A scalable framework to transform samples from one continuous distribution to another
- Resource Type
- Conference
- Authors
- Mesa, Diego; Kim, Sanggyun; Coleman, Todd
- Source
- 2015 IEEE International Symposium on Information Theory (ISIT) Information Theory (ISIT), 2015 IEEE International Symposium on. :676-680 Jun, 2015
- Subject
- Communication, Networking and Broadcast Technologies
Signal Processing and Analysis
Bayes methods
Approximation methods
Convex functions
Indexes
Uncertainty
Convergence
Logistics
machine learning
KL divergence
optimal transport
Bayesian inference
convex optimization
- Language
- ISSN
- 2157-8095
2157-8117
We present a framework to transform a sample from one continuous distribution ℙ to another ℚ. Our previous work considered the special case of Bayesian inference where ℙ is the prior and ℚ is the posterior, showing that this can be solved with convex optimization under appropriate conditions. Here, our contribution is two fold: (i) we consider the more general case of arbitrary ℙ and ℚ and show using optimal transport theory and KL divergence minimization that convexity holds provided that ℚ has a log-concave density; (ii) we develop a largescale distributed solver. With this general framework finding the optimal Bayesian map is done through a series of MAP estimation problems. Interesting applications are also presented.