Related papers: A Method for Compressing Parameters in Bayesian Mo…
This thesis responds to the challenges of using a large number, such as thousands, of features in regression and classification problems. There are two situations where such high dimensional features arise. One is when high dimensional…
As an alternative to variable selection or shrinkage in high dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the…
Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…
Bayesian computation of high dimensional linear regression models with a popular Gaussian scale mixture prior distribution using Markov Chain Monte Carlo (MCMC) or its variants can be extremely slow or completely prohibitive due to the…
In this article we consider Bayesian parameter inference associated to partially-observed stochastic processes that start from a set B0 and are stopped or killed at the first hitting time of a known set A. Such processes occur naturally…
We study the computational complexity of Markov chain Monte Carlo (MCMC) methods for high-dimensional Bayesian linear regression under sparsity constraints. We first show that a Bayesian approach can achieve variable-selection consistency…
Finding methods for making generalizable predictions is a fundamental problem of machine learning. By looking into similarities between the prediction problem for unknown data and the lossless compression we have found an approach that…
In large-scale genomic applications vast numbers of molecular features are scanned in order to find a small number of candidates which are linked to a particular disease or phenotype. This is a variable selection problem in the "large p,…
In this article we consider Bayesian estimation of static parameters for a class of partially observed McKean-Vlasov diffusion processes with discrete-time observations over a fixed time interval. This problem features several obstacles to…
Markov chain Monte Carlo (MCMC) is the predominant tool used in Bayesian parameter estimation for hierarchical models. When the model expands due to an increasing number of hierarchical levels, number of groups at a particular level, or…
Due to the escalating growth of big data sets in recent years, new Bayesian Markov chain Monte Carlo (MCMC) parallel computing methods have been developed. These methods partition large data sets by observations into subsets. However, for…
Presence-only data are referred to situations in which, given a censoring mechanism, a binary response can be observed only with respect to on outcome, usually called \textit{presence}. In this work we present a Bayesian approach to the…
In many application areas, data are collected on a categorical response and high-dimensional categorical predictors, with the goals being to build a parsimonious model for classification while doing inferences on the important predictors.…
High-dimensional feature selection arises in many areas of modern science. For example, in genomic research we want to find the genes that can be used to separate tissues of different classes (e.g. cancer and normal) from tens of thousands…
Markov chain Monte Carlo (MCMC) methods have not been broadly adopted in Bayesian neural networks (BNNs). This paper initially reviews the main challenges in sampling from the parameter posterior of a neural network via MCMC. Such…
High-throughput characterization often requires estimating parameters and model dimension from experimental data of limited quantity and quality. Such data may result in an ill-posed inverse problem, where multiple sets of parameters and…
Markov chain Monte Carlo (MCMC) algorithms have become powerful tools for Bayesian inference. However, they do not scale well to large-data problems. Divide-and-conquer strategies, which split the data into batches and, for each batch, run…
Dynamic Bayesian predictive synthesis is a formal approach to coherently synthesizing multiple predictive distributions into a single distribution. In sequential analysis, the computation of the synthesized predictive distribution has…
The predictive advantage of combining several different predictive models is widely accepted. Particularly in time series forecasting problems, this combination is often dynamic to cope with potential non-stationary sources of variation…
Univariate and multivariate general linear regression models, subject to linear inequality constraints, arise in many scientific applications. The linear inequality restrictions on model parameters are often available from phenomenological…