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We consider spin systems on the integer lattice graph $\mathbb{Z}^d$ with nearest-neighbor interactions. We develop a combinatorial framework for establishing that exponential decay with distance of spin correlations, specifically the…
We study the following problem: given an integer $k \ge 3$ and a simple graph $G$, sample a connected induced $k$-node subgraph of $G$ uniformly at random. This is a fundamental graph mining primitive with applications in social network…
We show that the Glauber dynamics on proper 9-colourings of the triangular lattice is rapidly mixing, which allows for efficient sampling. Consequently, there is a fully polynomial randomised approximation scheme (FPRAS) for counting proper…
Gibbs sampling on factor graphs is a widely used inference technique, which often produces good empirical results. Theoretical guarantees for its performance are weak: even for tree structured graphs, the mixing time of Gibbs may be…
Many applications in the field of statistics require Markov chain Monte Carlo methods. Determining appropriate starting values and run lengths can be both analytically and empirically challenging. A desire to overcome these problems has led…
Gibbs sampling is a Markov Chain Monte Carlo sampling technique that iteratively samples variables from their conditional distributions. There are two common scan orders for the variables: random scan and systematic scan. Due to the…
We present a simple combinatorial framework for establishing approximate tensorization of variance and entropy in the setting of spin systems (a.k.a. undirected graphical models) based on balanced separators of the underlying graph. Such…
The Gibbs sampler, also known as the coordinate hit-and-run algorithm, is a Markov chain that is widely used to draw samples from probability distributions in arbitrary dimensions. At each iteration of the algorithm, a randomly selected…
Sampling-based algorithms are classical approaches to perform Bayesian inference in inverse problems. They provide estimators with the associated credibility intervals to quantify the uncertainty on the estimators. Although these methods…
Gibbs sampling methods are standard tools to perform posterior inference for mixture models. These have been broadly classified into two categories: marginal and conditional methods. While conditional samplers are more widely applicable…
Probability measures on the sphere form an important class of statistical models and are used, for example, in modeling directional data or shapes. Due to their widespread use, but also as an algorithmic building block, efficient sampling…
The concept of metastate measures on the states of a random spin system was introduced to be able to treat the large-volume asymptotics for complex quenched random systems, like spin glasses, which may exhibit chaotic volume dependence in…
For the representation of spin-$s$ band-limited functions on the sphere, we propose a sampling scheme with optimal number of samples equal to the number of degrees of freedom of the function in harmonic space. In comparison to the existing…
On a finite graph, there is a natural family of Boltzmann probability measures on cycle-rooted spanning forests, parametrized by weights on cycles. For a certain subclass of those weights, we construct Gibbs measures in infinite volume, as…
We establish tight results for rapid mixing of Gibbs samplers for the Ferromagnetic Ising model on general graphs. We show that if \[(d-1)\tanh\beta<1,\] then there exists a constant C such that the discrete time mixing time of Gibbs…
We consider the problem of generating uniformly random partitions of the vertex set of a graph such that every piece induces a connected subgraph. For the case where we want to have partitions with linearly many pieces of bounded size, we…
Identifying the underlying models in a set of data points contaminated by noise and outliers, leads to a highly complex multi-model fitting problem. This problem can be posed as a clustering problem by the projection of higher order…
We consider a Random Graph Model on $\mathbb{Z}^{d}$ that incorporates the interplay between the statistics of the graph and the underlying space where the vertices are located. Based on a graphical construction of the model as the…
The target measure $\mu$ is the distribution of a random vector in a box $\cB$, a Cartesian product of bounded intervals. The Gibbs sampler is a Markov chain with invariant measure $\mu$. A ``coupling from the past'' construction of the…
We devise a deterministic algorithm to efficiently sample high-quality solutions of certain spin-glass systems that encode hard optimization problems. We employ tensor networks to represent the Gibbs distribution of all possible…