Related papers: Optimal Gaussian Approximation for Multiple Time S…
Gaussian Process (GP) regression is a flexible non-parametric approach to approximate complex models. In many cases, these models correspond to processes with bounded physical properties. Standard GP regression typically results in a proxy…
We design efficient approximation algorithms for maximizing the expectation of the supremum of families of Gaussian random variables. In particular, let $\mathrm{OPT}:=\max_{\sigma_1,\cdots,\sigma_n}\mathbb{E}\left[\sum_{j=1}^{m}\max_{i\in…
Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…
This paper focuses on the problem of determining as large a region as possible where a function exceeds a given threshold with high probability. We assume that we only have access to a noise-corrupted version of the function and that…
By combining the Minkowski inequality and the quantum Chernoff bound, we derive easy-to-compute upper bounds for the error probability affecting the optimal discrimination of Gaussian states. In particular, these bounds are useful when the…
Variable selection for Gaussian process models is often done using automatic relevance determination, which uses the inverse length-scale parameter of each input variable as a proxy for variable relevance. This implicitly determined…
We obtain almost sure limit theorems for partial maxima of norms of a sequence of Banach-valued Gaussian random variables.
In the setting where we have $n$ independent observations of a random variable $X$, we derive explicit error bounds in total variation distance when approximating the number of observations equal to the maximum of the sample (in the case…
The correlation length-scale next to the noise variance are the most used hyperparameters for the Gaussian processes. Typically, stationary covariance functions are used, which are only dependent on the distances between input points and…
We establish optimal logarithmic rates of convergence in the strong invariance principle for multivariate cumulative processes in the Smith's sense. Exponential probabilistic inequalities of Koml\'{o}s-Major-Tusn\'{a}dy type are obtained.…
The Laplace approximation is a popular method for constructing a Gaussian approximation to the Bayesian posterior and thereby approximating the posterior mean and variance. But approximation quality is a concern. One might consider using…
Model selection aims to find the best model in terms of accuracy, interpretability or simplicity, preferably all at once. In this work, we focus on evaluating model performance of Gaussian process models, i.e. finding a metric that provides…
Gaussian graphical model is a graphical representation of the dependence structure for a Gaussian random vector. It is recognized as a powerful tool in different applied fields such as bioinformatics, error-control codes, speech language,…
Time estimation is a fundamental task that underpins precision measurement, global navigation systems, financial markets, and the organisation of everyday life. Many biological processes also depend on time estimation by nanoscale clocks,…
The approximation of a discrete probability distribution $\mathbf{t}$ by an $M$-type distribution $\mathbf{p}$ is considered. The approximation error is measured by the informational divergence $\mathbb{D}(\mathbf{t}\Vert\mathbf{p})$, which…
We consider the problem of approximating a general Gaussian location mixture by finite mixtures. The minimum order of finite mixtures that achieve a prescribed accuracy (measured by various $f$-divergences) is determined within constant…
Although there is an extensive literature on the maxima of Gaussian processes, there are relatively few non-asymptotic bounds on their lower-tail probabilities. The aim of this paper is to develop such a bound, while also allowing for many…
We characterize the sample size required for accurate graphical model selection from non-stationary samples. The observed data is modeled as a vector-valued zero-mean Gaussian random process whose samples are uncorrelated but have different…
Gaussian Processes face two primary challenges: constructing models for large datasets and selecting the optimal model. This master's thesis tackles these challenges in the low-dimensional case. We examine recent convergence results to…
Gaussian Process Regression is a popular nonparametric regression method based on Bayesian principles that provides uncertainty estimates for its predictions. However, these estimates are of a Bayesian nature, whereas for some important…