean is very close to geometric mean?
Let's investigate the range of $x_1\le x_2 \le \cdots \le x_n$ given that their arithmetic mean (AM) is a small multiple $1+\delta$ of their geometric mean (GM) (with $\delta \ge 0$). In the question, $\delta\approx 0.001$ but w... | What can one conclude about the data when arithmetic mean is very close to geometric mean?
Let's investigate the range of $x_1\le x_2 \le \cdots \le x_n$ given that their arithmetic mean (AM) is a small multiple $1+\delta$ of their geometric mean (GM) (with $\delta \ge 0$). In the question |
10,968 | Functional principal component analysis (FPCA): what is it all about? | Exactly, as you state in the question and as @tdc puts in his answer, in case of extremely high dimensions even if the geometric properties of PCA remain valid, the covariance matrix is no longer a good estimate of the real population covariance.
There's a very interesting paper "Functional Principal Component
Analysi... | Functional principal component analysis (FPCA): what is it all about? | Exactly, as you state in the question and as @tdc puts in his answer, in case of extremely high dimensions even if the geometric properties of PCA remain valid, the covariance matrix is no longer a go | Functional principal component analysis (FPCA): what is it all about?
Exactly, as you state in the question and as @tdc puts in his answer, in case of extremely high dimensions even if the geometric properties of PCA remain valid, the covariance matrix is no longer a good estimate of the real population covariance.
Th... | Functional principal component analysis (FPCA): what is it all about?
Exactly, as you state in the question and as @tdc puts in his answer, in case of extremely high dimensions even if the geometric properties of PCA remain valid, the covariance matrix is no longer a go |
10,969 | Functional principal component analysis (FPCA): what is it all about? | I find "functional PCA" an unnecessarily confusing notion. It is not a separate thing at all, it is standard PCA applied to time series.
FPCA refers to the situations when each of the $n$ observations is a time series (i.e. a "function") observed at $t$ time points, so that the whole data matrix is of $n \times t$ size... | Functional principal component analysis (FPCA): what is it all about? | I find "functional PCA" an unnecessarily confusing notion. It is not a separate thing at all, it is standard PCA applied to time series.
FPCA refers to the situations when each of the $n$ observations | Functional principal component analysis (FPCA): what is it all about?
I find "functional PCA" an unnecessarily confusing notion. It is not a separate thing at all, it is standard PCA applied to time series.
FPCA refers to the situations when each of the $n$ observations is a time series (i.e. a "function") observed at ... | Functional principal component analysis (FPCA): what is it all about?
I find "functional PCA" an unnecessarily confusing notion. It is not a separate thing at all, it is standard PCA applied to time series.
FPCA refers to the situations when each of the $n$ observations |
10,970 | Functional principal component analysis (FPCA): what is it all about? | I worked for several years with Jim Ramsay on FDA, so I can perhaps add a few clarifications to @amoeba's answer. I think on a practical level, @amoeba is basically right. At least, that's the conclusion I finally reached after studying FDA. However, the FDA framework gives an interesting theoretical insight into why s... | Functional principal component analysis (FPCA): what is it all about? | I worked for several years with Jim Ramsay on FDA, so I can perhaps add a few clarifications to @amoeba's answer. I think on a practical level, @amoeba is basically right. At least, that's the conclus | Functional principal component analysis (FPCA): what is it all about?
I worked for several years with Jim Ramsay on FDA, so I can perhaps add a few clarifications to @amoeba's answer. I think on a practical level, @amoeba is basically right. At least, that's the conclusion I finally reached after studying FDA. However,... | Functional principal component analysis (FPCA): what is it all about?
I worked for several years with Jim Ramsay on FDA, so I can perhaps add a few clarifications to @amoeba's answer. I think on a practical level, @amoeba is basically right. At least, that's the conclus |
10,971 | Functional principal component analysis (FPCA): what is it all about? | I'm not sure about FPCA, but one thing to remember, is that in extremely high dimensions, there is a lot more "space", and points within the space start to look uniformly distributed (i.e. everything is far from everything else). At this point the covariance matrix will start to look essentially uniform, and will be ve... | Functional principal component analysis (FPCA): what is it all about? | I'm not sure about FPCA, but one thing to remember, is that in extremely high dimensions, there is a lot more "space", and points within the space start to look uniformly distributed (i.e. everything | Functional principal component analysis (FPCA): what is it all about?
