Method and apparatus for stochastic inference between multiple random variables via common representation
A method and system are herein disclosed. The method includes developing a joint latent variable model having a first variable, a second variable, and a joint latent variable representing common information between the first and second variables, generating a variational posterior of the joint latent variable model, training the variational posterior, and performing inference of the first variable from the second variable based on the variational posterior.
1. A method, comprising:
developing a joint latent variable model p θ (z)p θ (x|z)p θ (y|z) having a first variable X, a second variable Y, and a joint latent variable Z representing common information between the first and second variables,
wherein x and y represent paired data elements and 0 denotes a parameter of an underlying latent model,
wherein z is a data element,
wherein p θ (z) is a prior distribution,
wherein p θ (x|z) and p θ (y|z) are model likelihoods,
wherein the joint latent variable Z includes an amount information of both X and Y to satisfy a conditional independence X Y|Z,
wherein X represents P data (x) Y represents P data (y), and
wherein P data (x), and P data (y) are data distributions;
generating a variational posterior of the joint latent variable model;
training the variational posterior;
performing inference of the first variable from the second variable based on the variational posterior, wherein performing the inference comprises conditionally generating the first variable from the second variable; and
extracting common information between the first variable and the second variable, wherein extracting the common information comprises adding a regularization term λD(p data (x,y)q ϕ (w|x,y)∥p data (x,y)p θ (w)) to a loss function
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2. The method of claim 1 , further comprising adding local randomness to the joint latent variable model.
3. The method of claim 2 , wherein adding the local randomness comprises separating the joint latent variable into a common latent variable and a local latent variable.
4. The method of claim 2 , wherein performing the inference comprises generating a style for the first variable or the second variable.
5. The method of claim 1 , wherein training the variational posterior comprises training a decoder in the joint latent variable model with a full approximate posterior of the joint latent variable model.
6. The method of claim 5 , wherein training the variational posterior further comprises fixing parameters of the decoder and training a marginal variational posterior with the trained decoder.
7. The method of claim 1 , wherein training the variational posterior comprises training the joint latent variable model, a full approximate posterior, and a marginal variational posterior jointly using a hyperparameter.
8. A system, comprising:
at least one decoder;
at least one encoder; and
a processor configured to:
develop a joint latent variable model p θ (z) and p θ (x|z) p θ (y|z) having a first variable X, a second variable Y, and a joint latent variable Z representing common information between the first and second variables,
wherein x and y represent paired data elements and θ denotes a parameter of an underlying latent model,
wherein z is a data element,
wherein p θ (z) is a prior distribution,
wherein p θ (x|z) and p θ (y|z) are model likelihoods,
wherein the joint latent variable Z includes an amount information of both X and Y to satisfy a conditional independence X Y|Z,
wherein X represents P data (x) and Y represents P data (y), and
wherein P data (x), and P data (y) are data distributions;
generate a variational posterior of the joint latent variable model;
train the variational posterior; and
perform inference of the first variable from the second variable based on the variational posterior, by conditionally generating the first variable from the second variable; and
extract common information between the first variable and the second variable, by adding a regularization term λD(p data (x,y)q ϕ (w|x,y)∥p data (x,y)p θ (w)) to a loss function
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9. The system of claim 8 , wherein the processor is further configured to add local randomness to the joint latent variable model.
10. The system of claim 9 , wherein the processor is further configured to add the local randomness by separating the joint latent variable into a common latent variable and a local latent variable.
11. The system of claim 9 , wherein the processor is further configured to perform the inference by generating a style for the first variable or the second variable.
12. The system of claim 8 , wherein the processor is further configured to train the variational posterior by training the at least one decoder in the joint latent variable model with a full approximate posterior of the joint latent variable model.
13. The system of claim 12 , wherein the processor is further configured to train the variational posterior by fixing parameters of the at least one decoder and training a marginal variational posterior with the trained at least one decoder.
14. The system of claim 8 , wherein the processor is further configured to train the variational posterior by training the joint latent variable model, a full approximate posterior, and a marginal variational posterior jointly using a hyperparameter.