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Sequential Bayesian inference over predictive functions is a natural framework for continual learning from streams of data. However, applying it to neural networks has proved challenging in practice. Addressing the drawbacks of existing…
We investigate the asymptotic behavior of Bayesian posterior distributions under independent and identically distributed ($i.i.d.$) misspecified models. More specifically, we study the concentration of the posterior distribution on…
Bayesian inference was once a gold standard for learning with neural networks, providing accurate full predictive distributions and well calibrated uncertainty. However, scaling Bayesian inference techniques to deep neural networks is…
An efficient algorithm for the determination of Bayesian optimal discriminating designs for competing regression models is developed, where the main focus is on models with general distributional assumptions beyond the "classical" case of…
This study examines the optimal selections of bandwidth and semi-metric for a functional partial linear model. Our proposed method begins by estimating the unknown error density using a kernel density estimator of residuals, where the…
The capability of a novel Kullback-Leibler divergence method is examined herein within the Kalman filter framework to select the input-parameter-state estimation execution with the most plausible results. This identification suffers from…
Kullback-Leibler (KL) divergence is a fundamental concept in information theory that quantifies the discrepancy between two probability distributions. In the context of Variational Autoencoders (VAEs), it serves as a central regularization…
Prior sensitivity analysis is a fundamental method to check the effects of prior distributions on the posterior distribution in Bayesian inference. Exploring the posteriors under several alternative priors can be computationally intensive,…
In various applications, we deal with high-dimensional positive-valued data that often exhibits sparsity. This paper develops a new class of continuous global-local shrinkage priors tailored to analyzing gamma-distributed observations where…
In supervised learning, the output variable to be predicted is often represented as a function, such as a spectrum or probability distribution. Despite its importance, functional output regression remains relatively unexplored. In this…
Estimating Kullback Leibler (KL) divergence from samples of two distributions is essential in many machine learning problems. Variational methods using neural network discriminator have been proposed to achieve this task in a scalable…
The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the…
Motivated by the computation of the non-parametric maximum likelihood estimator (NPMLE) and the Bayesian posterior in statistics, this paper explores the problem of convex optimization over the space of all probability distributions. We…
Bayesian nonparametric statistics is an area of considerable research interest. While recently there has been an extensive concentration in developing Bayesian nonparametric procedures for model checking, the use of the Dirichlet process,…
We investigate the problem of estimating the causal effect of a treatment on individual subjects from observational data, this is a central problem in various application domains, including healthcare, social sciences, and online…
Recent advances in deep learning have brought to the fore models that can make multiple computational steps in the service of completing a task; these are capable of describ- ing long-term dependencies in sequential data. Novel recurrent…
Gaussian processes are distributions over functions that are versatile and mathematically convenient priors in Bayesian modelling. However, their use is often impeded for data with large numbers of observations, $N$, due to the cubic (in…
This paper describes a new Bayesian interpretation of a class of skew--Student $t$ distributions. We consider a hierarchical normal model with unknown covariance matrix and show that by imposing different restrictions on the parameter…
This paper proposes two linear projection methods for supervised dimension reduction using only the first and second-order statistics. The methods, each catering to a different parameter regime, are derived under the general Gaussian model…
In this study, simultaneous predictive distributions for independent Poisson observables were considered and the performance of predictive distributions was evaluated using the Kullback-Leibler (K-L) loss. This study proposes a class of…