Related papers: Posterior Consistency for Bayesian Relevance Vecto…

We consider a class of linear ill-posed inverse problems arising from inversion of a compact operator with singular values which decay exponentially to zero. We adopt a Bayesian approach, assuming a Gaussian prior on the unknown function.…

This paper focuses on Bayesian shrinkage for covariance matrix estimation. We examine posterior properties and frequentist risks of Bayesian estimators based on new hierarchical inverse-Wishart priors. More precisely, we give the existence…

Hyperspectral measurements from long range sensors can give a detailed picture of the items, materials, and chemicals in a scene but analysis can be difficult, slow, and expensive due to high spatial and spectral resolutions of…

Modern data analysis often involves massive datasets with hundreds of thousands of observations, making traditional inference algorithms computationally prohibitive. Coresets are selection methods designed to choose a smaller subset of…

We examine necessary and sufficient conditions for posterior consistency under $g$-priors, including extensions to hierarchical and empirical Bayesian models. The key features of this article are that we allow the number of regressors to…

This paper derives error bounds for regression in continuous time over subsets of certain types of Riemannian manifolds.The regression problem is typically driven by a nonlinear evolution law taking values on the manifold, and it is cast as…

Reproducing Kernel Hilbert spaces (RKHS) have been a very successful tool in various areas of machine learning. Recently, Barron spaces have been used to prove bounds on the generalisation error for neural networks. Unfortunately, Barron…

In inverse problems, the parameters of a model are estimated based on observations of the model response. The Bayesian approach is powerful for solving such problems; one formulates a prior distribution for the parameter state that is…

The quality of a Bayes factor crucially depends on the number of regressors, the sample size and the prior on the regression parameters, and hence it has to be established in a case-by-case basis. In this paper we analyze the consistency of…

Gaussian processes scale prohibitively with the size of the dataset. In response, many approximation methods have been developed, which inevitably introduce approximation error. This additional source of uncertainty, due to limited…

Error estimates for kernel interpolation in Reproducing Kernel Hilbert Spaces (RKHS) usually assume quite restrictive properties on the shape of the domain, especially in the case of infinitely smooth kernels like the popular Gaussian…

The Support Vector Machine (SVM) of Vapnik (1998) has become widely established as one of the leading approaches to pattern recognition and machine learning. It expresses predictions in terms of a linear combination of kernel functions…

This paper considers a Bayesian approach for inclusion detection in nonlinear inverse problems using two known and popular push-forward prior distributions: the star-shaped and level set prior distributions. We analyze the convergence of…

From a systems biology perspective the majority of cancer models, although interesting and providing a qualitative explanation of some problems, have a major disadvantage in that they usually miss a genuine connection with experimental…

Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…

This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information…

The expressive power of Bayesian kernel-based methods has led them to become an important tool across many different facets of artificial intelligence, and useful to a plethora of modern application domains, providing both power and…

Important information on the structure of complex systems, consisting of more than one component, can be obtained by measuring to which extent the individual components exchange information among each other. Such knowledge is needed to…

Calibration of computer models is a key step in making inferences, predictions, and decisions for complex science and engineering systems. We formulate and analyze a nonparametric Bayesian methodology for computer model calibration. This…

Obtaining reliable, adaptive confidence sets for prediction functions (hypotheses) is a central challenge in sequential decision-making tasks, such as bandits and model-based reinforcement learning. These confidence sets typically rely on…