Related papers: Lower bounds for posterior rates with Gaussian pro…

This paper is a continuation of work arXiv:2006.09583 devoted to establishment of the convergence rate in the strong invariance principle for cumulative processes. We establish optimal rate of convergence for the case when regeneration…

This paper investigates the approximation of Gaussian random variables in Banach spaces, focusing on the high-probability bounds for the approximation of Gaussian random variables using finitely many observations. We derive non-asymptotic…

Whilst deep neural networks have shown great empirical success, there is still much work to be done to understand their theoretical properties. In this paper, we study the relationship between random, wide, fully connected, feedforward…

The hyperparameters in Gaussian process regression (GPR) model with a specified kernel are often estimated from the data via the maximum marginal likelihood. Due to the non-convexity of marginal likelihood with respect to the…

We provide general conditions to derive posterior concentration rates for Aalen counting processes. The conditions are designed to resemble those proposed in the literature for the problem of density estimation, for instance in Ghosal et…

We derive some simple relations that demonstrate how the posterior convergence rate is related to two driving factors: a "penalized divergence" of the prior, which measures the ability of the prior distribution to propose a nonnegligible…

We prove rates of convergence and robustness to prior misspecification within a Generalised Variational Inference (GVI) framework with bounded divergences. This addresses a significant open challenge for GVI and Federated GVI that employ a…

The paper characterizes uniform convergence rate for general classes of wavelet expansions of stationary Gaussian random processes. The convergence in probability is considered.

We propose a lower bound on the log marginal likelihood of Gaussian process regression models that can be computed without matrix factorisation of the full kernel matrix. We show that approximate maximum likelihood learning of model…

We consider estimation of a sparse parameter vector that determines the covariance matrix of a Gaussian random vector via a sparse expansion into known "basis matrices". Using the theory of reproducing kernel Hilbert spaces, we derive lower…

This paper proposes a new algorithm for Gaussian process classification based on posterior linearisation (PL). In PL, a Gaussian approximation to the posterior density is obtained iteratively using the best possible linearisation of the…

Bounds on Bayesian posterior convergence rates, assuming the prior satisfies both local and global support conditions, are now readily available. In this paper we explore, in the context of density estimation, Bayesian convergence rates…

We study the performance of nonparametric Bayes procedures for one-dimensional diffusions with periodic drift. We improve existing convergence rate results for Gaussian process (GP) priors with fixed hyper parameters. Moreover, we exhibit…

The randomized Gauss--Seidel method and its extension have attracted much attention recently and their convergence rates have been considered extensively. However, the convergence rates are usually determined by upper bounds, which cannot…

New results on uniform convergence in probability for expansions of Gaussian random processes using compactly supported wavelets are given. The main result is valid for general classes of nonstationary processes. An application of the…

Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of…

We obtain a Bernstein type Gaussian concentration inequality for martingales. Our inequality improves the Azuma-Hoeffding inequality for moderate deviations $x$. Following the work of McDiarmid (1989), Talagrand (1996) and Boucheron, Lugosi…

Bayesian posterior distributions are widely used for inference, but their dependence on a statistical model creates some challenges. In particular, there may be lots of nuisance parameters that require prior distributions and posterior…

We consider the fractional posterior distribution that is obtained by updating a prior distribution via Bayes theorem with a fractional likelihood function, a usual likelihood function raised to a fractional power. First, we analyze the…

Gaussian processes are ubiquitous in nature and engineering. A case in point is a class of neural networks in the infinite-width limit, whose priors correspond to Gaussian processes. Here we perturbatively extend this correspondence to…