When binary linear error-correcting codes are used over symmetric channels, a relaxed
version of the maximum likelihood decoding problem can be stated as a linear program …

We consider the problem of high-dimensional Gaussian graphical model selection. We
identify a set of graphs for which an efficient estimation algorithm exists, and this algorithm is …

It has recently been observed that the permanent of a nonnegative square matrix, ie, of a
square matrix containing only nonnegative real entries, can very well be approximated by …

We present a combinatorial characterization of the Bethe entropy function of a factor graph,
such a characterization being in contrast to the original, analytical, definition of this function …

Abstract Gaussian Graphical Models (GGMs) have wide-ranging applications in machine
learning and the natural and social sciences. In most of the settings in which they are …

Gaussian belief propagation (GaBP) is an iterative algorithm for computing the mean (and
variances) of a multivariate Gaussian distribution, or equivalently, the minimum of a …

The max-product algorithm, a local message-passing scheme that attempts to compute the
most probable assignment (MAP) of a given probability distribution, has been successfully …

In this thesis, we leverage finite graph covers to analyze the SPA and the Bethe partition
function for both S-FGs and DE-FGs. There are two main contributions in this thesis. The first …

Computing the partition function of an arbitrary graphical model is generally intractable. As a
result, approximate inference techniques such as loopy belief propagation and expectation …

We consider the problem of high-dimensional Gaussian graphical model selection. We
identify a set of graphs for which an efficient estimation algorithm exists, and this algorithm is …