BAYSM 2025

Title: Data Augmentation Approaches for Inference of Partially Observed Epidemics with Individual Heterogeneity

Abstract: Understanding the dynamics of infectious disease transmissions requires models that account for both transmission processes and the evolving contact networks underlying them. We propose a generative framework that couples a stochastic epidemic model with a dynamic, adaptive network structure, allowing infection rates to vary with individual-level covariates and network evolution to depend on disease status. This joint process is formulated as a continuous-time Markov chain, capturing the interplay between disease transmission and contact network changes. To address the challenge of inference from partially observed epidemic data, we develop data-augmentation algorithms that efficiently impute missing infection and recovery times while respecting the constraints imposed by the dynamic network structure. Such data augmentation strategy can be implemented through a Markov chain Monte Carlo inference scheme or a stochastic expectation-maximization (EM) algorithm. Through extensive simulations and application to real-world influenza transmission data with high-resolution contact tracing, we demonstrate the efficiency and accuracy of our inference approaches in recovering epidemic parameters with uncertainty quantification. Our framework provides a powerful tool for studying disease transmission on dynamic social networks using modern epidemiological data sources.

Title: Advances in Distribution Compression and Its Consequences

Abstract: This talk will introduce a range of new tools (all part of the python repo goodpoints) for summarizing a probability distribution more effectively than independent sampling or standard Markov chain Monte Carlo thinning in near-linear time. We will also demonstrate how these methods provide provably and practically significant computational speeds ups for a range of machine learning tasks: Monte Carlo Integration, Debiasing Markov Chains, Hypothesis Testing, Kernel Smoothing, Kernel Regression, Attention in transformers, and Stochastic Gradient Methods.
Based on joint work with Kyuseong Choi, Carles-Domingo Enrich, Albert Gong, Lingxiao Li, Abhishek Shetty, Lester Mackey.
Kernel Thinning (arXiv:2105.05842)
Generalized Kernel Thinning (arXiv:2110.01593)
Distribution Compression in Near-linear Time (arXiv:2111.07941)
Compress Then Test: Powerful Kernel Testing in Near-linear Time (arXiv:2301.05974)
Debiased Distribution Compression (arxiv:2404.12290)
Supervised Kernel Thinning (arxiv:2410.13749)

Title: Spectral gap bounds for reversible hybrid Gibbs chains

Abstract: Hybrid Gibbs samplers represent a prominent class of approximated Gibbs algorithms that utilize Markov chains to approximate conditional distributions, with the Metropolis-within-Gibbs algorithm standing out as a well-known example. Despite their widespread use in both statistical and non-statistical applications, little is known about their convergence properties. In this talk, I will describe a new type of bound on the convergence rates of hybrid random-scan Gibbs algorithms. It is shown that the absolute spectral gap of a hybrid Gibbs chain can be bounded based on the absolute spectral gap of the exact Gibbs chain and the absolute spectral gaps of the Markov chains employed for conditional distribution approximations. The bound can be extended to other reversible MCMC algorithms with certain hybrid structures.

Title: Graph-Aligned Random Partition Model (GARP)

Abstract: Bayesian nonparametric mixtures and random partition models are powerful tools for probabilistic clustering. However, standard independent mixture models can be restrictive in some applications such as inference on cell lineage due to the biological relations of the clusters. The increasing availability of large genomic data requires new statistical tools to perform model-based clustering and infer the relationship between homogeneous subgroups of units. Motivated by single-cell RNA data we develop a novel dependent mixture model to jointly perform cluster analysis and align the clusters on a graph. Our flexible graph-aligned random partition model (GARP) exploits Gibbs-type priors as building blocks, allowing us to derive analytical results for the probability mass function (pmf) on the graph-aligned random partition. We derive a generalization of the Chinese restaurant process from the pmf and a related efficient and neat MCMC algorithm to implement Bayesian inference. We illustrate posterior inference under the GARP using single-cell RNA-seq data from mice stem cells. We further investigate the performance of the model in recovering the underlying clustering structure as well as the underlying graph by means of simulation studies.

Title: Bayesian analysis of product feature allocation models

Abstract: Feature allocation models are an extension of Bayesian nonparametric clustering models, where individuals can share multiple features. We study a broad class of models whose probability distribution has a product form, which includes the popular Indian buffet process. This class plays a prominent role among existing priors, and it shares structural characteristics with Gibbs-type priors in the species sampling framework. We develop a general theory for the entire class, obtaining closed form expressions for the predictive structure and the posterior law of the underlying stochastic process. Additionally, we describe the distribution for the number of features and the number of hitherto unseen features in a future sample, leading to the $\alpha$-diversity for feature models. We also examine notable novel examples, such as mixtures of Indian buffet processes and beta Bernoulli models, where the latter entails a finite random number of features. This methodology finds significant applications in ecology, allowing the estimation of species richness for incidence data, as we demonstrate by analyzing plant diversity in Danish forests and trees in Barro Colorado Island. Joint work with: Lorenzo Ghilotti and Federico Camerlenghi.

Title: Towards a turnkey approach to unbiased Monte Carlo estimation of smooth functions of expectations (with applications to exponential random graphs)

Abstract: Using Monte Carlo samples with expectation m, we develop a general approach to unbiasedly estimate f(m), where f is a smooth function. Specifically, we develop estimators that are based on randomly truncating the Taylor series expansion of f, and estimating the coefficients of the truncated series. We derive their properties, and propose a strategy to set their tuning parameters -- which depend on m -- automatically, with a view to make the whole approach simple to use. We develop our methods for the specific functions f(x)=log x and f(x)=1/x, as they arise in several statistical applications, such as maximum likelihood estimation of latent variable models, and Bayesian inference for un-normalised models.