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The Bayesian view of the brain hypothesizes that the brain constructs a generative model of the world, and uses it to make inferences via Bayes' rule. Although many types of approximate inference schemes have been proposed for hierarchical…

According to both domain expert knowledge and empirical evidence, wavelet coefficients of real signals tend to exhibit clustering patterns, in that they contain connected regions of coefficients of similar magnitude (large or small). A…

Mixture models with Gamma and or inverse-Gamma distributed mixture components are useful for medical image tissue segmentation or as post-hoc models for regression coefficients obtained from linear regression within a Generalised Linear…

Multifractal analysis (MFA) provides a framework for the global characterization of image textures by describing the spatial fluctuations of their local regularity based on the multifractal spectrum. Several works have shown the interest of…

Markov chain Monte Carlo methods for exponential family models with intractable normalizing constant, such as the exchange algorithm, require simulations of the sufficient statistics at every iteration of the Markov chain, which often…

Methods based on Deep Learning have recently been applied on astrophysical parameter recovery thanks to their ability to capture information from complex data. One of these methods is the approximate Bayesian Neural Networks (BNNs) which…

Bayesian nonparametric inferential procedures based on Markov chain Monte Carlo marginal methods typically yield point estimates in the form of posterior expectations. Though very useful and easy to implement in a variety of statistical…

Bayesian nonparametric mixtures and random partition models are powerful tools for probabilistic clustering. However, standard independent mixture models can be restrictive in some applications such as inference on cell lineage due to the…

We study the performance of a stochastic algorithm based on the power method that adaptively learns the large deviation functions characterizing the fluctuations of additive functionals of Markov processes, used in physics to model…

Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…

This paper provides a graphical characterization of Markov blankets in chain graphs (CGs) under the Lauritzen-Wermuth-Frydenberg (LWF) interpretation. The characterization is different from the well-known one for Bayesian networks and…

Gravitational-wave (GW) ringdown signals from black holes (BHs) encode crucial information about the gravitational dynamics in the strong-field regime, which offers unique insights into BH properties. In the future, the improving…

Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…

Wavelet based algorithms in numerical analysis are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in this new system of coordinates. However, due to the recursive…

We propose an empirical Bayes formulation of the structure learning problem, where the prior specification assumes that all node variables have the same error variance, an assumption known to ensure the identifiability of the underlying…

We propose a new neural network framework, termed Neural Network Machine Regression (NNMR), which integrates trainable input gating and adaptive depth regularization to jointly perform feature selection and function estimation in an…

Performing Bayesian inference on large spatio-temporal models requires extracting inverse elements of large sparse precision matrices for marginal variances, as well as estimating model hyperparameters. Although direct matrix factorizations…

Markov random fields are used to model high dimensional distributions in a number of applied areas. Much recent interest has been devoted to the reconstruction of the dependency structure from independent samples from the Markov random…

In recent years, Full-Waveform Inversion (FWI) has been extensively used to derive high-resolution subsurface velocity models from seismic data. However, due to the nonlinearity and ill-posed nature of the problem, FWI requires a good…

We present on-line policy gradient algorithms for computing the locally optimal policy of a constrained, average cost, finite state Markov Decision Process. The stochastic approximation algorithms require estimation of the gradient of the…