Title :
Efficient total probability prediction via convex optimization and optimal transport
Author :
Sanggyun Kim;Diego Mesa;Todd Coleman
Author_Institution :
Dept. of Bioengineering, University of California: San Diego, La Jolla, 92037, USA
fDate :
6/1/2015 12:00:00 AM
Abstract :
In this paper, we consider state space modeling for sequential continuous estimation. We consider the one-step prediction update, which transforms our previous belief state (posterior distribution of the previous state) to new belief state (posterior distribution of the current state). We demonstrate a recursive algorithm for updating the latent state at every time by avoiding intractable integral or Gaussian approximation. The construction of the desired map is pursued through the optimal transportation theory, and we demonstrate that for the large class of log-concave state transition functions, the one-step prediction problem for continuous hidden variable is solvable through convex optimization.
Keywords :
"Hidden Markov models","Convex functions","Polynomials","Mathematical model","Optimization","Transforms","Chaos"
Conference_Titel :
Information Theory (ISIT), 2015 IEEE International Symposium on
Electronic_ISBN :
2157-8117
DOI :
10.1109/ISIT.2015.7282541