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We develop methods for efficient amortized approximate Bayesian inference over posterior distributions of probabilistic clustering models, such as Dirichlet process mixture models. The approach is based on mapping distributed,…

This paper develops a methodology for approximating the posterior first two moments of the posterior distribution in Bayesian inference. Partially specified probability models, which are defined only by specifying means and variances, are…

This paper considers properties of an optimization based sampler for targeting the posterior distribution when the likelihood is intractable and auxiliary statistics are used to summarize information in the data. Our reverse sampler…

Comparing competing mathematical models of complex natural processes is a shared goal among many branches of science. The Bayesian probabilistic framework offers a principled way to perform model comparison and extract useful metrics for…

Semi-structured regression models enable the joint modeling of interpretable structured and complex unstructured feature effects. The structured model part is inspired by statistical models and can be used to infer the input-output…

In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…

When the likelihood is analytically unavailable and computationally intractable, approximate Bayesian computation (ABC) has emerged as a widely used methodology for approximate posterior inference; however, it suffers from severe…

Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are however sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this…

While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However,…

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…

We propose a framework for general Bayesian inference. We argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the…

The importance of interpretability of machine learning models has been increasing due to emerging enterprise predictive analytics, threat of data privacy, accountability of artificial intelligence in society, and so on. Piecewise linear…

When random effects are correlated with sample design variables, the usual approach of employing individual survey weights (constructed to be inversely proportional to the unit survey inclusion probabilities) to form a pseudo-likelihood no…

Finite mixtures are a flexible modeling tool for irregularly shaped densities and samples from heterogeneous populations. When modeling with mixtures using an exchangeable prior on the component features, the component labels are arbitrary…

Boosting methods are widely used in statistical learning to deal with high-dimensional data due to their variable selection feature. However, those methods lack straightforward ways to construct estimators for the precision of the…

Bayesian inference is often implemented using approximations, which can yield interval estimates that are too narrow, not fully capturing the uncertainty in the posterior distribution. We address the question of how to adjust these…

Parametric Bayesian modeling offers a powerful and flexible toolbox for machine learning. Yet the model, however detailed, may still be wrong, and this can make inferences untrustworthy. In this paper we introduce a new class of…

Linear mixed models are a versatile statistical tool to study data by accounting for fixed effects and random effects from multiple sources of variability. In many situations, a large number of candidate fixed effects is available and it is…

We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood function is constructed…

Bayesian decision theory provides an elegant framework for acting optimally under uncertainty when tractable posterior distributions are available. Modern Bayesian models, however, typically involve intractable posteriors that are…