Related papers: Refining Amortized Posterior Approximations using …

The Bayesian approach to inverse problems typically relies on posterior sampling approaches, such as Markov chain Monte Carlo, for which the generation of each sample requires one or more evaluations of the parameter-to-observable map or…

Inference for GP models with non-Gaussian noises is computationally expensive when dealing with large datasets. Many recent inference methods approximate the posterior distribution with a simpler distribution defined on a small number of…

This paper presents an improved implicit sampling method for hierarchical Bayesian inverse problems. A widely used approach for sampling posterior distribution is based on Markov chain Monte Carlo (MCMC). However, the samples generated by…

Amortized inference promises fast test-time Bayesian inference, but existing methods are inherently tied to fixed models. Extending amortization to unseen models typically requires retraining or costly test-time finetuning. In this paper,…

Gaussian processes (GPs) provide a framework for Bayesian inference that can offer principled uncertainty estimates for a large range of problems. For example, if we consider regression problems with Gaussian likelihoods, a GP model enjoys…

Gaussian variational approximations are widely used for summarizing posterior distributions in Bayesian models, especially in high-dimensional settings. However, a drawback of such approximations is the inability to capture skewness or more…

Learning the kernel parameters for Gaussian processes is often the computational bottleneck in applications such as online learning, Bayesian optimization, or active learning. Amortizing parameter inference over different datasets is a…

We propose a new stochastic optimization framework for empirical risk minimization problems such as those that arise in machine learning. The traditional approaches, such as (mini-batch) stochastic gradient descent (SGD), utilize an…

While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However,…

We consider the estimation of an i.i.d. (possibly non-Gaussian) vector $\xbf \in \R^n$ from measurements $\ybf \in \R^m$ obtained by a general cascade model consisting of a known linear transform followed by a probabilistic componentwise…

We propose a general framework for obtaining probabilistic solutions to PDE-based inverse problems. Bayesian methods are attractive for uncertainty quantification but assume knowledge of the likelihood model or data generation process. This…

This article revisits the problem of Bayesian shape-restricted inference in the light of a recently developed approximate Gaussian process that admits an equivalent formulation of the shape constraints in terms of the basis coefficients. We…

Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…

We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian \cite{gupta1999matrix} parameter posterior…

Multiplicative noise models are often used instead of additive noise models in cases in which the noise variance depends on the state. Furthermore, when Poisson distributions with relatively small counts are approximated with normal…

Data augmentation methods are commonly integrated into the training of anomaly detection models. Previous approaches have primarily focused on replicating real-world anomalies or enhancing diversity, without considering that the standard of…

This book chapter introduces regression approaches and regression adjustment for Approximate Bayesian Computation (ABC). Regression adjustment adjusts parameter values after rejection sampling in order to account for the imperfect match…

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…

Adaptive learning is necessary for non-stationary environments where the learning machine needs to forget past data distribution. Efficient algorithms require a compact model update to not grow in computational burden with the incoming data…

Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…