I'm not sure about FPCA, but one thing to remember, is that in extremely high dimensions, there is a lot more "space", and points within the space start to look uniformly distributed (i.e. everything is far from everything else). At this point the co... | Functional principal component analysis (FPCA): what is it all about?
I'm not sure about FPCA, but one thing to remember, is that in extremely high dimensions, there is a lot more "space", and points within the space start to look uniformly distributed (i.e. everything |
10,972 | Functional principal component analysis (FPCA): what is it all about? | Wikipedia has a comprehensive introduction to the functional principal component analysis. But it is too rigorous for people who have little experience in maths or statistics.
The name of functional PCA is "misleading" in some sense since theoretically, it operates on a stochastic process composed of infinite function... | Functional principal component analysis (FPCA): what is it all about? | Wikipedia has a comprehensive introduction to the functional principal component analysis. But it is too rigorous for people who have little experience in maths or statistics.
The name of functional | Functional principal component analysis (FPCA): what is it all about?
Wikipedia has a comprehensive introduction to the functional principal component analysis. But it is too rigorous for people who have little experience in maths or statistics.
The name of functional PCA is "misleading" in some sense since theoretica... | Functional principal component analysis (FPCA): what is it all about?
Wikipedia has a comprehensive introduction to the functional principal component analysis. But it is too rigorous for people who have little experience in maths or statistics.
The name of functional |
10,973 | Alternatives to classification trees, with better predictive (e.g: CV) performance? | I think it would be worth giving a try to Random Forests (randomForest); some references were provided in response to related questions: Feature selection for “final” model when performing cross-validation in machine learning; Can CART models be made robust?. Boosting/bagging render them more stable than a single CART ... | Alternatives to classification trees, with better predictive (e.g: CV) performance? | I think it would be worth giving a try to Random Forests (randomForest); some references were provided in response to related questions: Feature selection for “final” model when performing cross-valid | Alternatives to classification trees, with better predictive (e.g: CV) performance?
I think it would be worth giving a try to Random Forests (randomForest); some references were provided in response to related questions: Feature selection for “final” model when performing cross-validation in machine learning; Can CART ... | Alternatives to classification trees, with better predictive (e.g: CV) performance?
I think it would be worth giving a try to Random Forests (randomForest); some references were provided in response to related questions: Feature selection for “final” model when performing cross-valid |
10,974 | Alternatives to classification trees, with better predictive (e.g: CV) performance? | It's important to bear in mind that there's no one algorithm that's always better than others. As stated by Wolpert and Macready, "any two algorithms are equivalent when their performance is averaged across all possible problems." (See Wikipedia for details.)
For a given application, the "best" one is generally one tha... | Alternatives to classification trees, with better predictive (e.g: CV) performance? | It's important to bear in mind that there's no one algorithm that's always better than others. As stated by Wolpert and Macready, "any two algorithms are equivalent when their performance is averaged | Alternatives to classification trees, with better predictive (e.g: CV) performance?
It's important to bear in mind that there's no one algorithm that's always better than others. As stated by Wolpert and Macready, "any two algorithms are equivalent when their performance is averaged across all possible problems." (See ... | Alternatives to classification trees, with better predictive (e.g: CV) performance?
It's important to bear in mind that there's no one algorithm that's always better than others. As stated by Wolpert and Macready, "any two algorithms are equivalent when their performance is averaged |
10,975 | Alternatives to classification trees, with better predictive (e.g: CV) performance? | For multi-class classification, support vector machines are also a good choice. I typically use the the R kernlab package for this.
See the following JSS paper for a good discussion: http://www.jstatsoft.org/v15/i09/ | Alternatives to classification trees, with better predictive (e.g: CV) performance? | For multi-class classification, support vector machines are also a good choice. I typically use the the R kernlab package for this.
See the following JSS paper for a good discussion: http://www.jstat | Alternatives to classification trees, with better predictive (e.g: CV) performance?
For multi-class classification, support vector machines are also a good choice. I typically use the the R kernlab package for this.
See the following JSS paper for a good discussion: http://www.jstatsoft.org/v15/i09/ | Alternatives to classification trees, with better predictive (e.g: CV) performance?
