arXiv subjects

Jason Xu

Publications and source records attributed to Jason Xu.

At least 19 recordsLinked to original sources

arXiv2026

FIFA World Cup 2026 as a Contamination-Free Benchmark for LLM Forecasting Agents: Four Models, a Bookmaker, and 104 Matches

We introduce WC2026-Agents, a benchmark and dataset for evaluating large language models (LLMs) as autonomous forecasting agents on real, future events. For every one of the 104 matches of the 2026 FIFA World Cup, four frontier models -- Claude Opus 4.8, ChatGPT (GPT-5.5, high reasoning), Gemini 3.1 Pro, and Grok (Expert Mode) -- ran an identical search-act-reflect loop: gather evidence with a web tool, commit to a 1X2 (team-A win / draw / team-B win) distribution and a virtual 100-USD bet, and, after the match, reflect given only the final score. Because every match kicked off after the models' training cutoffs, the benchmark is contamination-free by construction. Crucially, we pair the four agents with a fifth competitor drawn from the same information environment -- the pre-match betting market -- collected as per-match 1X2 odds, giving an economically grounded baseline and letting us score not just what an agent predicts but what it does with money. The release contains 416 forecasts and 414 reflections with verbatim reasoning, ground truth (including penalty shootouts), odds, and a reproducible evaluation suite. A reference evaluation surfaces findings that raw accuracy hides: the four agents issue an identical top pick in 92% of matches and none beats the market's Brier score; indeed, a naive flat stake on the market favorite out-earns all four agents. Yet the agents diverge sharply as decision-makers: betting return-on-investment ranges from -18% to +10%, fading the market is unprofitable for all four, the share of forecasts that cite the market ranges from 12% to 100%, and self-reported error rates on wrong picks range from 36% to 86%. The benchmark thus measures calibration, decision quality, and self-knowledge -- axes on which frontier models differ even when their predictions do not. Data and code: https://github.com/graphuofm/FIFA2026LLM

cs.LG↗

arXiv2026

Constrained Weighted Bayesian Bootstrap

We prove the weighted Bayesian bootstrap, a method for approximate sampling of a posterior distribution, can be extended to sample from general constrained posterior distributions under mild assumptions. The method entails a simple algorithm that can take advantage of fast tools from convex optimization. Under regularity conditions, we show the asymptotic distribution of samples from the constrained weighted Bayesian bootstrap has a covariance matching the restricted maximum likelihood estimator, an efficient estimator. We assess the method empirically on a variety of constrained Bayesian problems, demonstrating broad applicability of the method as well as advantages over existing peer methods. The constrained weighted Bayesian bootstrap quickly samples from constrained posteriors, providing adequate uncertainty quantification for problems typically solved via optimization methods designed to deliver only a point estimate. As a case study, using constraints required in European-style option prices, uncertainty estimates of an option pricing surface are derived with constrained weighted Bayesian bootstrap.

stat.ME↗

arXiv2026

Affinity Graph Connectivity in Convex Clustering

We generalize finite-sample bounds for convex clustering to the setting where affinity weights appearing in the objective correspond to a general connected graph. These bounds and their analysis lead to a better understanding of clustering behavior under various implied connectivity structures behind the data and to new rates of convergence for centroid recovery. The new theoretical framework is based on random walks, which allow application of concentration inequalities related to random graph models, and formalizes the relationship between the clustering performance and the connectivity of the graph structures. Through the form of the bound and empirical results, we argue proper tuning of hyperparameters to convex clustering problems should also include tuning of input affinity weights.

