Related papers: Gibbs Measures and Phase Transitions on Sparse Ran…

Graphical modelling has a long history in statistics as a tool for the analysis of multivariate data, starting from Wright's path analysis and Gibbs' applications to statistical physics at the beginning of the last century. In its modern…

Neural networks and other machine learning models compute continuous representations, while humans communicate mostly through discrete symbols. Reconciling these two forms of communication is desirable for generating human-readable…

We consider the problem of estimating a sparse precision matrix of a multivariate Gaussian distribution, including the case where the dimension $p$ is large. Gaussian graphical models provide an important tool in describing conditional…

The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…

Building upon the theory of graph limits and the Aldous-Hoover representation and inspired by Panchenko's work on asymptotic Gibbs measures (Annals of Probability 2013), we construct continuous embeddings of discrete probability…

We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be…

We consider a countable system of interacting (possibly non-Markovian) stochastic differential equations driven by independent Brownian motions and indexed by the vertices of a locally finite graph $G = (V,E)$. The drift of the process at…

In the second part of the paper we consider a convolution of probability measures on spaces of locally finite configurations (subsets of a phase space) as well as their connection with the convolution of the corresponding correlation…

Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization.…

We study Gibbs partition models, also known as composition schemes. Our main results comprehensively describe their phase diagram, including a phase transition from the convergent case described in Stufler (2018, Random Structures \&…

An instance of a random constraint satisfaction problem defines a random subset S (the set of solutions) of a large product space (the set of assignments). We consider two prototypical problem ensembles (random k-satisfiability and…

In these notes we describe heuristics to predict computational-to-statistical gaps in certain statistical problems. These are regimes in which the underlying statistical problem is information-theoretically possible although no efficient…

We describe a general approach of determining the distribution of spanning subgraphs in the random graph $\G(n,p)$. In particular, we determine the distribution of spanning subgraphs of certain given degree sequences, which is a…

We study the spatial Gibbs random graphs introduced in [MV16] from the point of view of local convergence. These are random graphs embedded in an ambient space consisting of a line segment, defined through a probability measure that favors…

We verify a key component of the replica symmetry breaking hypothesis put forward in the physics literature [M\'ezard and Montanari 2009] on random factor graph models. For a broad class of these models we verify that the Gibbs measure can…

Estimating the probability distribution 'q' governing the behaviour of a certain variable by sampling its value a finite number of times most typically involves an error. Successive measurements allow the construction of a histogram, or…

This paper gives a way to simulate from the two star probability distribution on the space of simple graphs via auxiliary variables. Using this simulation scheme, the model is explored for various domains of the parameter values, and the…

We apply a theorem of Wick to rewrite certain classes of exponential measures on random graphs as integrals of Feynman-Gibbs type, on the real line. The analytic properties of these measures can then be studied in terms of phase…

We study random graphs with latent geometric structure, where the probability of each edge depends on the underlying random positions corresponding to the two endpoints. We focus on the setting where this conditional probability is a…

Gibbs partition models are the largest class of infinite exchangeable partitions of the positive integers generalizing the product form of the probability function of the two-parameter Poisson-Dirichlet family. Recently those models have…