How to find a transformation of a random process X so it has distribution of a reference process Y?
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I was thinking to use GAN or KL Divergence as a loss function to do the following:
Let $X sim D$ where $D$ is some distribution. Assume we know a reference asymptotic distribution $Y sim D_2$.
We would like to find a polynomial transformation of $X to f(X)$ such that $f(X) sim Y sim D_2$.
For the case of $Y sim D_2=N(0,1)$ the network potentially will find the z-score normalization or some mapping $f$, so $f(x) sim Y$.
I would like to get advice how to formalize this problem in order to be able to solve it using Neural Network.
machine-learning deep-learning statistics
asked yesterday
0x900x90
1237
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|
show 1 more comment
$begingroup$
I was thinking to use GAN or KL Divergence as a loss function to do the following:
Let $X sim D$ where $D$ is some distribution. Assume we know a reference asymptotic distribution $Y sim D_2$.
We would like to find a polynomial transformation of $X to f(X)$ such that $f(X) sim Y sim D_2$.
For the case of $Y sim D_2=N(0,1)$ the network potentially will find the z-score normalization or some mapping $f$, so $f(x) sim Y$.
I would like to get advice how to formalize this problem in order to be able to solve it using Neural Network.
machine-learning deep-learning statistics
asked yesterday
0x900x90
1237
$endgroup$
$begingroup$
What is the "polynomial" constraint for? Finite sum of polynomials? Generally, Neural networks can be approximated with infinite sum of polynomials.
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– Esmailian
13 hours ago
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@Esmailian, I would like the "network" to find a point-wise transformation, $f$, such that ${f(x) | forall x in X}$ will have the same distribution as $Y$. Yes I think we can assume a maximal degree for the polynomial (e.g. N=10) What do you mean by:Generally, Neural networks can be approximated with infinite sum of polynomials.
$endgroup$
– 0x90
12 hours ago
1
$begingroup$
Take a look at these kind of transformations: QuantileTransformer.
$endgroup$
– Esmailian
12 hours ago
$begingroup$
@Esmailian this is great for the normal distribution case. However, I wanted to approach it by minimizing the loss function of the KL div between two sequences.
$endgroup$
– 0x90
12 hours ago
$begingroup$
I meant you cannot place an upper bound on the number of polynomials when you use Neural Networks with non-linear activation functions to represent $f$.
$endgroup$
– Esmailian
12 hours ago
|
show 1 more comment
$begingroup$
I was thinking to use GAN or KL Divergence as a loss function to do the following:
Let $X sim D$ where $D$ is some distribution. Assume we know a reference asymptotic distribution $Y sim D_2$.
We would like to find a polynomial transformation of $X to f(X)$ such that $f(X) sim Y sim D_2$.
For the case of $Y sim D_2=N(0,1)$ the network potentially will find the z-score normalization or some mapping $f$, so $f(x) sim Y$.
I would like to get advice how to formalize this problem in order to be able to solve it using Neural Network.
machine-learning deep-learning statistics
asked yesterday
0x900x90
1237
$endgroup$
I was thinking to use GAN or KL Divergence as a loss function to do the following:
Let $X sim D$ where $D$ is some distribution. Assume we know a reference asymptotic distribution $Y sim D_2$.
We would like to find a polynomial transformation of $X to f(X)$ such that $f(X) sim Y sim D_2$.
For the case of $Y sim D_2=N(0,1)$ the network potentially will find the z-score normalization or some mapping $f$, so $f(x) sim Y$.
I would like to get advice how to formalize this problem in order to be able to solve it using Neural Network.
machine-learning deep-learning statistics
machine-learning deep-learning statistics
asked yesterday
0x900x90
1237
asked yesterday
0x900x90
1237
edited 1 min ago
0x90
asked yesterday
0x900x90
1237
asked yesterday
0x900x90
1237
asked yesterday
0x900x90
1237
1237
$begingroup$
What is the "polynomial" constraint for? Finite sum of polynomials? Generally, Neural networks can be approximated with infinite sum of polynomials.
$endgroup$
– Esmailian
13 hours ago
$begingroup$
@Esmailian, I would like the "network" to find a point-wise transformation, $f$, such that ${f(x) | forall x in X}$ will have the same distribution as $Y$. Yes I think we can assume a maximal degree for the polynomial (e.g. N=10) What do you mean by:Generally, Neural networks can be approximated with infinite sum of polynomials.
$endgroup$
– 0x90
12 hours ago
1
$begingroup$
Take a look at these kind of transformations: QuantileTransformer.
$endgroup$
– Esmailian
12 hours ago
$begingroup$
@Esmailian this is great for the normal distribution case. However, I wanted to approach it by minimizing the loss function of the KL div between two sequences.