For multi-class classification, support vector machines are also a good choice. I typically use the the R kernlab package for this.
See the following JSS paper for a good discussion: http://www.jstat |
10,976 | Alternatives to classification trees, with better predictive (e.g: CV) performance? | As already mentioned Random Forests are a natural "upgrade" and, these days, SVM are generally the recommended technique to use.
I want to add that more often than not switching to SVM yields very disappointing results. Thing is, whilst techniques like random trees are almost trivial to use, SVM are a bit trickier.
... | Alternatives to classification trees, with better predictive (e.g: CV) performance? | As already mentioned Random Forests are a natural "upgrade" and, these days, SVM are generally the recommended technique to use.
I want to add that more often than not switching to SVM yields very d | Alternatives to classification trees, with better predictive (e.g: CV) performance?
As already mentioned Random Forests are a natural "upgrade" and, these days, SVM are generally the recommended technique to use.
I want to add that more often than not switching to SVM yields very disappointing results. Thing is, whil... | Alternatives to classification trees, with better predictive (e.g: CV) performance?
As already mentioned Random Forests are a natural "upgrade" and, these days, SVM are generally the recommended technique to use.
I want to add that more often than not switching to SVM yields very d |
10,977 | Alternatives to classification trees, with better predictive (e.g: CV) performance? | Its worth to take a look at Naive Bayes classifiers. In R you can perform Naive Bayes classification in the packages e1071 and klaR. | Alternatives to classification trees, with better predictive (e.g: CV) performance? | Its worth to take a look at Naive Bayes classifiers. In R you can perform Naive Bayes classification in the packages e1071 and klaR. | Alternatives to classification trees, with better predictive (e.g: CV) performance?
Its worth to take a look at Naive Bayes classifiers. In R you can perform Naive Bayes classification in the packages e1071 and klaR. | Alternatives to classification trees, with better predictive (e.g: CV) performance?
Its worth to take a look at Naive Bayes classifiers. In R you can perform Naive Bayes classification in the packages e1071 and klaR. |
10,978 | Is Fisher's LSD as bad as they say it is? | Fisher's LSD is indeed a series of pairwise t-tests, with each test using the mean squared error from the significant ANOVA as its pooled variance estimate (and naturally taking the associated degrees of freedom). That the ANOVA be significant is an additional constraint of this test.
It restricts family-wise error r... | Is Fisher's LSD as bad as they say it is? | Fisher's LSD is indeed a series of pairwise t-tests, with each test using the mean squared error from the significant ANOVA as its pooled variance estimate (and naturally taking the associated degrees | Is Fisher's LSD as bad as they say it is?
Fisher's LSD is indeed a series of pairwise t-tests, with each test using the mean squared error from the significant ANOVA as its pooled variance estimate (and naturally taking the associated degrees of freedom). That the ANOVA be significant is an additional constraint of thi... | Is Fisher's LSD as bad as they say it is?
Fisher's LSD is indeed a series of pairwise t-tests, with each test using the mean squared error from the significant ANOVA as its pooled variance estimate (and naturally taking the associated degrees |
10,979 | Is Fisher's LSD as bad as they say it is? | How important are multiple comparisons when dealing with 6 groups? Well... with six groups you are dealing with a maximum of $\frac{6(6-1)}{2} = 15$ possible post hoc pairwise comparisons. I will let the inestimable Randall Munroe address the importance of multiple comparisons:
And I will add that if, as in your openi... | Is Fisher's LSD as bad as they say it is? | How important are multiple comparisons when dealing with 6 groups? Well... with six groups you are dealing with a maximum of $\frac{6(6-1)}{2} = 15$ possible post hoc pairwise comparisons. I will let | Is Fisher's LSD as bad as they say it is?
How important are multiple comparisons when dealing with 6 groups? Well... with six groups you are dealing with a maximum of $\frac{6(6-1)}{2} = 15$ possible post hoc pairwise comparisons. I will let the inestimable Randall Munroe address the importance of multiple comparisons:... | Is Fisher's LSD as bad as they say it is?
