arXiv subjects

David Dunson

Publications and source records attributed to David Dunson.

At least 19 recordsLinked to original sources

arXiv2026

Posterior Projection for Inference in Constrained Spaces

Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose these constraints via constraint-specific transformations or sampling approaches, or by truncating the posterior distribution. Such methods often result in computational challenges, limited flexibility, and a lack of generality. We propose a generalized framework for constrained Bayesian inference by projecting the unconstrained posterior distribution into the space of the parameter constraints, providing a computationally efficient and easily implementable solution for a large class of problems. We rigorously establish the theoretical foundations of the projected posterior distribution, as well as providing asymptotic results for posterior consistency, posterior contraction, and optimal coverage properties. Our methodology is validated through both theoretical arguments and practical applications.

stat.ME↗

arXiv2026

Using prior information to boost power in correlation structure support recovery

Hypothesis testing of structure in correlation and covariance matrices is of broad interest in many application areas. In high dimensions and/or small to moderate sample sizes, high error rates in testing is a substantial concern. This article focuses on increasing power through a frequentist assisted by Bayes (FAB) procedure. This FAB approach boosts power by including prior information on the correlation parameters. In particular, we suppose there is one of two sources of prior information: (i) a prior dataset that is distinct from the current data but related enough that it may contain valuable information about the correlation structure in the current data; and (ii) knowledge about a tendency for the correlations in different parameters to be similar so that it is appropriate to consider a hierarchical model. When the prior information is relevant, the proposed FAB approach can have significant gains in power. A divide-and-conquer algorithm is developed to reduce computational complexity in massive testing dimensions. We show improvements in power for detecting correlated gene pairs in genomic studies while maintaining control of Type I error or false discover rate (FDR).

stat.ME↗

arXiv2025

Variational bagging: a robust approach for Bayesian uncertainty quantification

Variational Bayes methods are popular due to their computational efficiency and adaptability to diverse applications. In specifying the variational family, mean-field classes are commonly used, which enables efficient algorithms such as coordinate ascent variational inference (CAVI) but fails to capture parameter dependence and typically underestimates uncertainty. In this work, we introduce a variational bagging approach that integrates a bagging procedure with variational Bayes, resulting in a bagged variational posterior for improved inference. We establish strong theoretical guarantees, including posterior contraction rates for general models and a Bernstein-von Mises (BVM) type theorem that ensures valid uncertainty quantification. Notably, our results show that even when using a mean-field variational family, our approach can recover off-diagonal elements of the limiting covariance structure and provide proper uncertainty quantification. In addition, variational bagging is robust to model misspecification, with covariance structures matching those of the target covariance. We illustrate our variational bagging method in numerical studies through applications to parametric models, finite mixture models, deep neural networks, and variational autoencoders (VAEs).

math.ST↗

arXiv2025

Discovering Spatial Patterns of Readmission Risk Using a Bayesian Competing Risks Model with Spatially Varying Coefficients

Time-to-event models are commonly used to study associations between risk factors and disease outcomes in the setting of electronic health records (EHR). In recent years, focus has intensified on social determinants of health, highlighting the need for methods that account for patients' locations. We propose a Bayesian approach for introducing point-referenced spatial effects into a competing risks proportional hazards model. Our method leverages Gaussian process (GP) priors for spatially varying intercept and slope. To improve computational efficiency under a large number of spatial locations, we implemented a Hilbert space low-rank approximation of the GP. We modeled the baseline hazard curves as piecewise constant, and introduced a novel multiplicative gamma process prior to induce shrinkage and smoothing. A loss-based clustering method was then used on the spatial random effects to identify high-risk regions. We demonstrate the utility of this method through simulation and a real-world analysis of EHR data from Duke Hospital to study readmission risk of elderly patients with upper extremity fractures. Our results showed that the proposed method improved inference efficiency and provided valuable insights for downstream policy decisions.

stat.AP↗

arXiv2025

Scalable Bayesian inference for time series via divide-and-conquer

Bayesian computational algorithms tend to scale poorly as data size increases. This has motivated divide-and-conquer-based approaches for scalable inference. These divide the data into subsets, perform inference for each subset in parallel, and then combine these inferences. While appealing theoretical properties and practical performance have been demonstrated for independent observations, scalable inference for dependent data remains challenging. In this work, we study the problem of Bayesian inference from very long time series. The literature in this area focuses mainly on approximate approaches that usually lack rigorous theoretical guarantees and may provide arbitrarily poor accuracy in practice. We propose a simple and scalable divide-and-conquer method, and provide accuracy guarantees. Numerical simulations and real data applications demonstrate the effectiveness of our approach.

