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Recursive Bayesian inference, in which posterior beliefs are updated in light of accumulating data, is a tool for implementing Bayesian models in applications with streaming and/or very large data sets. As the posterior of one iteration…
Mixture models are widely used in modeling heterogeneous data populations. A standard approach of mixture modeling assumes that the mixture component takes a parametric kernel form. In many applications, making parametric assumptions on the…
Bayesian posterior inference is prevalent in various machine learning problems. Variational inference provides one way to approximate the posterior distribution, however its expressive power is limited and so is the accuracy of resulting…
One of the core problems of modern statistics is to approximate difficult-to-compute probability densities. This problem is especially important in Bayesian statistics, which frames all inference about unknown quantities as a calculation…
The natural habitat of most Bayesian methods is data represented by exchangeable sequences of observations, for which de Finetti's theorem provides the theoretical foundation. Dirichlet process clustering, Gaussian process regression, and…
This paper presents a methodology for creating streaming, distributed inference algorithms for Bayesian nonparametric (BNP) models. In the proposed framework, processing nodes receive a sequence of data minibatches, compute a variational…
Learning the structure of Bayesian networks from data provides insights into underlying processes and the causal relationships that generate the data, but its usefulness depends on the homogeneity of the data population, a condition often…
In binary-transaction data-mining, traditional frequent itemset mining often produces results which are not straightforward to interpret. To overcome this problem, probability models are often used to produce more compact and conclusive…
Stochastic kinetic models are often used to describe complex biological processes. Typically these models are analytically intractable and have unknown parameters which need to be estimated from observed data. Ideally we would have…
The Bayesian approach to inference stands out for naturally allowing borrowing information across heterogeneous populations, with different samples possibly sharing the same distribution. A popular Bayesian nonparametric model for…
We consider the problem of analyzing the heterogeneity of clustering distributions for multiple groups of observed data, each of which is indexed by a covariate value, and inferring global clusters arising from observations aggregated over…
Mutual information is widely used in artificial intelligence, in a descriptive way, to measure the stochastic dependence of discrete random variables. In order to address questions such as the reliability of the empirical value, one must…
Mutual information is widely used in artificial intelligence, in a descriptive way, to measure the stochastic dependence of discrete random variables. In order to address questions such as the reliability of the empirical value, one must…
To understand biological diversification, it is important to account for large-scale processes that affect the evolutionary history of groups of co-distributed populations of organisms. Such events predict temporally clustered divergences…
Practical tools for clustering streaming data must be fast enough to handle the arrival rate of the observations. Typically, they also must adapt on the fly to possible lack of stationarity; i.e., the data statistics may be time-dependent…
Here we focus on the description of the mechanisms behind the process of information aggregation and decision making, a basic step to understand emergent phenomena in society, such as trends, information spreading or the wisdom of crowds.…
This article attempts to offer some perspectives on Bayesian inference for finite population quantities when the units in the population are assumed to exhibit complex dependencies. Beginning with an overview of Bayesian hierarchical…
In the streaming data setting, where data arrive continuously or in frequent batches and there is no pre-determined amount of total data, Bayesian models can employ recursive updates, incorporating each new batch of data into the model…
Bayesian analysis is increasingly popular for use in social science and other application areas where the data are observations from an informative sample. An informative sampling design leads to inclusion probabilities that are correlated…
We describe a new and computationally efficient Bayesian methodology for inferring species trees and demographics from unlinked binary markers. Likelihood calculations are carried out using diffusion models of allele frequency dynamics…