Related papers: Approximate inference on planar graphs using Loop …
In the context of inference with expectation constraints, we propose an approach based on the "loopy belief propagation" algorithm LBP, as a surrogate to an exact Markov Random Field MRF modelling. A prior information composed of…
Gaussian belief propagation (GBP) is a recursive computation method that is widely used in inference for computing marginal distributions efficiently. Depending on how the factorization of the underlying joint Gaussian distribution is…
We study approximations of the partition function of dense graphical models. Partition functions of graphical models play a fundamental role is statistical physics, in statistics and in machine learning. Two of the main methods for…
In recent years, researchers in decision analysis and artificial intelligence (AI) have used Bayesian belief networks to build models of expert opinion. Using standard methods drawn from the theory of computational complexity, workers in…
Approximate Bayesian computation (ABC) or likelihood-free inference algorithms are used to find approximations to posterior distributions without making explicit use of the likelihood function, depending instead on simulation of sample data…
Graph-based approximation methods are of growing interest in many areas, including transportation, biological and chemical networks, financial models, image processing, network flows, and more. In these applications, often a basis for the…
Partition of unity methods (PUMs) on graphs are simple and highly adaptive auxiliary tools for graph signal processing. Based on a greedy-type metric clustering and augmentation scheme, we show how a partition of unity can be generated in…
We study the expressibility and learnability of convex optimization solution functions and their multi-layer architectural extension. The main results are: \emph{(1)} the class of solution functions of linear programming (LP) and quadratic…
Model counting of Disjunctive Normal Form (DNF) formulas is a critical problem in applications such as probabilistic inference and network reliability. For example, it is often used for query evaluation in probabilistic databases. Due to…
Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…
Variational approximation, such as mean-field (MF) and tree-reweighted (TRW), provide a computationally efficient approximation of the log-partition function for a generic graphical model. TRW provably provides an upper bound, but the…
Many models for undirected graphs are based on factorizing the graph's adjacency matrix; these models find a vector representation of each node such that the predicted probability of a link between two nodes increases with the similarity…
An emerging trend in approximate counting is to show that certain `low-temperature' problems are easy on typical instances, despite worst-case hardness results. For the class of regular graphs one usually shows that expansion can be…
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…
In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…
We give an $\alpha(1+\epsilon)$-approximation algorithm for solving covering LPs, assuming the presence of a $(1/\alpha)$-approximation algorithm for a certain optimization problem. Our algorithm is based on a simple modification of the…
We present a novel inference algorithm for arbitrary, binary, undirected graphs. Unlike loopy belief propagation, which iterates fixed point equations, we directly descend on the Bethe free energy. The algorithm consists of two phases,…
We introduce collapsed compilation, a novel approximate inference algorithm for discrete probabilistic graphical models. It is a collapsed sampling algorithm that incrementally selects which variable to sample next based on the partial…
We consider the problem of approximating the partition function of the hard-core model on planar graphs of degree at most 4. We show that when the activity lambda is sufficiently large, there is no fully polynomial randomised approximation…
A number of problems in statistical physics and computer science can be expressed as the computation of marginal probabilities over a Markov random field. Belief propagation, an iterative message-passing algorithm, computes exactly such…