stat.ME↗

arXiv2025

A note on simulation methods for the Dirichlet-Laplace prior

Bhattacharya et al. (2015, Journal of the American Statistical Association 110(512): 1479-1490) introduce a novel prior, the Dirichlet-Laplace (DL) prior, and propose a Markov chain Monte Carlo (MCMC) method to simulate posterior draws under this prior in a conditionally Gaussian setting. The original algorithm samples from conditional distributions in the wrong order, i.e., it does not correctly sample from the joint posterior distribution of all latent variables. This note details the issue and provides two simple solutions: A correction to the original algorithm and a new algorithm based on an alternative, yet equivalent, formulation of the prior. This corrigendum does not affect the theoretical results in Bhattacharya et al. (2015).

stat.CO↗

arXiv2025

Efficient Bayesian Inference for Discretely Observed Continuous Time Markov Chains

Inference for continuous-time Markov chains (CTMCs) becomes challenging when the process is only observed at discrete time points. The exact likelihood is intractable, and existing methods often struggle even in medium-dimensional state-spaces. We propose a scalable Bayesian framework for CTMC inference based on a pseudo-likelihood that bypasses the need for the full intractable likelihood. Our approach jointly estimates the probability transition matrix and a biorthogonal spectral decomposition of the generator, enabling an efficient Gibbs sampling procedure that obeys embeddability. Existing methods typically integrate out the unobserved transitions, which becomes computationally burdensome as the number of data or dimensions increase. The computational cost of our method is near-invariant in the number of data and scales well to medium-high dimensions. We justify our pseudo-likelihood approach by establishing theoretical guarantees, including a Bernstein-von Mises theorem for the probability transition matrix and posterior consistency for the spectral parameters of the generator. Through simulation and applications, we showcase the flexibility and robustness of our approach, offering a tractable and scalable approach to Bayesian inference for CTMCs.

stat.ME↗

arXiv2025

Adaptive Bayesian Regression on Data with Low Intrinsic Dimensionality

We study how the posterior contraction rate under a Gaussian process (GP) prior depends on the intrinsic dimension of the predictors and the smoothness of the regression function. An open question is whether a generic GP prior that does not incorporate knowledge of the intrinsic lower-dimensional structure of the predictors can attain an adaptive rate for a broad class of such structures. We show that this is indeed the case, establishing conditions under which the posterior contraction rates become adaptive to the intrinsic dimension in terms of the covering number of the data domain (the Minkowski dimension) and prove the nonparametric posterior contraction rate, up to a logarithmic factor. When the domain is a compact manifold, we prove the RKHS approximation to intrinsically defined Hölder functions on the manifold of any order of smoothness by a novel analysis, leading to the optimal adaptive posterior contraction rate. We propose an empirical Bayes prior on the kernel bandwidth using kernel affinity and $k$-nearest neighbor statistics, bypassing explicit estimation of the intrinsic dimension. The efficiency of the proposed Bayesian regression approach is demonstrated in various numerical experiments.

math.ST↗

arXiv2024

Motion-Invariant Variational Auto-Encoding of Brain Structural Connectomes

Mapping of human brain structural connectomes via diffusion MRI offers a unique opportunity to understand brain structural connectivity and relate it to various human traits, such as cognition. However, head displacement during image acquisition can compromise the accuracy of connectome reconstructions and subsequent inference results. We develop a generative model to learn low-dimensional representations of structural connectomes invariant to motion-induced artifacts, so that we can link brain networks and human traits more accurately, and generate motion-adjusted connectomes. We apply the proposed model to data from the Adolescent Brain Cognitive Development (ABCD) study and the Human Connectome Project (HCP) to investigate how our motion-invariant connectomes facilitate understanding of the brain network and its relationship with cognition. Empirical results demonstrate that the proposed motion-invariant variational auto-encoder (inv-VAE) outperforms its competitors in various aspects. In particular, motion-adjusted structural connectomes are more strongly associated with a wide array of cognition-related traits than other approaches without motion adjustment.