stat.ML↗

arXiv2026

Bayesian Distance-to-Set Models: from Latent Variable to Latent Projection

Statistical models often assume that data are generated near a structured, smooth, or low-dimensional set. A common approach is to use Bayesian latent variable models, in which each observation is associated with a latent coordinate on the set, and the observed data are modeled as noisy deviations from these coordinates. The deviation is typically characterized by a location-scale distribution, such as Gaussian. Despite their intuitive appeal and popularity, latent variable models often present practical challenges in posterior computation. In particular, Markov chain Monte Carlo samplers may suffer from slow mixing, especially when the sample size is large and there is no closed form for integrating out the latent coordinates. In this article, we propose an alternative approach that replaces the deviation-from-coordinate with a distance-to-set. Specifically, the distance-to-set is defined as the distance between a data point and its projection onto the set, where the projection can be rapidly computed by optimization and replaces the latent coordinate in the likelihood. This change substantially reduces the dimensionality of the parameter X latent variable space, leading to efficient posterior computation. We establish several important statistical properties for the distance-to-set models, such as the independence between the normal-cone noise and fixed-effect parameters, posterior consistency, and an Occam's razor effect that automatically penalizes overfitting. We demonstrate the effectiveness of our approach through simulation studies, applications to multi-environment study and Bayesian transfer learning.

stat.ME↗

arXiv2026

Biconvex Biclustering

This article proposes a biconvex modification to convex biclustering in order to improve its performance in high-dimensional settings. In contrast to heuristics that discard a subset of noisy features a priori, our method jointly learns and accordingly weighs informative features while discovering biclusters. Moreover, the method is adaptive to the data, and is accompanied by an efficient algorithm based on proximal alternating minimization, complete with detailed guidance on hyperparameter tuning and efficient solutions to optimization subproblems. These contributions are theoretically grounded; we establish finite-sample bounds on the objective function under sub-Gaussian errors, and generalize these guarantees to cases where input affinities need not be uniform. Extensive simulation results reveal our method consistently recovers underlying biclusters while weighing and selecting features appropriately, outperforming peer methods. An application to a gene microarray dataset of lymphoma samples recovers biclusters matching an underlying classification, while giving additional interpretation to the mRNA samples via the column groupings and fitted weights.

stat.ML↗

arXiv2026

Robust Multi-Source Covid-19 Detection in CT Images

Deep learning models for COVID-19 detection from chest CT scans generally perform well when the training and test data originate from the same institution, but they often struggle when scans are drawn from multiple centres with differing scanners, imaging protocols, and patient populations. One key reason is that existing methods treat COVID-19 classification as the sole training objective, without accounting for the data source of each scan. As a result, the learned representations tend to be biased toward centres that contribute more training data. To address this, we propose a multi-task learning approach in which the model is trained to predict both the COVID-19 diagnosis and the originating data centre. The two tasks share an EfficientNet-B7 backbone, which encourages the feature extractor to learn representations that hold across all four participating centres. Since the training data is not evenly distributed across sources, we apply a logit-adjusted cross-entropy loss [1] to the source classification head to prevent underrepresented centres from being overlooked. Our pre-processing follows the SSFL framework with KDS [2], selecting eight representative slices per scan. Our method achieves an F1 score of 0.9098 and an AUC-ROC of 0.9647 on a validation set of 308 scans. The code is publicly available at https://github.com/Purdue-M2/-multisource-covid-ct.

cs.CV↗

arXiv2026

Marginal Likelihood Inference for Fitting Dynamical Survival Analysis Models to Epidemic Count Data

Stochastic compartmental models are prevalent tools for describing disease spread, but inference under these models is challenging for many types of surveillance data when the marginal likelihood function becomes intractable due to missing information. To address this, we develop a closed-form likelihood for discretely observed incidence count data under the dynamical survival analysis (DSA) paradigm. The method approximates the stochastic population-level hazard by a large population limit while retaining a count-valued stochastic model, and leads to survival analytic inferential strategies that are both computationally efficient and flexible to model generalizations. Through simulation, we show that parameter estimation is competitive with recent exact but computationally expensive likelihood-based methods in partially observed settings. Previous work has shown that the DSA approximation is generalizable, and we show that the inferential developments here also carry over to models featuring individual heterogeneity, such as frailty models. We consider case studies of both Ebola and COVID-19 data on variants of the model, including a network-based epidemic model and a model with distributions over susceptibility, demonstrating its flexibility and practical utility on real, partially observed datasets.