$endgroup$
– 0x90
12 hours ago
$begingroup$
I meant you cannot place an upper bound on the number of polynomials when you use Neural Networks with non-linear activation functions to represent $f$.
$endgroup$
– Esmailian
12 hours ago
|
show 1 more comment
$begingroup$
What is the "polynomial" constraint for? Finite sum of polynomials? Generally, Neural networks can be approximated with infinite sum of polynomials.
$endgroup$
– Esmailian
13 hours ago
$begingroup$
@Esmailian, I would like the "network" to find a point-wise transformation, $f$, such that ${f(x) | forall x in X}$ will have the same distribution as $Y$. Yes I think we can assume a maximal degree for the polynomial (e.g. N=10) What do you mean by:Generally, Neural networks can be approximated with infinite sum of polynomials.
$endgroup$
– 0x90
12 hours ago
1
$begingroup$
Take a look at these kind of transformations: QuantileTransformer.
$endgroup$
– Esmailian
12 hours ago
$begingroup$
@Esmailian this is great for the normal distribution case. However, I wanted to approach it by minimizing the loss function of the KL div between two sequences.
$endgroup$
– 0x90
12 hours ago
$begingroup$
I meant you cannot place an upper bound on the number of polynomials when you use Neural Networks with non-linear activation functions to represent $f$.
$endgroup$
– Esmailian
12 hours ago
$begingroup$
What is the "polynomial" constraint for? Finite sum of polynomials? Generally, Neural networks can be approximated with infinite sum of polynomials.
$endgroup$
– Esmailian
13 hours ago
$begingroup$
What is the "polynomial" constraint for? Finite sum of polynomials? Generally, Neural networks can be approximated with infinite sum of polynomials.
$endgroup$
– Esmailian
13 hours ago
$begingroup$
@Esmailian, I would like the "network" to find a point-wise transformation, $f$, such that ${f(x) | forall x in X}$ will have the same distribution as $Y$. Yes I think we can assume a maximal degree for the polynomial (e.g. N=10) What do you mean by:
Generally, Neural networks can be approximated with infinite sum of polynomials.$endgroup$
– 0x90
12 hours ago
$begingroup$
@Esmailian, I would like the "network" to find a point-wise transformation, $f$, such that ${f(x) | forall x in X}$ will have the same distribution as $Y$. Yes I think we can assume a maximal degree for the polynomial (e.g. N=10) What do you mean by:
Generally, Neural networks can be approximated with infinite sum of polynomials.$endgroup$
– 0x90
12 hours ago
1
1
$begingroup$
Take a look at these kind of transformations: QuantileTransformer.
$endgroup$
– Esmailian
12 hours ago
$begingroup$
Take a look at these kind of transformations: QuantileTransformer.
$endgroup$
– Esmailian
12 hours ago
$begingroup$
@Esmailian this is great for the normal distribution case. However, I wanted to approach it by minimizing the loss function of the KL div between two sequences.
$endgroup$
– 0x90
12 hours ago
$begingroup$
@Esmailian this is great for the normal distribution case. However, I wanted to approach it by minimizing the loss function of the KL div between two sequences.
$endgroup$
– 0x90
12 hours ago
$begingroup$
I meant you cannot place an upper bound on the number of polynomials when you use Neural Networks with non-linear activation functions to represent $f$.
$endgroup$
– Esmailian
12 hours ago
$begingroup$
I meant you cannot place an upper bound on the number of polynomials when you use Neural Networks with non-linear activation functions to represent $f$.
$endgroup$
– Esmailian
12 hours ago
|
show 1 more comment
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$begingroup$
What is the "polynomial" constraint for? Finite sum of polynomials? Generally, Neural networks can be approximated with infinite sum of polynomials.
$endgroup$
– Esmailian
13 hours ago
$begingroup$
@Esmailian, I would like the "network" to find a point-wise transformation, $f$, such that ${f(x) | forall x in X}$ will have the same distribution as $Y$. Yes I think we can assume a maximal degree for the polynomial (e.g. N=10) What do you mean by:
Generally, Neural networks can be approximated with infinite sum of polynomials.$endgroup$
– 0x90
12 hours ago
1
$begingroup$
Take a look at these kind of transformations: QuantileTransformer.
$endgroup$
– Esmailian
12 hours ago
$begingroup$
@Esmailian this is great for the normal distribution case. However, I wanted to approach it by minimizing the loss function of the KL div between two sequences.
$endgroup$
– 0x90
12 hours ago
$begingroup$
I meant you cannot place an upper bound on the number of polynomials when you use Neural Networks with non-linear activation functions to represent $f$.
$endgroup$
– Esmailian
12 hours ago