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We study distributed optimization problems over a network when the communication between the nodes is constrained, and so information that is exchanged between the nodes must be quantized. This imperfect communication poses a fundamental…
We present new MCMC algorithms for computing the posterior distributions and expectations of the unknown variables in undirected graphical models with regular structure. For demonstration purposes, we focus on Markov Random Fields (MRFs).…
Divide-and-conquer MCMC is a strategy for parallelising Markov Chain Monte Carlo sampling by running independent samplers on disjoint subsets of a dataset and merging their output. An ongoing challenge in the literature is to efficiently…
Sparse inversion and classification problems are ubiquitous in modern data science and imaging. They are often formulated as non-smooth minimisation problems. In sparse inversion, we minimise, e.g., the sum of a data fidelity term and an…
Exact inference for hidden Markov models requires the evaluation of all distributions of interest - filtering, prediction, smoothing and likelihood - with a finite computational effort. This article provides sufficient conditions for exact…
In this article we consider recursive approximations of the smoothing distribution associated to partially observed stochastic differential equations (SDEs), which are observed discretely in time. Such models appear in a wide variety of…
We provide time- and sample-efficient algorithms for learning and testing latent-tree Ising models, i.e. Ising models that may only be observed at their leaf nodes. On the learning side, we obtain efficient algorithms for learning a…
We use Markov categories to generalize the basic theory of Markov chains and hidden Markov models to an abstract setting. This comprises characterizations of hidden Markov models in terms of conditional independences and algorithms for…
We propose a distributed computing framework, based on a divide and conquer strategy and hierarchical modeling, to accelerate posterior inference for high-dimensional Bayesian factor models. Our approach distributes the task of…
We present a mathematical framework to represent turbostratic disorder in materials like carbon blacks, smectites, and twisted $n$-layer graphene. In particular, the set of all possible disordered layers, including rotated, shifted, and…
Stochastic gradient methods are the workhorse (algorithms) of large-scale optimization problems in machine learning, signal processing, and other computational sciences and engineering. This paper studies Markov chain gradient descent, a…
Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…
We deal with the problem of gradient estimation for stochastic differentiable relaxations of algorithms, operators, simulators, and other non-differentiable functions. Stochastic smoothing conventionally perturbs the input of a…
We consider distributed optimization with smooth convex objective functions defined on an undirected connected graph. Inspired by mirror descent mehod and RLC circuits, we propose a novel distributed mirror descent method. Compared with…
We consider online computation of expectations of additive state functionals under general path probability measures proportional to products of unnormalised transition densities. These transition densities are assumed to be intractable but…
We introduce a probabilistic framework for two-sample comparison based on a nonparametric process taking the form of a Markov model that transitions between a "divide" and a "merge" state on a multi-resolution partition tree of the sample…
We are concerned with a novel Bayesian statistical framework for the characterization of natural subsurface formations, a very challenging task. Because of the large dimension of the stochastic space of the prior distribution in the…
This paper deals with the estimation of the unknown distribution of hidden random variables from the observation of pairwise comparisons between these variables. This problem is inspired by recent developments on Bradley-Terry models in…
Based on decision trees, many fields have arguably made tremendous progress in recent years. In simple words, decision trees use the strategy of "divide-and-conquer" to divide the complex problem on the dependency between input features and…
Random forest regression is a powerful non-parametric method that adapts to local data characteristics through data-driven partitioning, making it effective across diverse application domains. However, the piecewise constant nature of…