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Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the…
Data-driven optimization of sampling patterns in MRI has recently received a significant attention.Following recent observations on the combinatorial number of minimizers in off-the-grid optimization, we propose a framework to globally…
This paper addresses the problem of neighborhood selection for Gaussian graphical models. We present two heuristic algorithms: a forward-backward greedy algorithm for general Gaussian graphical models based on mutual information test, and a…
The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general…
In a previous paper (gr-qc/0105100) we derived a set of near-optimal signal detection techniques for gravitational wave detectors whose noise probability distributions contain non-Gaussian tails. The methods modify standard methods by…
In this work, we study scaling limits of shallow Bayesian neural networks (BNNs) via their connection to Gaussian processes (GPs), with an emphasis on statistical modeling, identifiability, and scalable inference. We first establish a…
Score-based algorithms that learn Bayesian Network (BN) structures provide solutions ranging from different levels of approximate learning to exact learning. Approximate solutions exist because exact learning is generally not applicable to…
Link prediction is a fundamental task in statistical network analysis. Recent advances have been made on learning flexible nonparametric Bayesian latent feature models for link prediction. In this paper, we present a max-margin learning…
Low-discrepancy designs play a central role in quasi-Monte Carlo methods and are increasingly influential in other domains such as machine learning, robotics and computer graphics, to name a few. In recent years, one such low-discrepancy…
In this paper, we examine previous work on the naive Bayesian classifier and review its limitations, which include a sensitivity to correlated features. We respond to this problem by embedding the naive Bayesian induction scheme within an…
For most optimisation methods an essential assumption is the vector space structure of the feasible set. This condition is not fulfilled if we consider optimisation problems over the sphere. We present an algorithm for solving a special…
Bayesian optimization through Gaussian process regression is an effective method of optimizing an unknown function for which every measurement is expensive. It approximates the objective function and then recommends a new measurement point…
K-Nearest Neighbours (k-NN) is a popular classification and regression algorithm, yet one of its main limitations is the difficulty in choosing the number of neighbours. We present a Bayesian algorithm to compute the posterior probability…
In most gene expression data, the number of training samples is very small compared to the large number of genes involved in the experiments. However, among the large amount of genes, only a small fraction is effective for performing a…
Knot-based, sparse Gaussian processes have enjoyed considerable success as scalable approximations to full Gaussian processes. Problems can occur, however, when knot selection is done by optimizing the marginal likelihood. For example, the…
Bayesian optimisation has proven to be a powerful tool for expensive global black-box optimisation problems. In this paper, we propose new Bayesian optimisation variants of the popular Knowledge Gradient acquisition functions for problems…
Computing the exact likelihood of data in large Bayesian networks consisting of thousands of vertices is often a difficult task. When these models contain many deterministic conditional probability tables and when the observed values are…
Bayesian estimation of Gaussian graphical models has proven to be challenging because the conjugate prior distribution on the Gaussian precision matrix, the G-Wishart distribution, has a doubly intractable partition function. Recent…
Bayesian networks are convenient graphical expressions for high dimensional probability distributions representing complex relationships between a large number of random variables. They have been employed extensively in areas such as…