Title: Sparsity Promotion Using the Choquet Integral

Speaker: Andres Mendez-Vazquez, CISE, UF

Time: 3:00-4:00PM, Friday, April 20

Place: CSE 404

Abstract:

In this paper, we present a novel algorithm for
learning fuzzy measures for Choquet integration. There are two
novel aspects of the algorithm: it seeks to explicitly reduce the
number of nonzero parameters in the measure to eliminate
noninformative or useless information sources and it uses a
Bayesian model for parameter estimation which has not been
previously applied to the fuzzy measure learning problem. The
method uses a hierarchical model that implements a sparsity
promotion algorithm through a Gibbs sampler. This approach
builds on the methods proposed by Figueiredo et. al which
uses Expectation Maximization (EM) to maximize the Least
Absolute Shrinkage and Selection Operator (LASSO) criterion
under a distribution that promotes sparsity. Additional constraints
are needed to satisfy the requirements of fuzzy measures.
Figueiredo's algorithm does not have a mechanism for imposing
these constraints. The constraints are imposed by sequentially
exploring the lattice tree of the power set and requiring that
each fuzzy measure value assigned to a set lies in the domain
of a truncated Gaussian determined by the fuzzy measures of
supersets of the set under consideration.