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The normalizing constant plays an important role in Bayesian computation, and there is a large literature on methods for computing or approximating normalizing constants that cannot be evaluated in closed form. When the normalizing constant…

Downscaling is a landmark task in climate science and meteorology in which the goal is to use coarse scale, spatio-temporal data to infer values at finer scales. Statistical downscaling aims to approximate this task using statistical…

In this manuscript, we consider the problem of learning a flow or diffusion-based generative model parametrized by a two-layer auto-encoder, trained with online stochastic gradient descent, on a high-dimensional target density with an…

This paper is on the construction of structure-preserving, online-efficient reduced models for the barotropic Euler equations with a friction term on networks. The nonlinear flow problem finds broad application in the context of gas…

Deep learning models are used in critical applications, in which mistakes can have serious consequences. Therefore, it is crucial to understand how and why models generate predictions. This understanding provides useful information to check…

Clustering task of mixed data is a challenging problem. In a probabilistic framework, the main difficulty is due to a shortage of conventional distributions for such data. In this paper, we propose to achieve the mixed data clustering with…

In conducting non-linear dimensionality reduction and feature learning, it is common to suppose that the data lie near a lower-dimensional manifold. A class of model-based approaches for such problems includes latent variables in an unknown…

We consider the inverse Ising problem, i.e. the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the…

Compared to mean regression and quantile regression, the literature on modal regression is very sparse. A unifying framework for Bayesian modal regression is proposed, based on a family of unimodal distributions indexed by the mode, along…

Mixtures of high dimensional Gaussian distributions have been studied extensively in statistics and learning theory. While the total variation distance appears naturally in the sample complexity of distribution learning, it is analytically…

Generalized linear mixed models (GLMM) are used for inference and prediction in a wide range of different applications providing a powerful scientific tool. An increasing number of sources of data are becoming available, introducing a…

This paper interprets the stabilized finite element method via residual minimization as a variational multiscale method. We approximate the solution to the partial differential equations using two discrete spaces that we build on a…

Gaussian process state-space models (GPSSMs) provide a principled and flexible approach to modeling the dynamics of a latent state, which is observed at discrete-time points via a likelihood model. However, inference in GPSSMs is…

We present a new subspace-based method to construct probabilistic models for high-dimensional data and highlight its use in anomaly detection. The approach is based on a statistical estimation of probability density using densities of…

We present a novel framework exploiting the cascade of phase transitions occurring during a simulated annealing of the Expectation-Maximisation algorithm to cluster datasets with multi-scale structures. Using the weighted local covariance,…

Gaussian graphical models are of great interest in statistical learning. Because the conditional independencies between different nodes correspond to zero entries in the inverse covariance matrix of the Gaussian distribution, one can learn…

Ising models originated in statistical physics and are widely used in modeling spatial data and computer vision problems. However, statistical inference of this model remains challenging due to intractable nature of the normalizing constant…

Bayesian methods estimate a measure of uncertainty by using the posterior distribution. One source of difficulty in these methods is the computation of the normalizing constant. Calculating exact posterior is generally intractable and we…

Multi-fidelity methods are prominently used when cheaply-obtained, but possibly biased and noisy, observations must be effectively combined with limited or expensive true data in order to construct reliable models. This arises in both…

Variational inference (VI) is a popular approach in Bayesian inference, that looks for the best approximation of the posterior distribution within a parametric family, minimizing a loss that is typically the (reverse) Kullback-Leibler (KL)…