Related papers: Learning Sparse Fixed-Structure Gaussian Bayesian …

Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…

We develop optimal algorithms for learning undirected Gaussian trees and directed Gaussian polytrees from data. We consider both problems of distribution learning (i.e. in KL distance) and structure learning (i.e. exact recovery). The first…

We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…

We propose a new class of Bayesian neural networks (BNNs) that can be trained using noisy data of variable fidelity, and we apply them to learn function approximations as well as to solve inverse problems based on partial differential…

Gaussian graphical models are a popular tool to learn the dependence structure in the form of a graph among variables of interest. Bayesian methods have gained in popularity in the last two decades due to their ability to simultaneously…

Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…

Structure learning of Bayesian networks is an important problem that arises in numerous machine learning applications. In this work, we present a novel approach for learning the structure of Bayesian networks using the solution of an…

Learning high-dimensional distributions is a significant challenge in machine learning and statistics. Classical research has mostly concentrated on asymptotic analysis of such data under suitable assumptions. While existing works…

Bayesian networks provide a method of representing conditional independence between random variables and computing the probability distributions associated with these random variables. In this paper, we extend Bayesian network structures to…

It is well known in the literature that the problem of learning the structure of Bayesian networks is very hard to tackle: its computational complexity is super-exponential in the number of nodes in the worst case and polynomial in most…

A Bayesian network is a directed acyclic graph that represents statistical dependencies between variables of a joint probability distribution. A fundamental task in data science is to learn a Bayesian network from observed data.…

We consider Bayesian optimization of the output of a network of functions, where each function takes as input the output of its parent nodes, and where the network takes significant time to evaluate. Such problems arise, for example, in…

We propose a mixed integer programming (MIP) model and iterative algorithms based on topological orders to solve optimization problems with acyclic constraints on a directed graph. The proposed MIP model has a significantly lower number of…

In this paper, we study the problem of structure learning for Bayesian networks in which nodes take discrete values. The problem is NP-hard in general but we show that under certain conditions we can recover the true structure of a Bayesian…

We address the problem of Bayesian structure learning for domains with hundreds of variables by employing non-parametric bootstrap, recursively. We propose a method that covers both model averaging and model selection in the same framework.…

Many asymptotically minimax procedures for function estimation often rely on somewhat arbitrary and restrictive assumptions such as isotropy or spatial homogeneity. This work enhances the theoretical understanding of Bayesian additive…

Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…

Efficiently quantifying predictive uncertainty in medical images remains a challenge. While Bayesian neural networks (BNN) offer predictive uncertainty, they require substantial computational resources to train. Although Bayesian…

We consider a Bayesian approach to model selection in Gaussian linear regression, where the number of predictors might be much larger than the number of observations. From a frequentist view, the proposed procedure results in the penalized…

In Bayesian structure learning, we are interested in inferring a distribution over the directed acyclic graph (DAG) structure of Bayesian networks, from data. Defining such a distribution is very challenging, due to the combinatorially…