Related papers: Posterior Variance Analysis of Gaussian Processes …

Vanilla variational inference finds an optimal approximation to the Bayesian posterior distribution, but even the exact Bayesian posterior is often not meaningful under model misspecification. We propose predictive variational inference…

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…

Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data…

Accurate tuning of hyperparameters is crucial to ensure that models can generalise effectively across different settings. In this paper, we present theoretical guarantees for hyperparameter selection using variational Bayes in the…

We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set G up to the smallest possible additive term, called the convergence rate. When the reference set…

Adversarial example (AE) is an attack method for machine learning, which is crafted by adding imperceptible perturbation to the data inducing misclassification. In the current paper, we investigated the upper bound of the probability of…

Consider a normal location model $X \mid \theta \sim N(\theta, \sigma^2)$ with known $\sigma^2$. Suppose $\theta \sim G_0$, where the prior $G_0$ has zero mean and variance bounded by $V$. Let $G_1$ be a possibly misspecified prior with…

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 consider Bayesian inference of banded covariance matrices and propose a post-processed posterior. The post-processing of the posterior consists of two steps. In the first step, posterior samples are obtained from the conjugate…

We introduce a novel stochastic variational inference method for Gaussian process ($\mathcal{GP}$) regression, by deriving a posterior over a learnable set of coresets: i.e., over pseudo-input/output, weighted pairs. Unlike former free-form…

Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower…

Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…

Information-theoretic generalization bounds analyze stochastic optimization by relating expected generalization error to the mutual information between learned parameters and training data. Virtual perturbation analyses of SGD add auxiliary…

We provide sample complexity upper bounds for agnostically learning multivariate Gaussians under the constraint of approximate differential privacy. These are the first finite sample upper bounds for general Gaussians which do not impose…

In this position paper, we argue that many post-mortem generalization measures -- those computed on trained networks -- are \textbf{fragile}: small training modifications that barely affect the performance of the underlying deep neural…

Many control tasks can be formulated as a tracking problem of a known or unknown reference signal. Examples are movement compensation in collaborative robotics, the synchronisation of oscillations for power systems or reference tracking of…

The PAC-Bayesian approach is a powerful set of techniques to derive non- asymptotic risk bounds for random estimators. The corresponding optimal distribution of estimators, usually called the Gibbs posterior, is unfortunately intractable.…

Running a reliability analysis on engineering problems involving complex numerical models can be computationally very expensive, requiring advanced simulation methods to reduce the overall numerical cost. Gaussian process based active…

Gaussian process models are commonly used as emulators for computer experiments. However, developing a Gaussian process emulator can be computationally prohibitive when the number of experimental samples is even moderately large. Local…

In Bayesian decision theory, it is known that robustness with respect to the loss and the prior can be improved by adding new observations. In this article we study the rate of robustness improvement with respect to the number of…