How important are multiple comparisons when dealing with 6 groups? Well... with six groups you are dealing with a maximum of $\frac{6(6-1)}{2} = 15$ possible post hoc pairwise comparisons. I will let |
10,980 | Is Fisher's LSD as bad as they say it is? | Fisher's test is as bad as everyone says it is from a Neyman-Pearson point of view and if you do what your question implies---after a significant ANOVA test each individual difference. You can see this in many published papers. But, testing all the differences after an ANOVA, or any of them, is neither necessary nor re... | Is Fisher's LSD as bad as they say it is? | Fisher's test is as bad as everyone says it is from a Neyman-Pearson point of view and if you do what your question implies---after a significant ANOVA test each individual difference. You can see thi | Is Fisher's LSD as bad as they say it is?
Fisher's test is as bad as everyone says it is from a Neyman-Pearson point of view and if you do what your question implies---after a significant ANOVA test each individual difference. You can see this in many published papers. But, testing all the differences after an ANOVA, o... | Is Fisher's LSD as bad as they say it is?
Fisher's test is as bad as everyone says it is from a Neyman-Pearson point of view and if you do what your question implies---after a significant ANOVA test each individual difference. You can see thi |
10,981 | Is Fisher's LSD as bad as they say it is? | The reasoning behind Fisher's LSD can be extended to cases beyond N=3.
I'll discuss the case of four groups in detail. To keep the familywise Type-I error rate at 0.05 or below, a multiple-comparison correction factor of 3 (i.e. a per-comparison alpha of 0.05/3) suffices, although there are six post-hoc comparisons amo... | Is Fisher's LSD as bad as they say it is? | The reasoning behind Fisher's LSD can be extended to cases beyond N=3.
I'll discuss the case of four groups in detail. To keep the familywise Type-I error rate at 0.05 or below, a multiple-comparison | Is Fisher's LSD as bad as they say it is?
The reasoning behind Fisher's LSD can be extended to cases beyond N=3.
I'll discuss the case of four groups in detail. To keep the familywise Type-I error rate at 0.05 or below, a multiple-comparison correction factor of 3 (i.e. a per-comparison alpha of 0.05/3) suffices, altho... | Is Fisher's LSD as bad as they say it is?
The reasoning behind Fisher's LSD can be extended to cases beyond N=3.
I'll discuss the case of four groups in detail. To keep the familywise Type-I error rate at 0.05 or below, a multiple-comparison |
10,982 | How to present box plot with an extreme outlier? | I'd say that with data like these you really need to show results on a transformed scale. That is the first imperative and a more important issue than precisely how to draw a box plot.
But I echo Frank Harrell in urging something more informative than a minimal box plot, even with some extreme points identified. You ... | How to present box plot with an extreme outlier? | I'd say that with data like these you really need to show results on a transformed scale. That is the first imperative and a more important issue than precisely how to draw a box plot.
But I echo Fr | How to present box plot with an extreme outlier?
I'd say that with data like these you really need to show results on a transformed scale. That is the first imperative and a more important issue than precisely how to draw a box plot.
But I echo Frank Harrell in urging something more informative than a minimal box plo... | How to present box plot with an extreme outlier?
I'd say that with data like these you really need to show results on a transformed scale. That is the first imperative and a more important issue than precisely how to draw a box plot.
But I echo Fr |
10,983 | How to present box plot with an extreme outlier? | Not to take anything away from Nick's excellent answer, which I think is well worth a tick and an upvote - but I wanted to explore some possibilities.
With such heavily skew data across several orders of magnitude, plotting on a log-scale is often quite revealing; note that you can still have tick marks and tick mark l... | How to present box plot with an extreme outlier? | Not to take anything away from Nick's excellent answer, which I think is well worth a tick and an upvote - but I wanted to explore some possibilities.
With such heavily skew data across several orders | How to present box plot with an extreme outlier?
Not to take anything away from Nick's excellent answer, which I think is well worth a tick and an upvote - but I wanted to explore some possibilities.
With such heavily skew data across several orders of magnitude, plotting on a log-scale is often quite revealing; note t... | How to present box plot with an extreme outlier?
Not to take anything away from Nick's excellent answer, which I think is well worth a tick and an upvote - but I wanted to explore some possibilities.
