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We study the mixing time of Glauber dynamics for Ising models in which the interaction matrix contains a single negative spectral outlier. This class includes the anti-ferromagnetic Curie-Weiss model, the anti-ferromagnetic Ising model on…
Certain tasks in high-dimensional statistics become easier when the underlying distribution satisfies a local-to-global property called approximate tensorization of entropy (ATE). For example, the Glauber dynamics Markov chain of an ATE…
Gibbs sampling is a common procedure used to fit finite mixture models. However, it is known to be slow to converge when exploring correlated regions of a parameter space and so blocking correlated parameters is sometimes implemented in…
Gaussian graphical model selection is usually studied under independent sampling, but in many applications observations arise from dependent dynamics. We study structure learning when the data consist of a single trajectory of Gaussian…
Combinatorial optimization is a well-established area in operations research and computer science. Until recently, its methods have focused on solving problem instances in isolation, ignoring that they often stem from related data…
We propose a notion of contraction function for a family of graphs and establish its connection to the strong spatial mixing for spin systems. More specifically, we show that for anti-ferromagnetic Potts model on families of graphs…
Non-Gaussian and multimodal distributions are an important part of many recent robust sensor fusion algorithms. In difference to robust cost functions, they are probabilistically founded and have good convergence properties. Since their…
For a graph $G$, let $Z(G,\lambda)$ be the partition function of the monomer-dimer system defined by $\sum_k m_k(G)\lambda^k$, where $m_k(G)$ is the number of matchings of size $k$ in $G$. We consider graphs of bounded degree and develop a…
An important paradigm in the understanding of mixing times of Glauber dynamics for spin systems is the correspondence between spatial mixing properties of the models and bounds on the mixing time of the dynamics. This includes, in…
We present novel results for fast mixing of Glauber dynamics using the newly introduced and powerful Spectral Independence method from [Anari, Liu, Oveis-Gharan: FOCS 2020]. We mainly focus on the Hard-core model and the Ising model. We…
We introduce and analyze a natural class of nonlinear dynamics for spin systems such as the Ising model. This class of dynamics is based on the framework of mass action kinetics, which models the evolution of systems of entities under…
We study the stochastic dynamics of Ising spin models with random bonds, interacting on finitely connected Poissonnian random graphs. We use the dynamical replica method to derive closed dynamical equations for the joint spin-field…
Mixtures of linear mixed models (MLMMs) are useful for clustering grouped data and can be estimated by likelihood maximization through the EM algorithm. The conventional approach to determining a suitable number of components is to compare…
Graphical Gaussian models have proven to be useful tools for exploring network structures based on multivariate data. Applications to studies of gene expression have generated substantial interest in these models, and resulting recent…
We give a near-linear time sampler for the Gibbs distribution of the ferromagnetic Ising models with edge activities $\boldsymbol{\beta} > 1$ and external fields $\boldsymbol{\lambda}<1$ (or symmetrically, $\boldsymbol{\lambda}>1$) on…
We show that the Potts model on a graph can be approximated by a sequence of independent and identically distributed spins in terms of Wasserstein distance at high temperatures. We prove a similar result for the Curie--Weiss--Potts model on…
Many problems in robotics involve both continuous and discrete components, and modeling them together for estimation tasks has been a long standing and difficult problem. Hybrid Factor Graphs give us a mathematical framework to model these…
We show that for weakly dependent random variables the relative entropy functional satisfies an approximate version of the standard tensorization property which holds in the independent case. As a corollary we obtain a family of…
It was recently shown that path integral Monte Carlo can be used to directly compute partition functions of Hamiltonians with vibronic coupling [J. Chem. Phys. 148, 194110 (2018)]. While the importance sampling Monte Carlo integration…
A key goal in the design of probabilistic inference algorithms is identifying and exploiting properties of the distribution that make inference tractable. Lifted inference algorithms identify symmetry as a property that enables efficient…