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Gaussian Processes (GPs) are a generic modelling tool for supervised learning. While they have been successfully applied on large datasets, their use in safety-critical applications is hindered by the lack of good performance guarantees. To…
We consider hypothesis testing for the null hypothesis being represented as an arbitrary-shaped region in the parameter space. We compute an approximate p-value by counting how many times the null hypothesis holds in bootstrap replicates.…
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 Bayesian inference, making deductions about a parameter of interest requires one to sample from or compute an integral against a posterior distribution. A popular method to make these computations cheaper in high-dimensional settings is…
Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…
Approximate Bayesian computation (ABC) methods are used to approximate posterior distributions using simulation rather than likelihood calculations. We introduce Gaussian process (GP) accelerated ABC, which we show can significantly reduce…
In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…
We study the use of Gaussian process emulators to approximate the parameter-to-observation map or the negative log-likelihood in Bayesian inverse problems. We prove error bounds on the Hellinger distance between the true posterior…
This paper derives a new strong Gaussian approximation bound for the sum of independent random vectors. The approach relies on the optimal transport theory and yields \textit{explicit} dependence on the dimension size $p$ and the sample…
In this article, we present data-subsetting algorithms that allow for the approximate and scalable implementation of the Bayesian bootstrap. They are analogous to two existing algorithms in the frequentist literature: the bag of little…
For any $\varepsilon > 0$, we prove that $k$-Dimensional Matching is hard to approximate within a factor of $k/(12 + \varepsilon)$ for large $k$ unless $\textsf{NP} \subseteq \textsf{BPP}$. Listed in Karp's 21 $\textsf{NP}$-complete…
Probabilistic regression models typically use the Maximum Likelihood Estimation or Cross-Validation to fit parameters. These methods can give an advantage to the solutions that fit observations on average, but they do not pay attention to…
Many functions have approximately-known upper and/or lower bounds, potentially aiding the modeling of such functions. In this paper, we introduce Gaussian process models for functions where such bounds are (approximately) known. More…
Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
In this paper, we address the problem of conducting statistical inference in settings involving large-scale data that may be high-dimensional and contaminated by outliers. The high volume and dimensionality of the data require distributed…
Scalable Gaussian process (GP) inference is essential for sequential decision-making tasks, yet improving GP scalability remains a challenging problem with many open avenues of research. This paper focuses on iterative GPs, where iterative…
We propose an extensive simulation study to compare some variable selection procedures in a high-dimensional framework. Assuming that the relationship between the actives variables and the response variable is linear, the high-dimensional…
The Gaussian mechanism is one differential privacy mechanism commonly used to protect numerical data. However, it may be ill-suited to some applications because it has unbounded support and thus can produce invalid numerical answers to…
Maximizing high-dimensional, non-convex functions through noisy observations is a notoriously hard problem, but one that arises in many applications. In this paper, we tackle this challenge by modeling the unknown function as a sample from…