q-bio.NC↗

arXiv2024

Efficiently resolving rotational ambiguity in Bayesian matrix sampling with matching

A wide class of Bayesian models involve unidentifiable random matrices that display rotational ambiguity, with the Gaussian factor model being a typical example. A rich variety of Markov chain Monte Carlo (MCMC) algorithms have been proposed for sampling the parameters of these models. However, without identifiability constraints, reliable posterior summaries of the parameters cannot be obtained directly from the MCMC output. As an alternative, we propose a computationally efficient post-processing algorithm that allows inference on non-identifiable parameters. We first orthogonalize the posterior samples using Varimax and then tackle label and sign switching with a greedy matching algorithm. We compare the performance and computational complexity with other methods using a simulation study and chemical exposures data. The algorithm implementation is available in the infinitefactor R package on CRAN.

stat.CO↗

arXiv2024

Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AI

In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets. However, a broader perspective reveals a multitude of overlooked metrics, tasks, and data types, such as uncertainty, active and continual learning, and scientific data, that demand attention. Bayesian deep learning (BDL) constitutes a promising avenue, offering advantages across these diverse settings. This paper posits that BDL can elevate the capabilities of deep learning. It revisits the strengths of BDL, acknowledges existing challenges, and highlights some exciting research avenues aimed at addressing these obstacles. Looking ahead, the discussion focuses on possible ways to combine large-scale foundation models with BDL to unlock their full potential.

cs.LG↗

arXiv2024

Bag of DAGs: Inferring Directional Dependence in Spatiotemporal Processes

We propose a class of nonstationary processes to characterize space- and time-varying directional associations in point-referenced data. We are motivated by spatiotemporal modeling of air pollutants in which local wind patterns are key determinants of the pollutant spread, but information regarding prevailing wind directions may be missing or unreliable. We propose to map a discrete set of wind directions to edges in a sparse directed acyclic graph (DAG), accounting for uncertainty in directional correlation patterns across a domain. The resulting Bag of DAGs processes (BAGs) lead to interpretable nonstationarity and scalability for large data due to sparsity of DAGs in the bag. We outline Bayesian hierarchical models using BAGs and illustrate inferential and performance gains of our methods compared to other state-of-the-art alternatives. We analyze fine particulate matter using high-resolution data from low-cost air quality sensors in California during the 2020 wildfire season. An R package is available on GitHub.

stat.ME↗

arXiv2024

Inferring Synergistic and Antagonistic Interactions in Mixtures of Exposures

There is abundant interest in assessing the joint effects of multiple exposures on human health. This is often referred to as the mixtures problem in environmental epidemiology and toxicology. Classically, studies have examined the adverse health effects of different chemicals one at a time, but there is concern that certain chemicals may act together to amplify each other's effects. Such amplification is referred to as synergistic interaction, while chemicals that inhibit each other's effects have antagonistic interactions. Current approaches for assessing the health effects of chemical mixtures do not explicitly consider synergy or antagonism in the modeling, instead focusing on either parametric or unconstrained nonparametric dose response surface modeling. The parametric case can be too inflexible, while nonparametric methods face a curse of dimensionality that leads to overly wiggly and uninterpretable surface estimates. We propose a Bayesian approach that decomposes the response surface into additive main effects and pairwise interaction effects, and then detects synergistic and antagonistic interactions. Variable selection decisions for each interaction component are also provided. This Synergistic Antagonistic Interaction Detection (SAID) framework is evaluated relative to existing approaches using simulation experiments and an application to data from NHANES.

stat.AP↗

arXiv2024

Spatial predictions on physically constrained domains: Applications to Arctic sea salinity data

