Related papers: Learning with Sparsely Permuted Data: A Robust Bay…
Achieving robust uncertainty quantification for deep neural networks represents an important requirement in many real-world applications of deep learning such as medical imaging where it is necessary to assess the reliability of a neural…
Robust Bayesian inference is the calculation of posterior probability bounds given perturbations in a probabilistic model. This paper focuses on perturbations that can be expressed locally in Bayesian networks through convex sets of…
Shuffled regression concerns settings in which covariates and responses are observed without their correct pairing. In dependent-data problems, a second form of missing correspondence can arise when responses are also detached from the…
Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…
We extend the work of Hahn and Carvalho (2015) and develop a doubly-regularized sparse regression estimator by synthesizing Bayesian regularization with penalized least squares within a decision-theoretic framework. In contrast to existing…
Recent progress in variational inference has paid much attention to the flexibility of variational posteriors. One promising direction is to use implicit distributions, i.e., distributions without tractable densities as the variational…
We propose a novel adaptive importance sampling scheme for Bayesian inversion problems where the inference of the variables of interest and the power of the data noise is split. More specifically, we consider a Bayesian analysis for the…
The efficient resolution of Bayesian inverse problems remains challenging due to the high computational cost of traditional sampling methods. In this paper, we propose a novel framework that integrates Conditional Flow Matching (CFM) with a…
We propose a new approach to Bayesian prediction that caters for models with a large number of parameters and is robust to model misspecification. Given a class of high-dimensional (but parametric) predictive models, this new approach…
This paper proposes a flexible Bayesian approach to multiple imputation using conditional Gaussian mixtures. We introduce novel shrinkage priors for covariate-dependent mixing proportions in the mixture models to automatically select the…
Sparse regression on a library of candidate features has developed as the prime method to discover the partial differential equation underlying a spatio-temporal data-set. These features consist of higher order derivatives, limiting model…
Bayesian hierarchical models can provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models typically comprise a conditionally Gaussian prior model for the unknown which is augmented by a generalized…
This work addresses the problem of high-dimensional classification by exploring the generalized Bayesian logistic regression method under a sparsity-inducing prior distribution. The method involves utilizing a fractional power of the…
This paper investigates the high-dimensional linear regression with highly correlated covariates. In this setup, the traditional sparsity assumption on the regression coefficients often fails to hold, and consequently many model selection…
Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical…
In indirect measurements, the measurand is determined by solving an inverse problem which requires a model of the measurement process. Such models are often approximations and introduce systematic errors leading to a bias of the posterior…
Learning with limited data is one of the biggest problems of machine learning. Current approaches to this issue consist in learning general representations from huge amounts of data before fine-tuning the model on a small dataset of…
In this work, we address the problem of solving a series of underdetermined linear inverse problems subject to a sparsity constraint. We generalize the spike-and-slab prior distribution to encode a priori correlation of the support of the…
Selection bias arises when the probability that an observation enters a dataset depends on variables related to the quantities of interest, leading to systematic distortions in estimation and uncertainty quantification. For example, in…
We present a novel binary convex reformulation of the sparse regression problem that constitutes a new duality perspective. We devise a new cutting plane method and provide evidence that it can solve to provable optimality the sparse…