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In these short notes, we adapt and systematically apply Guerra's interpolation techniques on a class of disordered mean-field spin glasses equipped with crystal fields and multi-value spin variables. These models undergo the phenomenon of…
We develop and analyze a method for stochastic simulation optimization based on Gaussian process models within a trust-region framework. We focus on settings where the variance of the objective function is large, making accurate estimation…
Bayesian network is a complete model for the variables and their relationships, it can be used to answer probabilistic queries about them. A Bayesian network can thus be considered a mechanism for automatically applying Bayes' theorem to…
In this talk I will review the approach to spin glasses based on the spontaneously broken replica symmetry. I will concentrate my attention mostly on more general ideas, skipping technical details and stressing the characteristic…
The objective of Bayesian inference is often to infer, from data, a probability measure for a random variable that can be used as input for Monte Carlo simulation. When datasets for Bayesian inference are small, a principle challenge is…
Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…
In this work, we adopt a general framework based on the Gibbs posterior to update belief distributions for inverse problems governed by partial differential equations (PDEs). The Gibbs posterior formulation is a generalization of standard…
Full Bayesian posteriors are rarely analytically tractable, which is why real-world Bayesian inference heavily relies on approximate techniques. Approximations generally differ from the true posterior and require diagnostic tools to assess…
In this paper we propose a new Bayesian estimation method to solve linear inverse problems in signal and image restoration and reconstruction problems which has the property to be scale invariant. In general, Bayesian estimators are {\em…
A Bayesian framework is attractive in the context of prediction, but a fast recursive update of the predictive distribution has apparently been out of reach, in part because Monte Carlo methods are generally used to compute the predictive.…
Bayesian inference provides a rigorous framework to encapsulate our knowledge and uncertainty regarding various physical quantities in a well-defined and self-contained manner. Utilising modern tools, such Bayesian models can be constructed…
Integrative modeling of macromolecular assemblies allows for structural characterization of large assemblies that are recalcitrant to direct experimental observation. A Bayesian inference approach facilitates combining data from…
Invariant inference algorithms such as interpolation-based inference and IC3/PDR show that it is feasible, in practice, to find inductive invariants for many interesting systems, but non-trivial upper bounds on the computational complexity…
In a variety of scientific applications we wish to characterize a physical system using measurements or observations. This often requires us to solve an inverse problem, which usually has non-unique solutions so uncertainty must be…
Mixture models are widely used in Bayesian statistics and machine learning, in particular in computational biology, natural language processing and many other fields. Variational inference, a technique for approximating intractable…
A modification of the Adaptive Biasing Force method is introduced, in which the free energy is approximated by a sum of tensor products of one-dimensional functions. This enables to handle a larger number of reaction coordinates than the…
We put forward an adaptive alpha (Type I Error) that decreases as the information grows, for hypothesis tests in which nested linear models are compared. A less elaborate adaptation was already presented in \citet{PP2014} for comparing…
Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential…
Several recent works have developed a new, probabilistic interpretation for numerical algorithms solving linear systems in which the solution is inferred in a Bayesian framework, either directly or by inferring the unknown action of the…
A reciprocal LASSO (rLASSO) regularization employs a decreasing penalty function as opposed to conventional penalization approaches that use increasing penalties on the coefficients, leading to stronger parsimony and superior model…