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Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the…

Estimating the predictive uncertainty of a Bayesian learning model is critical in various decision-making problems, e.g., reinforcement learning, detecting adversarial attack, self-driving car. As the model posterior is almost always…

Gaussian Processes (GPs) can be used as flexible, non-parametric function priors. Inspired by the growing body of work on Normalizing Flows, we enlarge this class of priors through a parametric invertible transformation that can be made…

In this work we introduce a novel stochastic algorithm dubbed SNIPS, which draws samples from the posterior distribution of any linear inverse problem, where the observation is assumed to be contaminated by additive white Gaussian noise.…

Uncertainty quantification for large-scale inverse problems remains a challenging task. For linear inverse problems with additive Gaussian noise and Gaussian priors, the posterior is Gaussian but sampling can be challenging, especially for…

Ill-posed linear inverse problems arise frequently in various applications, from computational photography to medical imaging. A recent line of research exploits Bayesian inference with informative priors to handle the ill-posedness of such…

Bayesian deep learning counts on the quality of posterior distribution estimation. However, the posterior of deep neural networks is highly multi-modal in nature, with local modes exhibiting varying generalization performance. Given a…

Unlike the classical linear model, nonlinear generative models have been addressed sparsely in the literature of statistical learning. This work aims to bringing attention to these models and their secrecy potential. To this end, we invoke…

Inverse problems involving partial differential equations (PDEs) are widely used in science and engineering. Although such problems are generally ill-posed, different regularisation approaches have been developed to ameliorate this problem.…

Recently, combinations of generative and Bayesian machine learning have been introduced in particle physics for both fast detector simulation and inference tasks. These neural networks aim to quantify the uncertainty on the generated…

A common task in experimental sciences is to fit mathematical models to real-world measurements to improve understanding of natural phenomenon (reverse-engineering or inverse modeling). When complex dynamical systems are considered, such as…

Bayesian optimization is a powerful paradigm to optimize black-box functions based on scarce and noisy data. Its data efficiency can be further improved by transfer learning from related tasks. While recent transfer models meta-learn a…

Bayesian models based on Gaussian processes (GPs) offer a flexible framework to predict spatially distributed variables with uncertainty. But the use of nonstationary priors, often necessary for capturing complex spatial patterns, makes…

In this article, we study the binary classification problem with supervised data, in the case where the covariate-to-probability-of-success map is possibly spatially inhomogeneous. We devise nonparametric Bayesian procedures with…

A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…

Current methods for regularization in machine learning require quite specific model assumptions (e.g. a kernel shape) that are not derived from prior knowledge about the application, but must be imposed merely to make the method work. We…

We propose a new variational inference algorithm for learning in Gaussian Process State-Space Models (GPSSMs). Our algorithm enables learning of unstable and partially observable systems, where previous algorithms fail. Our main algorithmic…

We adopt Bayesian approach to consider the inverse problem of estimate a function from noisy observations. One important component of this approach is the prior measure. Total variation prior has been proved with no discretization invariant…

Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…

We present a novel approach for constrained Bayesian inference. Unlike current methods, our approach does not require convexity of the constraint set. We reduce the constrained variational inference to a parametric optimization over the…