Related papers: A Robbins--Monro Sequence That Can Exploit Prior I…

In this article, we propose a sampling-based motion planning algorithm equipped with an information-theoretic convergence criterion for incremental informative motion planning. The proposed approach allows dense map representations and…

This dissertation shows that careful injection of noise into sample data can substantially speed up Expectation-Maximization algorithms. Expectation-Maximization algorithms are a class of iterative algorithms for extracting maximum…

A novel block prior is proposed for adaptive Bayesian estimation. The prior does not depend on the smoothness of the function or the sample size. It puts sufficient prior mass near the true signal and automatically concentrates on its…

We apply nonparametric Bayesian methods to study the problem of estimating the intensity function of an inhomogeneous Poisson process. We exhibit a prior on intensities which both leads to a computationally feasible method and enjoys…

Minimizing the empirical risk is a popular training strategy, but for learning tasks where the data may be noisy or heavy-tailed, one may require many observations in order to generalize well. To achieve better performance under less…

We consider nonparametric estimation for functional autoregressive processes with Markov switching. First, we study the case where complete data is available; i.e. when we observe the Markov switching regime. Then we estimate the regression…

Prior information is often incorporated informally when planning a clinical trial. Here, we present an approach on how to incorporate prior information, such as data from historical clinical trials, into the nuisance parameter based sample…

This paper considers the problem of recovering a structured signal from a relatively small number of noisy measurements with the aid of a similar signal which is known beforehand. We propose a new approach to integrate prior information…

Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…

Using instruments comprising ordered responses to items are ubiquitous for studying many constructs of interest. However, using such an item response format may lead to items with response categories infrequently endorsed or unendorsed…

In Bayesian statistics, the choice of prior distribution is often debatable, especially if prior knowledge is limited or data are scarce. In imprecise probability, sets of priors are used to accurately model and reflect prior knowledge.…

The goal of this paper is to provide theorems on convergence rates of posterior distributions that can be applied to obtain good convergence rates in the context of density estimation as well as regression. We show how to choose priors so…

In recent years deep neural networks have been successfully applied to the domains of reinforcement learning \cite{bengio2009learning,krizhevsky2012imagenet,hinton2006reducing}. Deep reinforcement learning \cite{mnih2015human} is reported…

In Bayesian analysis, reference priors are widely recognized for their objective nature. Yet, they often lead to intractable and improper priors, which complicates their application. Besides, informed prior elicitation methods are penalized…

In this paper, we propose a Robbins-Monro augmented Lagrangian method (RMALM) to solve a class of constrained stochastic convex optimization, which can be regarded as a hybrid of the Robbins-Monro type stochastic approximation method and…

Bayesian inversion is central to the quantification of uncertainty within problems arising from numerous applications in science and engineering. To formulate the approach, four ingredients are required: a forward model mapping the unknown…

Motivated by Bayesian inference with highly informative data we analyze the performance of random walk-like Metropolis-Hastings algorithms for approximate sampling of increasingly concentrating target distributions. We focus on Gaussian…

Denoising Diffusion Probabilistic Models (DDPMs) have achieved impressive performance on various generation tasks. By modeling the reverse process of gradually diffusing the data distribution into a Gaussian distribution, generating a…

In many high-dimensional prediction or classification tasks, complementary data on the features are available, e.g. prior biological knowledge on (epi)genetic markers. Here we consider tasks with numerical prior information that provide an…

In the past few years, the problem of distributed consensus has received a lot of attention, particularly in the framework of ad hoc sensor networks. Most methods proposed in the literature address the consensus averaging problem by…