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Piecewise Aggregate Approximation (PAA) is a competitive basic dimension reduction method for high-dimensional time series mining. When deployed, however, the limitations are obvious that some important information will be missed,…
Approximate Bayesian Computation (ABC) methods are applicable to statistical models specified by generative processes with analytically intractable likelihoods. These methods try to approximate the posterior density of a model parameter by…
A statistical theory of the mean field is developed. It is based on the proposition that the mean field can be obtained as an energy average. Moreover, it is assumed that the matrix elements of the residual interaction, obtained after the…
We present the fundamentals of a measure transport approach to sampling. The idea is to construct a deterministic coupling---i.e., a transport map---between a complex "target" probability measure of interest and a simpler reference measure.…
System modeling is a classical approach to ensure their reliability since it is suitable both for a formal verification and for software testing techniques. In the context of model-based testing an approach combining random testing and…
This paper proposes a Bayesian method for estimating the parameters of a normal distribution when only limited summary statistics (sample mean, minimum, maximum, and sample size) are available. To estimate the parameters of a normal…
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…
We formulate self-consistency equations for the distribution of links in spin models and of plaquettes in gauge theories. This improves upon known mean-field, mean-link, and mean-plaquette approximations in such that we self-consistently…
In this work we discuss a short range version of the $p$-spin model. The model is provided with a parameter that allows to control the crossover with the mean field behaviour. We detect a discrepancy between the perturbative approach and…
In regression modelling approach, the main step is to fit the regression line as close as possible to the target variable. In this process most algorithms try to fit all of the data in a single line and hence fitting all parts of target…
Motivated by recent progress in using restricted Boltzmann machines as preprocessing algorithms for deep neural network, we revisit the mean-field equations (belief-propagation and TAP equations) in the best understood such machine, namely…
We develop a general variational inference method that preserves dependency among the latent variables. Our method uses copulas to augment the families of distributions used in mean-field and structured approximations. Copulas model the…
Context: Adaptive monitoring is a method used in a variety of domains for responding to changing conditions. It has been applied in different ways, from monitoring systems' customization to re-composition, in different application domains.…
The asymmetric simple exclusion process with random-force disorder is studied within the mean field approximation. The stationary current through a domain with reversed bias is analyzed and the results are found to be in accordance with…
In real-world scenarios, achieving domain adaptation and generalization poses significant challenges, as models must adapt to or generalize across unknown target distributions. Extending these capabilities to unseen multimodal…
Reachability analysis is an important method in providing safety guarantees for systems with unknown or uncertain dynamics. Due to the computational intractability of exact reachability analysis for general nonlinear, high-dimensional…
We propose a fast and theoretically grounded method for Bayesian variable selection and model averaging in latent variable regression models. Our framework addresses three interrelated challenges: (i) intractable marginal likelihoods, (ii)…
Combinatorial optimization is a fertile testing ground for statistical physics methods developed in the context of disordered systems, allowing one to confront theoretical mean field predictions with actual properties of finite dimensional…
Domain adaptation algorithms are designed to minimize the misclassification risk of a discriminative model for a target domain with little training data by adapting a model from a source domain with a large amount of training data. Standard…
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…