With such heavily skew data across several orders |
10,984 | How to present box plot with an extreme outlier? | I prefer extended box plot or violin plots because they contain so much more information. I scale extended box plots to the 0.01 and 0.99 quantiles of the combined samples. See https://hbiostat.org/doc/graphscourse.pdf for details. | How to present box plot with an extreme outlier? | I prefer extended box plot or violin plots because they contain so much more information. I scale extended box plots to the 0.01 and 0.99 quantiles of the combined samples. See https://hbiostat.org/ | How to present box plot with an extreme outlier?
I prefer extended box plot or violin plots because they contain so much more information. I scale extended box plots to the 0.01 and 0.99 quantiles of the combined samples. See https://hbiostat.org/doc/graphscourse.pdf for details. | How to present box plot with an extreme outlier?
I prefer extended box plot or violin plots because they contain so much more information. I scale extended box plots to the 0.01 and 0.99 quantiles of the combined samples. See https://hbiostat.org/ |
10,985 | What are the disadvantages of using mean for missing values? | Example with normal data. Suppose the real data are a random sample of size $n=200$ from $\mathsf{Norm}(\mu=100, \sigma=15),$ but you don't know $\mu$ or $\sigma$ and seek to estimate them. In the example below I'd estimate $\mu$ by $\bar X = 100.21$ and $\sigma$ by $S = 14.5,$ Both estimates are pretty good. (Simulati... | What are the disadvantages of using mean for missing values? | Example with normal data. Suppose the real data are a random sample of size $n=200$ from $\mathsf{Norm}(\mu=100, \sigma=15),$ but you don't know $\mu$ or $\sigma$ and seek to estimate them. In the exa | What are the disadvantages of using mean for missing values?
Example with normal data. Suppose the real data are a random sample of size $n=200$ from $\mathsf{Norm}(\mu=100, \sigma=15),$ but you don't know $\mu$ or $\sigma$ and seek to estimate them. In the example below I'd estimate $\mu$ by $\bar X = 100.21$ and $\si... | What are the disadvantages of using mean for missing values?
Example with normal data. Suppose the real data are a random sample of size $n=200$ from $\mathsf{Norm}(\mu=100, \sigma=15),$ but you don't know $\mu$ or $\sigma$ and seek to estimate them. In the exa |
10,986 | What are the disadvantages of using mean for missing values? | Using the mean for missing values is not ALWAYS a bad thing. In econometrics, this is a recommended course of action in some cases provided you understand what the consequences may be and in what cases it is helpful. As you have read, replacing missing values with the mean can reduce the variance but there are other ... | What are the disadvantages of using mean for missing values? | Using the mean for missing values is not ALWAYS a bad thing. In econometrics, this is a recommended course of action in some cases provided you understand what the consequences may be and in what ca | What are the disadvantages of using mean for missing values?
Using the mean for missing values is not ALWAYS a bad thing. In econometrics, this is a recommended course of action in some cases provided you understand what the consequences may be and in what cases it is helpful. As you have read, replacing missing valu... | What are the disadvantages of using mean for missing values?
Using the mean for missing values is not ALWAYS a bad thing. In econometrics, this is a recommended course of action in some cases provided you understand what the consequences may be and in what ca |
10,987 | What are the disadvantages of using mean for missing values? | Another possible disadvantage with using the mean for missing values is that the reason the values are missing in the first place could be dependent on the missing values themselves. (This is called missing not at random.)
For example, on a health questionnaire, heavier respondents may be less willing to disclose thei... | What are the disadvantages of using mean for missing values? | Another possible disadvantage with using the mean for missing values is that the reason the values are missing in the first place could be dependent on the missing values themselves. (This is called | What are the disadvantages of using mean for missing values?
Another possible disadvantage with using the mean for missing values is that the reason the values are missing in the first place could be dependent on the missing values themselves. (This is called missing not at random.)
For example, on a health questionna... | What are the disadvantages of using mean for missing values?
Another possible disadvantage with using the mean for missing values is that the reason the values are missing in the first place could be dependent on the missing values themselves. (This is called |
10,988 | What are the disadvantages of using mean for missing values? | The problem isn’t specifically that it reduces the variance, but that it changes the variance of the dataset, making it a less accurate estimate for the variance of the actual population. More generally, it will make the dataset a less accurate reflection of the population, in many ways.