stat.ME↗

arXiv2025

Gradient-bridged Posterior: Bayesian Inference for Models with Implicit Functions

Many statistical problems include model parameters that are defined as the solutions to optimization sub-problems. These include classical approaches such as profile likelihood as well as modern applications involving flow networks or Procrustes distances. In such cases, the likelihood of the data involves an implicit function, often complicating inferential procedures and entailing prohibitive computational cost. In this article, we propose an intuitive and tractable posterior inference approach for this setting. We introduce a class of continuous models that handle implicit function values using the first-order optimality of the sub-problems. Specifically, we apply a shrinkage kernel to the gradient norm, which retains a probabilistic interpretation within a generative model. This can be understood as a generalization of the Gibbs posterior framework to newly enable concentration around partial minimizers in a subset of the parameters. We show that this method, termed the gradient-bridged posterior, is amenable to efficient posterior computation, and enjoys theoretical guarantees, establishing a Bernstein--von Mises theorem for asymptotic normality. The advantages of our approach are highlighted on a synthetic flow network experiment and an application to data integration using Procrustes distances.

stat.ME↗

arXiv2025

A Bayesian decision-theoretic approach to sparse estimation

We extend the work of Hahn and Carvalho (2015) and develop a doubly-regularized sparse regression estimator by synthesizing Bayesian regularization with penalized least squares within a decision-theoretic framework. In contrast to existing Bayesian decision-theoretic formulation chiefly reliant upon the symmetric 0-1 loss, the new method -- which we call Bayesian Decoupling -- employs a family of penalized loss functions indexed by a sparsity-tuning parameter. We propose a class of reweighted l1 penalties, with two specific instances that achieve simultaneous bias reduction and convexity. The design of the penalties incorporates considerations of signal sizes, as enabled by the Bayesian paradigm. The tuning parameter is selected using a posterior benchmarking criterion, which quantifies the drop in predictive power relative to the posterior mean which is the optimal Bayes estimator under the squared error loss. Additionally, in contrast to the widely used median probability model technique which selects variables by thresholding posterior inclusion probabilities at the fixed threshold of 1/2, Bayesian Decoupling enables the use of a data-driven threshold which automatically adapts to estimated signal sizes and offers far better performance in high-dimensional settings with highly correlated predictors. Our numerical results in such settings show that certain combinations of priors and loss functions significantly improve the solution path compared to existing methods, prioritizing true signals early along the path before false signals are selected. Consequently, Bayesian Decoupling produces estimates with better prediction and selection performance. Finally, a real data application illustrates the practical advantages of our approaches which select sparser models with larger coefficient estimates.

stat.ME↗

arXiv2024

A Bayesian approach for fitting semi-Markov mixture models of cancer latency to individual-level data

Multi-state models of cancer natural history are widely used for designing and evaluating cancer early detection strategies. Calibrating such models against longitudinal data from screened cohorts is challenging, especially when fitting non-Markovian mixture models against individual-level data. Here, we consider a family of semi-Markov mixture models of cancer natural history and introduce an efficient data-augmented Markov chain Monte Carlo sampling algorithm for fitting these models to individual-level screening and cancer diagnosis histories. Our fully Bayesian approach supports rigorous uncertainty quantification and model selection through leave-one-out cross-validation, and it enables the estimation of screening-related overdiagnosis rates. We demonstrate the effectiveness of our approach using simulated data, showing that the sampling algorithm efficiently explores the joint posterior distribution of model parameters and latent variables. Finally, we apply our method to data from the US Breast Cancer Surveillance Consortium and estimate the extent of breast cancer overdiagnosis associated with mammography screening. The sampler and model comparison method are available in the R package baclava.

stat.CO↗

arXiv2024

Bridged Posterior: Optimization, Profile Likelihood and a New Approach to Generalized Bayes

Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss function to form a posterior density. Nevertheless, Gibbs posteriors are supported in high-dimensional spaces, and do not inherit the computational efficiency or constraint formulations from optimization. In this article, we explore a new generalized Bayes approach, viewing the likelihood as a function of data, parameters, and latent variables conditionally determined by an optimization sub-problem. Marginally, the latent variable given the data remains stochastic, and is characterized by its posterior distribution. This framework, coined bridged posterior, conforms to the Bayesian paradigm. Besides providing a novel generative model, we obtain a positively surprising theoretical finding that under mild conditions, the $\sqrt{n}$-adjusted posterior distribution of the parameters under our model converges to the same normal distribution as that of the canonical integrated posterior. Therefore, our result formally dispels a long-held belief that partial optimization of latent variables may lead to underestimation of parameter uncertainty. We demonstrate the practical advantages of our approach under several settings, including maximum-margin classification, latent normal models, and harmonization of multiple networks.

stat.ME↗

arXiv2023

Bayesian Transfer Learning

Transfer learning is a burgeoning concept in statistical machine learning that seeks to improve inference and/or predictive accuracy on a domain of interest by leveraging data from related domains. While the term "transfer learning" has garnered much recent interest, its foundational principles have existed for years under various guises. Prior literature reviews in computer science and electrical engineering have sought to bring these ideas into focus, primarily surveying general methodologies and works from these disciplines. This article highlights Bayesian approaches to transfer learning, which have received relatively limited attention despite their innate compatibility with the notion of drawing upon prior knowledge to guide new learning tasks. Our survey encompasses a wide range of Bayesian transfer learning frameworks applicable to a variety of practical settings. We discuss how these methods address the problem of finding the optimal information to transfer between domains, which is a central question in transfer learning. We illustrate the utility of Bayesian transfer learning methods via a simulation study where we compare performance against frequentist competitors.

stat.ML↗

arXiv2023

Inferring Covariance Structure from Multiple Data Sources via Subspace Factor Analysis

Factor analysis provides a canonical framework for imposing lower-dimensional structure such as sparse covariance in high-dimensional data. High-dimensional data on the same set of variables are often collected under different conditions, for instance in reproducing studies across research groups. In such cases, it is natural to seek to learn the shared versus condition-specific structure. Existing hierarchical extensions of factor analysis have been proposed, but face practical issues including identifiability problems. To address these shortcomings, we propose a class of SUbspace Factor Analysis (SUFA) models, which characterize variation across groups at the level of a lower-dimensional subspace. We prove that the proposed class of SUFA models lead to identifiability of the shared versus group-specific components of the covariance, and study their posterior contraction properties. Taking a Bayesian approach, these contributions are developed alongside efficient posterior computation algorithms. Our sampler fully integrates out latent variables, is easily parallelizable and has complexity that does not depend on sample size. We illustrate the methods through application to integration of multiple gene expression datasets relevant to immunology.

stat.ME↗

arXiv2023

Fast Computation of Branching Process Transition Probabilities via ADMM

Branching processes are a class of continuous-time Markov chains (CTMCs) prevalent for modeling stochastic population dynamics in ecology, biology, epidemiology, and many other fields. The transient or finite-time behavior of these systems is fully characterized by their transition probabilities. However, computing them requires marginalizing over all paths between endpoint-conditioned values, which often poses a computational bottleneck. Leveraging recent results that connect generating function methods to a compressed sensing framework, we recast this task from the lens of sparse optimization. We propose a new solution method using variable splitting; in particular, we derive closed form updates in a highly efficient ADMM algorithm. Notably, no matrix products -- let alone inversions -- are required at any step. This reduces computational cost by orders of magnitude over existing methods, and the resulting algorithm is easily parallelizable and fairly insensitive to tuning parameters. A comparison to prior work is carried out in two applications to models of blood cell production and transposon evolution, showing that the proposed method is orders of magnitudes more scalable than existing work.

