arXiv subjects

Alexander Dombowsky

Publications and source records attributed to Alexander Dombowsky.

5 recordsLinked to original sources

arXiv2026

Besag-Clifford e-values for unnormalized testing

Unnormalized probability distributions are frequently used in machine learning for modeling complex data generating processes. Though Markov chain Monte Carlo (MCMC) algorithms can approximately sample from unnormalized distributions, intractability of their normalizing constants renders likelihood ratio testing infeasible. We propose to use the parallel method of Besag and Clifford to generate samples that are exchangeable with the data under the null, to then generate valid e-values for any number of iterations or algorithmic steps. We show that as the number of samples grows, these Besag-Clifford e-values constructed using the unnormalized likelihood ratio are actually log-optimal up to a multiplicative term that diminishes with the mixing time of the Markov chain. Additionally, averaging over the output of multiple chains retains validity while increasing the e-power. We extend Besag-Clifford e-values to the general problem of unnormalized test statistics, which allows application to composite hypotheses, uncertainty quantification, generative model evaluation, and sequential testing. Through simulations and an application to galaxy velocity modeling, we empirically verify our theory, explore the impact of autocorrelation and mixing, and evaluate the performance of Besag-Clifford e-values.

stat.ME↗

arXiv2025

Learning discrete Bayesian networks with hierarchical Dirichlet shrinkage

A discrete Bayesian network is a directed acyclic graph (DAG) consisting of categorical variables. Two popular approaches for DBN modeling include classification and nonparametric methods. However, both methods often require a large number of parameters, such as high-order interactions in the former and cell probabilities in the latter. In this article, we propose a hierarchical model for node-parent conditional probabilities, inducing shrinkage to low-dimensional latent parameters aposteriori. We generate samples from the posterior distribution of these latent variables using the Metropolis-adjusted Langevin algorithm within a Gibbs sampler. Moreover, we verify that the full conditional distribution is log-concave under mild conditions, facilitating efficient sampling. We then detail several algorithms for structure learning that incorporate our hierarchical prior and preserve the DAG property. Through simulations, we evaluate the performance of our method for sparse counts, discovering graph structure, and selecting between competing DAGs. We conclude with an application to uncovering prognostic network structure from a breast cancer dataset.

stat.ME↗

arXiv2024

Bayesian Learning of Clinically Meaningful Sepsis Phenotypes in Northern Tanzania

Sepsis is a life-threatening condition caused by a dysregulated host response to infection. Recently, researchers have hypothesized that sepsis consists of a heterogeneous spectrum of distinct subtypes, motivating several studies to identify clusters of sepsis patients that correspond to subtypes, with the long-term goal of using these clusters to design subtype-specific treatments. Therefore, clinicians rely on clusters having a concrete medical interpretation, usually corresponding to clinically meaningful regions of the sample space that have a concrete implication to practitioners. In this article, we propose Clustering Around Meaningful Regions (CLAMR), a Bayesian clustering approach that explicitly models the medical interpretation of each cluster center. CLAMR favors clusterings that can be summarized via meaningful feature values, leading to medically significant sepsis patient clusters. We also provide details on measuring the effect of each feature on the clustering using Bayesian hypothesis tests, so one can assess what features are relevant for cluster interpretation. Our focus is on clustering sepsis patients from Moshi, Tanzania, where patients are younger and the prevalence of HIV infection is higher than in previous sepsis subtyping cohorts.

stat.AP↗

arXiv2023

Product Centered Dirichlet Processes for Bayesian Multiview Clustering

While there is an immense literature on Bayesian methods for clustering, the multiview case has received little attention. This problem focuses on obtaining distinct but statistically dependent clusterings in a common set of entities for different data types. For example, clustering patients into subgroups with subgroup membership varying according to the domain of the patient variables. A challenge is how to model the across-view dependence between the partitions of patients into subgroups. The complexities of the partition space make standard methods to model dependence, such as correlation, infeasible. In this article, we propose CLustering with Independence Centering (CLIC), a clustering prior that uses a single parameter to explicitly model dependence between clusterings across views. CLIC is induced by the product centered Dirichlet process (PCDP), a novel hierarchical prior that bridges between independent and equivalent partitions. We show appealing theoretic properties, provide a finite approximation and prove its accuracy, present a marginal Gibbs sampler for posterior computation, and derive closed form expressions for the marginal and joint partition distributions for the CLIC model. On synthetic data and in an application to epidemiology, CLIC accurately characterizes view-specific partitions while providing inference on the dependence level.

stat.ME↗

arXiv2023

Bayesian Clustering via Fusing of Localized Densities

Bayesian clustering typically relies on mixture models, with each component interpreted as a different cluster. After defining a prior for the component parameters and weights, Markov chain Monte Carlo (MCMC) algorithms are commonly used to produce samples from the posterior distribution of the component labels. The data are then clustered by minimizing the expectation of a clustering loss function that favours similarity to the component labels. Unfortunately, although these approaches are routinely implemented, clustering results are highly sensitive to kernel misspecification. For example, if Gaussian kernels are used but the true density of data within a cluster is even slightly non-Gaussian, then clusters will be broken into multiple Gaussian components. To address this problem, we develop Fusing of Localized Densities (FOLD), a novel clustering method that melds components together using the posterior of the kernels. FOLD has a fully Bayesian decision theoretic justification, naturally leads to uncertainty quantification, can be easily implemented as an add-on to MCMC algorithms for mixtures, and favours a small number of distinct clusters. We provide theoretical support for FOLD including clustering optimality under kernel misspecification. In simulated experiments and real data, FOLD outperforms competitors by minimizing the number of clusters while inferring meaningful group structure.

stat.ME↗