It’s helpful to consider alter... | What are the disadvantages of using mean for missing values? | The problem isn’t specifically that it reduces the variance, but that it changes the variance of the dataset, making it a less accurate estimate for the variance of the actual population. More genera | What are the disadvantages of using mean for missing values?
The problem isn’t specifically that it reduces the variance, but that it changes the variance of the dataset, making it a less accurate estimate for the variance of the actual population. More generally, it will make the dataset a less accurate reflection of... | What are the disadvantages of using mean for missing values?
The problem isn’t specifically that it reduces the variance, but that it changes the variance of the dataset, making it a less accurate estimate for the variance of the actual population. More genera |
10,989 | What are the disadvantages of using mean for missing values? | "Why is this variance reduction considered as a bad thing?"
As an oversimplified example: imagine, for a moment, that you have an extremely small economy on an island somewhere, with just 5 people. Their Annual Incomes are as follows:
Person 1: ♦10,000
Person 2: ♦10,000
Person 3: ♦12,000
Person 4: ♦13,000
Person 5: ... | What are the disadvantages of using mean for missing values? | "Why is this variance reduction considered as a bad thing?"
As an oversimplified example: imagine, for a moment, that you have an extremely small economy on an island somewhere, with just 5 people. | What are the disadvantages of using mean for missing values?
"Why is this variance reduction considered as a bad thing?"
As an oversimplified example: imagine, for a moment, that you have an extremely small economy on an island somewhere, with just 5 people. Their Annual Incomes are as follows:
Person 1: ♦10,000
Per... | What are the disadvantages of using mean for missing values?
"Why is this variance reduction considered as a bad thing?"
As an oversimplified example: imagine, for a moment, that you have an extremely small economy on an island somewhere, with just 5 people. |
10,990 | What are the disadvantages of using mean for missing values? | Yes, I like to idea of sampling from a distribution, when one has many missing values, to get a replacement value for missing value k.
My choice, however, is a distribution centered at the sample median (not mean) and with variance given here https://www.jstor.org/stable/30037287?seq=1 .
Perhaps sample from a truncated... | What are the disadvantages of using mean for missing values? | Yes, I like to idea of sampling from a distribution, when one has many missing values, to get a replacement value for missing value k.
My choice, however, is a distribution centered at the sample medi | What are the disadvantages of using mean for missing values?
Yes, I like to idea of sampling from a distribution, when one has many missing values, to get a replacement value for missing value k.
My choice, however, is a distribution centered at the sample median (not mean) and with variance given here https://www.jsto... | What are the disadvantages of using mean for missing values?
Yes, I like to idea of sampling from a distribution, when one has many missing values, to get a replacement value for missing value k.
My choice, however, is a distribution centered at the sample medi |
10,991 | Why is it so important to have principled and mathematical theories for Machine Learning? | There's no right answer to this but, maybe, "everything in moderation." While many recent improvements in machine learning, i.e., dropout, residual connections, dense connections, batch normalization, aren't rooted in particularly deep theory (most can be justified in a few paragraphs), I think there's ultimately a bot... | Why is it so important to have principled and mathematical theories for Machine Learning? | There's no right answer to this but, maybe, "everything in moderation." While many recent improvements in machine learning, i.e., dropout, residual connections, dense connections, batch normalization, | Why is it so important to have principled and mathematical theories for Machine Learning?
There's no right answer to this but, maybe, "everything in moderation." While many recent improvements in machine learning, i.e., dropout, residual connections, dense connections, batch normalization, aren't rooted in particularly... | Why is it so important to have principled and mathematical theories for Machine Learning?
There's no right answer to this but, maybe, "everything in moderation." While many recent improvements in machine learning, i.e., dropout, residual connections, dense connections, batch normalization, |
10,992 | Why is it so important to have principled and mathematical theories for Machine Learning? | The answer to this question is actually very simple. With theoretical justification behind the machine learning model we at least can prove that when some more or less realistic conditions are met, there are some guarantees of optimality for the solution. Without it, we don't have any guarantees whatsoever. Sure, you c... | Why is it so important to have principled and mathematical theories for Machine Learning? | The answer to this question is actually very simple. With theoretical justification behind the machine learning model we at least can prove that when some more or less realistic conditions are met, th | Why is it so important to have principled and mathematical theories for Machine Learning?
