Related papers: Using random graphs to sample repulsive Gibbs poin…
Given a locally finite graph $\Gamma$, an amenable subgroup $G$ of graph automorphisms acting freely and almost transitively on its vertices, and a $G$-invariant activity function $\lambda$, consider the free energy $f_G(\Gamma,\lambda)$ of…
Can we use machine learning to compress graph data? The absence of ordering in graphs poses a significant challenge to conventional compression algorithms, limiting their attainable gains as well as their ability to discover relevant…
Given a graphical model (GM), computing its partition function is the most essential inference task, but it is computationally intractable in general. To address the issue, iterative approximation algorithms exploring certain local…
Gibbs sampling from continuous real-valued functions is a challenging problem of interest in machine learning. Here we leverage quantum Fourier transforms to build a quantum algorithm for this task when the function is periodic. We use the…
Given a Gibbs point process $\P^{\Psi}$ on $\R^d$ having a weak enough potential $\Psi$, we consider the random measures $\mu_\la := \sum_{x \in \P^{\Psi} \cap Q_\la} \xi(x, \P^{\Psi} \cap Q_\la) \delta_{x/\la^{1/d}}$, where $Q_{\la} :=…
Gaussian process (GP) regression is a non-parametric, Bayesian framework to approximate complex models. Standard GP regression can lead to an unbounded model in which some points can take infeasible values. We introduce a new GP method that…
Given a Poisson process on a bounded interval, its random geometric graph is the graph whose vertices are the points of the Poisson process and edges exist between two points if and only if their distance is less than a fixed given…
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…
For a given homogeneous Poisson point process in $\mathbb{R}^d$ two points are connected by an edge if their distance is bounded by a prescribed distance parameter. The behaviour of the resulting random graph, the Gilbert graph or random…
Gaussian processes (GPs) are ubiquitous tools for modeling and predicting continuous processes in physical and engineering sciences. This is partly due to the fact that one may employ a Gaussian process as an interpolator while facilitating…
We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to…
In an effort to effectively model observed patterns in the spatial configuration of individuals of multiple species in nature, we introduce the saturated pairwise interaction Gibbs point process. Its main strength lies in its ability to…
Statistical physics models with hard constraints, such as the discrete hard-core gas model (random independent sets in a graph), are inherently combinatorial and present the discrete mathematician with a relatively comfortable setting for…
We study the problem of deterministic approximate counting of matchings and independent sets in graphs of bounded connective constant. More generally, we consider the problem of evaluating the partition functions of the monomer-dimer model…
We develop the partitioning technique for quantum discrete systems. The graph consists of several subgraphs: a central graph and several branch graphs, with each branch graph being rooted by an individual node on the central one. We show…
Identifying ordered structures hidden in the packings of particles is a common scientific question in multiple fields. In this work, we investigate the dynamical organizations of a large number of initially randomly packed repulsive…
Mat\'ern's hard-core processes are valuable point process models in spatial statistics. In order to extend their field of application, Mat\'ern's original models are generalized here, both as point processes and particle processes. The…
Graphical models for finite-dimensional spin glasses and real-world combinatorial optimization and satisfaction problems usually have an abundant number of short loops. The cluster variation method and its extension, the region graph…
Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…
Efficient sampling from a classical Gibbs distribution is an important computational problem with applications ranging from statistical physics over Monte Carlo and optimization algorithms to machine learning. We introduce a family of…