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One of the primary applications of classical Boltzmann machines is generative modeling, wherein the goal is to tune the parameters of a model distribution so that it closely approximates a target distribution. Training relies on estimating…
The main difficulty that arises in the analysis of most machine learning algorithms is to handle, analytically and numerically, a large number of interacting random variables. In this Ph.D manuscript, we revisit an approach based on the…
The Boltzmann equation, a fundamental equation in kinetic theory, serves as a bridge between microscopic particle dynamics and macroscopic continuum mechanics. However, deriving closed macroscopic moment systems from the Boltzmann equation…
The game dynamical equations are derived from Boltzmann-like equations for individual pair interactions by assuming a certain kind of imitation behavior, the so-called proportional imitation rule. They can be extended to a stochastic…
We present a drifting-based framework for amortized sampling of Boltzmann distributions defined by energy functions. The method trains a one-step neural generator by projecting samples along a Gaussian-smoothed score field from the current…
State-space models are a popular statistical framework for analysing sequential data. Within this framework, particle filters are often used to perform inference on non-linear state-space models. We introduce a new method, StateMixNN, that…
Generative models, particularly normalizing flows, have shown exceptional performance in learning probability distributions across various domains of physics, including statistical mechanics, collider physics, and lattice field theory. In…
Neural quantum states efficiently represent many-body wavefunctions with neural networks, but the cost of Monte Carlo sampling limits their scaling to large system sizes. Here we address this challenge by combining sparse Boltzmann machine…
This review deals with Restricted Boltzmann Machine (RBM) under the light of statistical physics. The RBM is a classical family of Machine learning (ML) models which played a central role in the development of deep learning. Viewing it as a…
Efficient sampling from the Boltzmann distribution given its energy function is a key challenge for modeling complex physical systems such as molecules. Boltzmann Generators address this problem by leveraging continuous normalizing flows to…
Boltzmann machines (BMs) are powerful energy-based generative models, but their heavy training cost has largely confined practical use to Restricted BMs (RBMs) trained with an efficient learning method called contrastive divergence. More…
A Gaussian restricted Boltzmann machine (GRBM) is a Boltzmann machine defined on a bipartite graph and is an extension of usual restricted Boltzmann machines. A GRBM consists of two different layers: a visible layer composed of continuous…
Molecules are frequently represented as graphs, but the underlying 3D molecular geometry (the locations of the atoms) ultimately determines most molecular properties. However, most molecules are not static and at room temperature adopt a…
Flow-based generative models have been employed for sampling the Boltzmann distribution, but their application to high-dimensional systems is hindered by the significant computational cost of obtaining the Jacobian of the flow. To overcome…
We present the Boltzmann classifier, a novel distance based probabilistic classification algorithm inspired by the Boltzmann distribution. Unlike traditional classifiers that produce hard decisions or uncalibrated probabilities, the…
Many problems in machine learning are naturally expressed in the language of undirected graphical models. Here, we propose black-box learning and inference algorithms for undirected models that optimize a variational approximation to the…
We construct a novel class of stochastic blockmodels using Bayesian nonparametric mixtures. These model allows us to jointly estimate the structure of multiple networks and explicitly compare the community structures underlying them, while…
The mean field methods, which entail approximating intractable probability distributions variationally with distributions from a tractable family, enjoy high efficiency, guaranteed convergence, and provide lower bounds on the true…
The filtering distribution in hidden Markov models evolves according to the law of a mean-field model in state-observation space. The ensemble Kalman filter (EnKF) approximates this mean-field model with an ensemble of interacting…
When working with multimodal Bayesian posterior distributions, Markov chain Monte Carlo (MCMC) algorithms have difficulty moving between modes, and default variational or mode-based approximate inferences will understate posterior…