The answer to this question is actually very simple. With theoretical justification behind the machine learning model we at least can prove that when some more or less realistic conditions are met, there are some guarantees of opt... | Why is it so important to have principled and mathematical theories for Machine Learning?
The answer to this question is actually very simple. With theoretical justification behind the machine learning model we at least can prove that when some more or less realistic conditions are met, th |
10,993 | Why is it so important to have principled and mathematical theories for Machine Learning? | Just looking at the question: Is theoretical and principled pursue of machine learning really that important?
Define what you mean by "important". Coming from a philosophical point of view it's a fundamental distinction if you want to describe something or understand something. In a somewhat crude answer it is the diff... | Why is it so important to have principled and mathematical theories for Machine Learning? | Just looking at the question: Is theoretical and principled pursue of machine learning really that important?
Define what you mean by "important". Coming from a philosophical point of view it's a fund | Why is it so important to have principled and mathematical theories for Machine Learning?
Just looking at the question: Is theoretical and principled pursue of machine learning really that important?
Define what you mean by "important". Coming from a philosophical point of view it's a fundamental distinction if you wan... | Why is it so important to have principled and mathematical theories for Machine Learning?
Just looking at the question: Is theoretical and principled pursue of machine learning really that important?
Define what you mean by "important". Coming from a philosophical point of view it's a fund |
10,994 | Why is it so important to have principled and mathematical theories for Machine Learning? | Here's a simple example from my own work.
I fit a lot of neural nets to continuous outcomes. One determines the weights by backpropagation. Eventually, it'll converge.
Now, the top-layer activation function is identity, and my loss is squared error. Because of theory, I know that the top-level weight vector that mini... | Why is it so important to have principled and mathematical theories for Machine Learning? | Here's a simple example from my own work.
I fit a lot of neural nets to continuous outcomes. One determines the weights by backpropagation. Eventually, it'll converge.
Now, the top-layer activation f | Why is it so important to have principled and mathematical theories for Machine Learning?
Here's a simple example from my own work.
I fit a lot of neural nets to continuous outcomes. One determines the weights by backpropagation. Eventually, it'll converge.
Now, the top-layer activation function is identity, and my lo... | Why is it so important to have principled and mathematical theories for Machine Learning?
Here's a simple example from my own work.
I fit a lot of neural nets to continuous outcomes. One determines the weights by backpropagation. Eventually, it'll converge.
Now, the top-layer activation f |
10,995 | Why is it so important to have principled and mathematical theories for Machine Learning? | Humans have been able to build ships, carriages and buildings for centuries without the laws of physics. But since modern science, we have been able to take those technologies to a whole new level. A proven theory allows to make improvements in a principled manner. We would have never made it to the moon or have comput... | Why is it so important to have principled and mathematical theories for Machine Learning? | Humans have been able to build ships, carriages and buildings for centuries without the laws of physics. But since modern science, we have been able to take those technologies to a whole new level. A | Why is it so important to have principled and mathematical theories for Machine Learning?
Humans have been able to build ships, carriages and buildings for centuries without the laws of physics. But since modern science, we have been able to take those technologies to a whole new level. A proven theory allows to make i... | Why is it so important to have principled and mathematical theories for Machine Learning?
Humans have been able to build ships, carriages and buildings for centuries without the laws of physics. But since modern science, we have been able to take those technologies to a whole new level. A |
10,996 | Why is it so important to have principled and mathematical theories for Machine Learning? | Empiricism vs Theory
You wrote:
One of the biggest criticism of theory is that because its so hard to do, they usually end up studying some very restricted case or the assumptions that have to be brought essentially make the results useless.
This I think demonstrates the main divide between the two views which we can... | Why is it so important to have principled and mathematical theories for Machine Learning? | Empiricism vs Theory
You wrote:
One of the biggest criticism of theory is that because its so hard to do, they usually end up studying some very restricted case or the assumptions that have to be bro | Why is it so important to have principled and mathematical theories for Machine Learning?
Empiricism vs Theory
You wrote:
One of the biggest criticism of theory is that because its so hard to do, they usually end up studying some very restricted case or the assumptions that have to be brought essentially make the resu... | Why is it so important to have principled and mathematical theories for Machine Learning?
