Related papers: Belief Propagation for Continuous State Spaces: St…
The estimation of a random vector with independent components passed through a linear transform followed by a componentwise (possibly nonlinear) output map arises in a range of applications. Approximate message passing (AMP) methods, based…
Vector approximate message passing (VAMP) is an efficient approximate inference algorithm used for generalized linear models. Although VAMP exhibits excellent performance, particularly when measurement matrices are sampled from rotationally…
High-dimensional signal recovery of standard linear regression is a key challenge in many engineering fields, such as, communications, compressed sensing, and image processing. The approximate message passing (AMP) algorithm proposed by…
Recently, M. Chertkov and V.Y. Chernyak derived an exact expression for the partition sum (normalization constant) corresponding to a graphical model, which is an expansion around the Belief Propagation solution. By adding correction terms…
The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…
In this paper, we propose a new combined message passing algorithm which allows belief propagation (BP) and mean filed (MF) applied on a same factor node, so that MF can be applied to hard constraint factors. Based on the proposed message…
This paper considers optimization problems where the objective is the sum of a function given by an expectation and a closed convex composite function, and proposes stochastic composite proximal bundle (SCPB) methods for solving it.…
We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al. We show that the message…
We develop a categorical foundation for belief propagation on factor graphs. We construct the free hypergraph category \(\Syn_\Sigma\) on a typed signature and prove its universal property, yielding compositional semantics via a unique…
It is well known that an arbitrary graphical model of statistical inference defined on a tree, i.e. on a graph without loops, is solved exactly and efficiently by an iterative Belief Propagation (BP) algorithm convergent to unique minimum…
In this paper, we compute finite sample bounds for data-driven approximations of the solution to stochastic reachability problems. Our approach uses a nonparametric technique known as kernel distribution embeddings, and provides…
We explore training Binary Neural Networks (BNNs) as a discrete variable inference problem over a factor graph. We study the behaviour of this conversion in an under-parameterized BNN setting and propose stochastic versions of Belief…
Factor graphs are important models for succinctly representing probability distributions in machine learning, coding theory, and statistical physics. Several computational problems, such as computing marginals and partition functions, arise…
Partially observable Markov decision processes (POMDPs) are a general mathematical model for sequential decision-making in stochastic environments under state uncertainty. POMDPs are often solved \textit{online}, which enables the algorithm…
The growing prevalence of nonsmooth optimization problems in machine learning has spurred significant interest in generalized smoothness assumptions. Among these, the (L0, L1)-smoothness assumption has emerged as one of the most prominent.…
We consider the problem of interactive partially observable Markov decision processes (I-POMDPs), where the agents are located at the nodes of a communication network. Specifically, we assume a certain message type for all messages.…
We propose an original particle-based implementation of the Loopy Belief Propagation (LPB) algorithm for pairwise Markov Random Fields (MRF) on a continuous state space. The algorithm constructs adaptively efficient proposal distributions…
We derive novel conditions that guarantee convergence of the Sum-Product algorithm (also known as Loopy Belief Propagation or simply Belief Propagation) to a unique fixed point, irrespective of the initial messages. The computational…
Harnessing the predictive capability of Markov process models requires propagating probability density functions (beliefs) through the model. For many existing models however, belief propagation is analytically infeasible, requiring…
We propose and analyze an approximate message passing (AMP) algorithm for the matrix tensor product model, which is a generalization of the standard spiked matrix models that allows for multiple types of pairwise observations over a…