stat.CO↗

arXiv2023

Inferring HIV Transmission Patterns from Viral Deep-Sequence Data via Latent Typed Point Processes

Viral deep-sequencing data play a crucial role toward understanding disease transmission network flows, because the higher resolution of these data compared to standard Sanger sequencing provide evidence into the direction of infectious disease transmission. To more fully utilize these rich data and account for the uncertainties in phylogenetic analysis outcomes, we propose a spatial Poisson process model to uncover HIV transmission flow patterns at the population level. We represent pairings of two individuals with viral sequence data as typed points, with coordinates representing covariates such as gender and age, and the point type representing the unobserved transmission statuses (linkage and direction). Points are associated with observed scores on the strength of evidence for each transmission status that are obtained through standard deep-sequenece phylogenetic analysis. Our method is able to jointly infer the latent transmission statuses for all pairings and the transmission flow surface on the source-recipient covariate space. In contrast to existing methods, our framework does not require pre-classification of the transmission statuses of data points, instead learning them probabilistically through a fully Bayesian inference scheme. By directly modeling continuous spatial processes with smooth densities, our method enjoys significant computational advantages compared to previous methods that rely on discretization of the covariate space. We demonstrate that our framework can capture age structures in HIV transmission at high resolution, and bring valuable insights in a case study on viral deep-sequencing data from Southern Uganda.

stat.ME↗

arXiv2022

Detecting Changes in the Transmission Rate of a Stochastic Epidemic Model

Throughout the course of an epidemic, the rate at which disease spreads varies with behavioral changes, the emergence of new disease variants, and the introduction of mitigation policies. Estimating such changes in transmission rates can help us better model and predict the dynamics of an epidemic, and provide insight into the efficacy of control and intervention strategies. We present a method for likelihood-based estimation of parameters in the stochastic SIR model under a time-inhomogeneous transmission rate comprised of piecewise constant components. In doing so, our method simultaneously learns change points in the transmission rate via a Markov chain Monte Carlo algorithm. The method targets the exact model posterior in a difficult missing data setting given only partially observed case counts over time. We validate performance on simulated data before applying our approach to data from an Ebola outbreak in Western Africa and COVID-19 outbreak on a university campus.

stat.ME↗

arXiv2022

Distance-to-Set Priors and Constrained Bayesian Inference

Constrained learning is prevalent in many statistical tasks. Recent work proposes distance-to-set penalties to derive estimators under general constraints that can be specified as sets, but focuses on obtaining point estimates that do not come with corresponding measures of uncertainty. To remedy this, we approach distance-to-set regularization from a Bayesian lens. We consider a class of smooth distance-to-set priors, showing that they yield well-defined posteriors toward quantifying uncertainty for constrained learning problems. We discuss relationships and advantages over prior work on Bayesian constraint relaxation. Moreover, we prove that our approach is optimal in an information geometric-sense for finite penalty parameters $\rho$, and enjoys favorable statistical properties when $\rho\to\infty$. The method is designed to perform effectively within gradient-based MCMC samplers, as illustrated on a suite of simulated and real data applications.

stat.ME↗

arXiv2022

The Stochastic Proximal Distance Algorithm

Stochastic versions of proximal methods have gained much attention in statistics and machine learning. These algorithms tend to admit simple, scalable forms, and enjoy numerical stability via implicit updates. In this work, we propose and analyze a stochastic version of the recently proposed proximal distance algorithm, a class of iterative optimization methods that recover a desired constrained estimation problem as a penalty parameter $\rho \rightarrow \infty$. By uncovering connections to related stochastic proximal methods and interpreting the penalty parameter as the learning rate, we justify heuristics used in practical manifestations of the proximal distance method, establishing their convergence guarantees for the first time. Moreover, we extend recent theoretical devices to establish finite error bounds and a complete characterization of convergence rates regimes. We validate our analysis via a thorough empirical study, also showing that unsurprisingly, the proposed method outpaces batch versions on popular learning tasks.

stat.ML↗