Empiricism vs Theory
You wrote:
One of the biggest criticism of theory is that because its so hard to do, they usually end up studying some very restricted case or the assumptions that have to be bro |
10,997 | Why is it so important to have principled and mathematical theories for Machine Learning? | You mentioned some reasons, of which the ability to interpret ML results is the most important, in my opinion. Let us say the AI driven property guard decided to shoot the neighbor's dog. It would be important to understand why it did so. If not to prevent this from happening in future, then at least to understand who'... | Why is it so important to have principled and mathematical theories for Machine Learning? | You mentioned some reasons, of which the ability to interpret ML results is the most important, in my opinion. Let us say the AI driven property guard decided to shoot the neighbor's dog. It would be | Why is it so important to have principled and mathematical theories for Machine Learning?
You mentioned some reasons, of which the ability to interpret ML results is the most important, in my opinion. Let us say the AI driven property guard decided to shoot the neighbor's dog. It would be important to understand why it... | Why is it so important to have principled and mathematical theories for Machine Learning?
You mentioned some reasons, of which the ability to interpret ML results is the most important, in my opinion. Let us say the AI driven property guard decided to shoot the neighbor's dog. It would be |
10,998 | Why is it so important to have principled and mathematical theories for Machine Learning? | I think it is very difficult for this not to be a philosophical discussion. My answer is really a rewording of good points already mentioned here (+1s for all); I just want to point to a quote from Andrew Gelman that really spoke to me as someone who trained as a computer scientist. I have the impression that many of t... | Why is it so important to have principled and mathematical theories for Machine Learning? | I think it is very difficult for this not to be a philosophical discussion. My answer is really a rewording of good points already mentioned here (+1s for all); I just want to point to a quote from An | Why is it so important to have principled and mathematical theories for Machine Learning?
I think it is very difficult for this not to be a philosophical discussion. My answer is really a rewording of good points already mentioned here (+1s for all); I just want to point to a quote from Andrew Gelman that really spoke ... | Why is it so important to have principled and mathematical theories for Machine Learning?
I think it is very difficult for this not to be a philosophical discussion. My answer is really a rewording of good points already mentioned here (+1s for all); I just want to point to a quote from An |
10,999 | How do I check if my data fits an exponential distribution? | I would do it by first estimating the only distribution parameter rate using fitdistr. This won't tell you if the distribution fits or not, so you must then use goodness of fit test. For this, you can use ks.test:
require(vcd)
require(MASS)
# data generation
ex <- rexp(10000, rate = 1.85) # generate some exponential d... | How do I check if my data fits an exponential distribution? | I would do it by first estimating the only distribution parameter rate using fitdistr. This won't tell you if the distribution fits or not, so you must then use goodness of fit test. For this, you can | How do I check if my data fits an exponential distribution?
I would do it by first estimating the only distribution parameter rate using fitdistr. This won't tell you if the distribution fits or not, so you must then use goodness of fit test. For this, you can use ks.test:
require(vcd)
require(MASS)
# data generation
... | How do I check if my data fits an exponential distribution?
I would do it by first estimating the only distribution parameter rate using fitdistr. This won't tell you if the distribution fits or not, so you must then use goodness of fit test. For this, you can |
11,000 | How do I check if my data fits an exponential distribution? | While I'd normally recommend checking exponentiality by use of diagnostic plots (such as Q-Q plots), I'll discuss tests, since people often want them:
As Tomas suggests, the Kolmogorov-Smirnov test is not suitable for testing exponentiality with an unspecified parameter.
However, if you adjust the tables for the parame... | How do I check if my data fits an exponential distribution? | While I'd normally recommend checking exponentiality by use of diagnostic plots (such as Q-Q plots), I'll discuss tests, since people often want them:
As Tomas suggests, the Kolmogorov-Smirnov test is | How do I check if my data fits an exponential distribution?
While I'd normally recommend checking exponentiality by use of diagnostic plots (such as Q-Q plots), I'll discuss tests, since people often want them:
As Tomas suggests, the Kolmogorov-Smirnov test is not suitable for testing exponentiality with an unspecified... | How do I check if my data fits an exponential distribution?
While I'd normally recommend checking exponentiality by use of diagnostic plots (such as Q-Q plots), I'll discuss tests, since people often want them:
As Tomas suggests, the Kolmogorov-Smirnov test is |
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