Related papers: Computationally sufficient statistics for Ising mo…
We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…
Solving an ill-posed linear inverse problem requires knowledge about the underlying signal model. In many applications, this model is a priori unknown and has to be learned from data. However, it is impossible to learn the model using…
Exact solution of the Ising model on the simple cubic lattice is one of the long-standing open problems in rigorous statistical mechanics. Indeed, it is generally believed that settling it would constitute a methodological breakthrough,…
The construction of good effective models is an essential part of understanding and simulating complex systems in many areas of science. It is a particular challenge for correlated many body quantum systems displaying emergent physics. We…
Promising results have driven a recent surge of interest in continuous optimization methods for Bayesian network structure learning from observational data. However, there are theoretical limitations on the identifiability of underlying…
We present a simple algorithm that perfectly samples configurations from the unique Gibbs measure of a spin system on a potentially infinite graph $G$. The sampling algorithm assumes strong spatial mixing together with subexponential growth…
Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and…
Real-world data is often incomplete and contains missing values. To train accurate models over real-world datasets, users need to spend a substantial amount of time and resources imputing and finding proper values for missing data items. In…
Usual estimation methods for the parameters of extreme values distribution employ only a few values, wasting a lot of information. More precisely, in the case of the Gumbel distribution, only the block maxima values are used. In this work,…
The notion of duality -- that a given physical system can have two different mathematical descriptions -- is a key idea in modern theoretical physics. Establishing a duality in lattice statistical mechanics models requires the construction…
We address the problem of learning of continuous exponential family distributions with unbounded support. While a lot of progress has been made on learning of Gaussian graphical models, we still lack scalable algorithms for reconstructing…
We show that evolutionary computation can be implemented as standard Markov-chain Monte-Carlo (MCMC) sampling. With some care, `genetic algorithms' can be constructed that are reversible Markov chains that satisfy detailed balance; it…
We expand upon a natural analogy between Bayesian statistics and statistical physics in which sample size corresponds to inverse temperature. This analogy motivates the definition of two novel statistical quantities: a learning capacity and…
This paper deals with Gibbs samplers that include high dimensional conditional Gaussian distributions. It proposes an efficient algorithm that avoids the high dimensional Gaussian sampling and relies on a random excursion along a small set…
We consider the stabilization of Vlasov--Poisson plasma dynamics, a central control problem in nuclear fusion. Our focus is the gap between what an ideal controller would use and what experiments can actually observe: while optimal policy…
Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…
In this paper we study the inference of the kinetic Ising model on sparse graphs by the decimation method. The decimation method, which was first proposed in [Phys. Rev. Lett. 112, 070603] for the static inverse Ising problem, tries to…
Learning representations purely from observations concerns the problem of learning a low-dimensional, compact representation which is beneficial to prediction models. Under the hypothesis that the intrinsic latent factors follow some casual…
One of the fundamental tasks of science is to find explainable relationships between observed phenomena. One approach to this task that has received attention in recent years is based on probabilistic graphical modelling with sparsity…
Dependency networks (Heckerman et al., 2000) are potential probabilistic graphical models for systems comprising a large number of variables. Like Bayesian networks, the structure of a dependency network is represented by a directed graph,…