In this paper we predict sea surface salinity (SSS) in the Arctic Ocean based on satellite measurements. SSS is a crucial indicator for ongoing changes in the Arctic Ocean and can offer important insights about climate change. We particularly focus on areas of water mistakenly flagged as ice by satellite algorithms. To remove bias in the retrieval of salinity near sea ice, the algorithms use conservative ice masks, which result in considerable loss of data. We aim to produce realistic SSS values for such regions to obtain more complete understanding about the SSS surface over the Arctic Ocean and benefit future applications that may require SSS measurements near edges of sea ice or coasts. We propose a class of scalable nonstationary processes that can handle large data from satellite products and complex geometries of the Arctic Ocean. Barrier overlap-removal acyclic directed graph GP (BORA-GP) constructs sparse directed acyclic graphs (DAGs) with neighbors conforming to barriers and boundaries, enabling characterization of dependence in constrained domains. The BORA-GP models produce more sensible SSS values in regions without satellite measurements and show improved performance in various constrained domains in simulation studies compared to state-of-the-art alternatives. An R package is available at https://github.com/jinbora0720/boraGP.

stat.AP↗

arXiv2024

Efficient posterior sampling for high-dimensional imbalanced logistic regression

High-dimensional data are routinely collected in many areas. We are particularly interested in Bayesian classification models in which one or more variables are imbalanced. Current Markov chain Monte Carlo algorithms for posterior computation are inefficient as $n$ and/or $p$ increase due to worsening time per step and mixing rates. One strategy is to use a gradient-based sampler to improve mixing while using data sub-samples to reduce per-step computational complexity. However, usual sub-sampling breaks down when applied to imbalanced data. Instead, we generalize piece-wise deterministic Markov chain Monte Carlo algorithms to include importance-weighted and mini-batch sub-sampling. These approaches maintain the correct stationary distribution with arbitrarily small sub-samples, and substantially outperform current competitors. We provide theoretical support and illustrate gains in simulated and real data applications.

stat.ME↗

arXiv2023

Interpretable AI for relating brain structural and functional connectomes

One of the central problems in neuroscience is understanding how brain structure relates to function. Naively one can relate the direct connections of white matter fiber tracts between brain regions of interest (ROIs) to the increased co-activation in the same pair of ROIs, but the link between structural and functional connectomes (SCs and FCs) has proven to be much more complex. To learn a realistic generative model characterizing population variation in SCs, FCs, and the SC-FC coupling, we develop a graph auto-encoder that we refer to as Staf-GATE. We trained Staf-GATE with data from the Human Connectome Project (HCP) and show state-of-the-art performance in predicting FC and joint generation of SC and FC. In addition, as a crucial component of the proposed approach, we provide a masking-based algorithm to extract interpretable inferences about SC-FC coupling. Our interpretation methods identified important SC subnetworks for FC coupling and relating SC and FC with sex.

q-bio.NC↗

arXiv2023

Spectral Gap Regularization of Neural Networks

We introduce Fiedler regularization, a novel approach for regularizing neural networks that utilizes spectral/graphical information. Existing regularization methods often focus on penalizing weights in a global/uniform manner that ignores the connectivity structure of the neural network. We propose to use the Fiedler value of the neural network's underlying graph as a tool for regularization. We provide theoretical motivation for this approach via spectral graph theory. We demonstrate several useful properties of the Fiedler value that make it useful as a regularization tool. We provide an approximate, variational approach for faster computation during training. We provide an alternative formulation of this framework in the form of a structurally weighted $\text{L}_1$ penalty, thus linking our approach to sparsity induction. We provide uniform generalization error bounds for Fiedler regularization via a Rademacher complexity analysis. We performed experiments on datasets that compare Fiedler regularization with classical regularization methods such as dropout and weight decay. Results demonstrate the efficacy of Fiedler regularization. This is a journal extension of the conference paper by Tam and Dunson (2020).

stat.ML↗

arXiv2023

Estimating a Brain Network Predictive of Stress and Genotype with Supervised Autoencoders

Targeted stimulation of the brain has the potential to treat mental illnesses. We propose an approach to help design the stimulation protocol by identifying electrical dynamics across many brain regions that relate to illness states. We model multi-region electrical activity as a superposition of activity from latent networks, where the weights on the latent networks relate to an outcome of interest. In order to improve on drawbacks of latent factor modeling in this context, we focus on supervised autoencoders (SAEs), which can improve predictive performance while maintaining a generative model. We explain why SAEs yield improved predictions, describe the distributional assumptions under which SAEs are an appropriate modeling choice, and provide modeling constraints to ensure biological relevance of the learned network. We use the analysis strategy to find a network associated with stress that characterizes a genotype associated with bipolar disorder. This discovered network aligns with a previously used stimulation technique, providing experimental validation of our approach.

stat.ML↗