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Image reconstruction based on indirect, noisy, or incomplete data remains an important yet challenging task. While methods such as compressive sensing have demonstrated high-resolution image recovery in various settings, there remain issues…

Generative Bayesian Computation (GBC) methods are developed for Casual Inference. Generative methods are simulation-based methods that use a large training dataset to represent posterior distributions as a map (a.k.a. optimal transport) to…

Estimation of the response probability distributions of computer simulators in the presence of randomness is a crucial task in many fields. However, achieving this task with guaranteed accuracy remains an open computational challenge,…

Modeling the distribution of natural images is challenging, partly because of strong statistical dependencies which can extend over hundreds of pixels. Recurrent neural networks have been successful in capturing long-range dependencies in a…

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the…

Conventional frequentist learning, as assumed by existing federated learning protocols, is limited in its ability to quantify uncertainty, incorporate prior knowledge, guide active learning, and enable continual learning. Bayesian learning…

The classification of MRI images according to the anatomical field of view is a necessary task to solve when faced with the increasing quantity of medical images. In parallel, advances in deep learning makes it a suitable tool for computer…

Using Markov chain Monte Carlo to sample from posterior distributions was the key innovation which made Bayesian data analysis practical. Notoriously, however, MCMC is hard to tune, hard to diagnose, and hard to parallelize. This…

Bayesian neural networks (BNNs) have received an increased interest in the last years. In BNNs, a complete posterior distribution of the unknown weight and bias parameters of the network is produced during the training stage. This…

Purpose: To develop a deep learning-based Bayesian inference for MRI reconstruction. Methods: We modeled the MRI reconstruction problem with Bayes's theorem, following the recently proposed PixelCNN++ method. The image reconstruction from…

Uncertainty estimation in deep models is essential in many real-world applications and has benefited from developments over the last several years. Recent evidence suggests that existing solutions dependent on simple Gaussian formulations…

The Bayesian approach to solving inverse problems relies on the choice of a prior. This critical ingredient allows the formulation of expert knowledge or physical constraints in a probabilistic fashion and plays an important role for the…

Image classification is an essential task in computer vision, which aims to categorise a set of images into different groups based on some visual criteria. Existing methods, such as convolutional neural networks, have been successfully…

We introduce a deep generative framework for high-dimensional Bayesian inference that enables efficient posterior sampling. As telescopes and simulations rapidly expand the volume and resolution of astrophysical data, fast simulation-based…

The determination of the physical parameters of gravitational wave events is a fundamental pillar in the analysis of the signals observed by the current ground-based interferometers. Typically, this is done using Bayesian inference…

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…

This is a course project report with complete methodology, experiments, references and mathematical derivations. Matrix factorization [1] is a widely used technique in recommendation systems. Probabilistic Matrix Factorization (PMF) [2]…

In this dissertation, we present a generative model to capture the relation between facial image quality features (like pose, illumination direction, etc) and face recognition performance. Such a model can be used to predict the performance…

We consider the situation where a temporal process is composed of contiguous segments with differing slopes and replicated noise-corrupted time series measurements are observed. The unknown mean of the data generating process is modelled as…

Bayesian inference with deep generative prior has received considerable interest for solving imaging inverse problems in many scientific and engineering fields. The selection of the prior distribution is learned from, and therefore an…