Related papers: Optimal information deletion and Bayes' theorem

Bayesian optimal experimental design (OED) provides a principled framework for selecting observations or experiments. We introduce new Bayesian design criteria based on the expected Wasserstein-$p$ distance between the prior and posterior…

Methods have been developed to identify the probability distribution of a random vector $Z$ from information consisting of its bounded range and the probability density function or moments of a quantity of interest, $Q(Z)$. The mapping from…

Theory refinement is the task of updating a domain theory in the light of new cases, to be done automatically or with some expert assistance. The problem of theory refinement under uncertainty is reviewed here in the context of Bayesian…

An efficient algorithm is developed that identifies all independencies implied by the topology of a Bayesian network. Its correctness and maximality stems from the soundness and completeness of d-separation with respect to probability…

Of the various attempts to generalize information theory to multiple variables, the most widely utilized, interaction information, suffers from the problem that it is sometimes negative. Here we reconsider from first principles the general…

The classical approach to inverse problems is based on the optimization of a misfit function. Despite its computational appeal, such an approach suffers from many shortcomings, e.g., non-uniqueness of solutions, modeling prior knowledge,…

Formulating a statistical inverse problem as one of inference in a Bayesian model has great appeal, notably for what this brings in terms of coherence, the interpretability of regularisation penalties, the integration of all uncertainties,…

In this article, a general problem of sequential statistical inference for general discrete-time stochastic processes is considered. The problem is to minimize an average sample number given that Bayesian risk due to incorrect decision does…

Bayesian neural networks (BNNs) offer a natural probabilistic formulation for inference in deep learning models. Despite their popularity, their optimality has received limited attention through the lens of statistical decision theory. In…

The problem of assigning probability distributions which objectively reflect the prior information available about experiments is one of the major stumbling blocks in the use of Bayesian methods of data analysis. In this paper the method of…

We consider a sequential decision making task, where the goal is to optimize an unknown function without evaluating parameters that violate an a~priori unknown (safety) constraint. A common approach is to place a Gaussian process prior on…

We consider the decentralized binary hypothesis testing problem on trees of bounded degree and increasing depth. For a regular tree of depth t and branching factor k>=2, we assume that the leaves have access to independent and identically…

We investigate the data distribution valuation problem, which aims to quantify the values of data distributions from their samples. This is a recently proposed problem that is related to but different from classical data valuation and can…

Modern machine learning applications should be able to address the intrinsic challenges arising over inference on massive real-world datasets, including scalability and robustness to outliers. Despite the multiple benefits of Bayesian…

We propose a distributed Bayesian quickest change detection algorithm for sensor networks, based on a random gossip inter-sensor communication structure. Without a control or fusion center, each sensor executes its local change detection…

Machine unlearning refers to the task of removing a subset of training data, thereby removing its contributions to a trained model. Approximate unlearning are one class of methods for this task which avoid the need to retrain the model from…

Consider a network where a wireless base station (BS) connects multiple source-destination pairs. Packets from each source are generated according to a renewal process and are enqueued in a single-packet queue that stores only the freshest…

Bounded confidence opinion dynamics model the propagation of information in social networks. However in the existing literature, opinions are only viewed as abstract quantities without semantics rather than as part of a decision-making…

Optimum parameter estimation methods require knowledge of a parametric probability density that statistically describes the available observations. In this work we examine Bayesian and non-Bayesian parameter estimation problems under a…

Bayesian inference gets its name from *Bayes's theorem*, expressing posterior probabilities for hypotheses about a data generating process as the (normalized) product of prior probabilities and a likelihood function. But Bayesian inference…