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We consider a novel Bayesian approach to estimation, uncertainty quantification, and variable selection for a high-dimensional linear regression model under sparsity. The number of predictors can be nearly exponentially large relative to…
Computer simulations have become an important tool across the biomedical sciences and beyond. For many important problems several different models or hypotheses exist and choosing which one best describes reality or observed data is not…
As the amount of economic and other data generated worldwide increases vastly, a challenge for future generations of econometricians will be to master efficient algorithms for inference in empirical models with large information sets. This…
We study the high-dimensional linear regression problem with categorical predictors that have many levels. We propose a new estimation approach, which performs model compression via two mechanisms by simultaneously encouraging (a)…
This paper presents a Bayesian framework for assessing the adequacy of a model without the necessity of explicitly enumerating a specific alternate model. A test statistic is developed for tracking the performance of the model across…
The diagnosis of cyber-physical systems aims to detect faulty behaviour, its root cause and a mitigation or even prevention policy. Therefore, diagnosis relies on a representation of the system's functional and faulty behaviour combined…
Given a supervised machine learning problem where the training set has been subject to a known sampling bias, how can a model be trained to fit the original dataset? We achieve this through the Bayesian inference framework by altering the…
Data dispersed across multiple files are commonly integrated through probabilistic linkage methods, where even minimal error rates in record matching can significantly contaminate subsequent statistical analyses. In regression problems, we…
In this paper, we propose a new Bayesian inference method for a high-dimensional sparse factor model that allows both the factor dimensionality and the sparse structure of the loading matrix to be inferred. The novelty is to introduce a…
Subset selection is a valuable tool for interpretable learning, scientific discovery, and data compression. However, classical subset selection is often avoided due to selection instability, lack of regularization, and difficulties with…
In this paper, we study weakly-supervised laparoscopic image segmentation with sparse annotations. We introduce a novel Bayesian deep learning approach designed to enhance both the accuracy and interpretability of the model's segmentation,…
For nearly any challenging scientific problem evaluation of the likelihood is problematic if not impossible. Approximate Bayesian computation (ABC) allows us to employ the whole Bayesian formalism to problems where we can use simulations…
A fully Bayesian approach is proposed for ultrahigh-dimensional nonparametric additive models in which the number of additive components may be larger than the sample size, though ideally the true model is believed to include only a small…
Over the past decades, statisticians and machine-learning researchers have developed literally thousands of new tools for the reduction of high-dimensional data in order to identify the variables most responsible for a particular trait.…
This paper studies the problem of estimating a large coefficient matrix in a multiple response linear regression model when the coefficient matrix could be both of low rank and sparse in the sense that most nonzero entries concentrate on a…
We consider the following multi-component sparse PCA problem: given a set of data points, we seek to extract a small number of sparse components with disjoint supports that jointly capture the maximum possible variance. These components can…
Bayesian shrinkage methods have generated a lot of recent interest as tools for high-dimensional regression and model selection. These methods naturally facilitate tractable uncertainty quantification and incorporation of prior information.…
We consider the problem of sampling from the posterior distribution of a $d$-dimensional coefficient vector $\boldsymbol{\theta}$, given linear observations $\boldsymbol{y} = \boldsymbol{X}\boldsymbol{\theta}+\boldsymbol{\varepsilon}$. In…
The past decades have seen enormous improvements in computational inference based on statistical models, with continual enhancement in a wide range of computational tools, in competition. In Bayesian inference, first and foremost, MCMC…
This paper reviews recent developments in statistical structure learning; namely, Bayesian model reduction. Bayesian model reduction is a method for rapidly computing the evidence and parameters of probabilistic models that differ only in…