Related papers: On MAP Inference by MWSS on Perfect Graphs
Graph Neural Networks (GNN) exhibit superior performance in graph representation learning, but their inference cost can be high, due to an aggregation operation that can require a memory fetch for a very large number of nodes. This…
In this paper we describe how MAP inference can be used to sample efficiently from Gibbs distributions. Specifically, we provide means for drawing either approximate or unbiased samples from Gibbs' distributions by introducing low…
We present a new approach to Bayesian inference that entirely avoids Markov chain simulation, by constructing a map that pushes forward the prior measure to the posterior measure. Existence and uniqueness of a suitable measure-preserving…
Learning the structure of Markov random fields (MRFs) plays an important role in multivariate analysis. The importance has been increasing with the recent rise of statistical relational models since the MRF serves as a building block of…
Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. In this paper, we propose a novel framework for learning/estimating graphs from data. The proposed framework includes (i)…
The theoretical models providing mathematical abstractions for several significant optimization problems in machine learning, combinatorial optimization, computer vision and statistical physics have intrinsic similarities. We propose a…
We consider learning a sparse pairwise Markov Random Field (MRF) with continuous-valued variables from i.i.d samples. We adapt the algorithm of Vuffray et al. (2019) to this setting and provide finite-sample analysis revealing sample…
Parameter estimation in Markov random fields (MRFs) is a difficult task, in which inference over the network is run in the inner loop of a gradient descent procedure. Replacing exact inference with approximate methods such as loopy belief…
We present an information-based uncertainty quantification method for general Markov Random Fields. Markov Random Fields (MRF) are structured, probabilistic graphical models over undirected graphs, and provide a fundamental unifying…
In the Maximum Weight Independent Set of Rectangles problem (MWISR) we are given a weighted set of $n$ axis-parallel rectangles in the plane. The task is to find a subset of pairwise non-overlapping rectangles with the maximum possible…
We consider MAP estimators for structured prediction with exponential family models. In particular, we concentrate on the case that efficient algorithms for uniform sampling from the output space exist. We show that under this assumption…
Let n denote the number of variables and m the number of equations in a sparse polynomial system over the binary field. We study the inconsistency probability of randomly generated sparse polynomial systems over the binary field, where each…
The Markov chain random field (MCRF) model/theory provides a non-linear spatial Bayesian updating solution at the neighborhood nearest data level for simulating categorical spatial variables. In the MCRF solution, the spatial dependencies…
This paper addresses robust waveform design for multiple-input-multiple-output (MIMO) radar detection. A probabilistic model is proposed to describe the target uncertainty. Considering that waveform design based on maximizing the…
The maximum independent set problem is one of the most important problems in graph algorithms and has been extensively studied in the line of research on the worst-case analysis of exact algorithms for NP-hard problems. In the weighted…
The problem of finding the maximum-weight, planar subgraph of a finite, simple graph with nonnegative real edge weights is well known in industrial and electrical engineering, systems biology, sociology and finance. As the problem is known…
This work introduces the IB-score, a family of independence-based score functions for robust learning of Markov networks independence structures. Markov networks are a widely used graphical representation of probability distributions, with…
This paper introduces new efficient algorithms for two problems: sampling conditional on vertex degrees in unweighted graphs, and sampling conditional on vertex strengths in weighted graphs. The algorithms can sample conditional on the…
Probabilistic graphical models, such as Markov random fields (MRFs), are useful for describing high-dimensional distributions in terms of local dependence structures. The probabilistic inference is a fundamental problem related to graphical…
Purpose of Review Planning collision-free paths for multiple robots is important for real-world multi-robot systems and has been studied as an optimization problem on graphs, called Multi-Agent Path Finding (MAPF). This review surveys…