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This article expands the framework of Bayesian inference and provides direct probabilistic methods for approaching inference tasks that are typically handled with information theory. We treat Bayesian probability updating as a random…

Online learning is an inferential paradigm in which parameters are updated incrementally from sequentially available data, in contrast to batch learning, where the entire dataset is processed at once. In this paper, we assume that…

Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance,…

We address the problem of learning of continuous exponential family distributions with unbounded support. While a lot of progress has been made on learning of Gaussian graphical models, we still lack scalable algorithms for reconstructing…

Bayesian inference is an important technique throughout statistics. The essence of Beyesian inference is to derive the posterior belief updated from prior belief by the learned information, which is a set of differentially private answers…

The classical Bayesian posterior arises naturally as the unique solution of several different optimization problems, without the necessity of interpreting data as conditional probabilities and then using Bayes' Theorem. For example, the…

Large-scale randomized experiments, sometimes called A/B tests, are increasingly prevalent in many industries. Though such experiments are often analyzed via frequentist $t$-tests, arguably such analyses are deficient: $p$-values are hard…

We derive a novel generative model from iterative Gaussian posterior inference. By treating the generated sample as an unknown variable, we can formulate the sampling process in the language of Bayesian probability. Our model uses a…

The link with exponential families has allowed $k$-means clustering to be generalized to a wide variety of data generating distributions in exponential families and clustering distortions among Bregman divergences. Getting the framework to…

This paper presents an approximate method for performing Bayesian inference in models with conditional independence over a decentralized network of learning agents. The method first employs variational inference on each individual learning…

Bayesian estimation is increasingly popular for performing model based inference to support policymaking. These data are often collected from surveys under informative sampling designs where subject inclusion probabilities are designed to…

Updating $\textit{a priori}$ information given some observed data is the core tenet of Bayesian inference. Bayesian transfer learning extends this idea by incorporating information from a related dataset to improve the inference on the…

Increasingly complex applications involve large datasets in combination with non-linear and high dimensional mathematical models. In this context, statistical inference is a challenging issue that calls for pragmatic approaches that take…

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…

An agent is a misspecified Bayesian if she updates her belief using Bayes' rule given a subjective, possibly misspecified model of her signals. This paper shows that a belief sequence is consistent with misspecified Bayesian updating if and…

Mixture models are widely used in Bayesian statistics and machine learning, in particular in computational biology, natural language processing and many other fields. Variational inference, a technique for approximating intractable…

In statistical practice, whether a Bayesian or frequentist approach is used in inference depends not only on the availability of prior information but also on the attitude taken toward partial prior information, with frequentists tending to…

Score-driven models update time-varying parameters using conditional likelihood scores. This paper develops a Bayesian interpretation of such updates through Tweedie's formula, which connects posterior mean corrections with marginal scores.…

This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…

Entropic tilting (ET) is a Bayesian decision-analytic method for constraining distributions to satisfy defined targets or bounds for sets of expectations. This report recapitulates the foundations and basic theory of ET for conditioning…