Program

The integration of statistics and generative AI plays a pivotal role in accelerating trustworthy, cross-domain scientific discovery. Recent advances in generative models have dramatically expanded the availability and use of synthetic data across scientific domains. While these developments create exciting opportunities to enhance data analysis, they also raise fundamental statistical challenges regarding how synthetic data can be used in a valid, reliable, and principled manner. In this talk, we first discuss the generation of high-fidelity, high-dimensional synthetic data for real-world applications using generative AI models, including transformers, diffusion models, and latent flow-matching models. We then present a principled framework for integrating observed and synthetic data in downstream analyses to ensure valid statistical inference, even when generative AI models are misspecified. Specifically, we introduce synthetic-data-assisted methods for continuous and discrete outcomes based on an augmented synthetic data likelihood that integrates observed and synthetic data. We show that these methods are robust to misspecification of black-box generative models and can improve statistical power when the generative models provide informative synthetic data. We demonstrate the utility of these methods through applications to UK Biobank data, including genome-wide association studies (GWAS) of proteomic data, whole-genome sequencing (WGS) analyses of brain imaging phenotypes, and analyses of binary mental health survey outcomes. These applications involve substantial missingness, with approximately 70–90% of the relevant data missing, highlighting the potential of synthetic-data-assisted methods to enable more powerful and reliable scientific discovery in challenging real-world settings.

Distributional reinforcement learning (RL) estimates the complete distribution of returns, enabling effective risk-sensitive decision-making. By capturing the entire return distribution, agents gain a richer characterization of the environment’s dynamics, including its variance, quantiles, tail risks, and other forms of uncertainty, enabling more robust and reliable decision-making. Quantile temporal difference (QTD) learning is a cornerstone algorithm for distributional RL with strong empirical performance, yet its theoretical guarantees remain limited. Analyzing QTD is challenging due to quantile semi-gradient bias, discretization errors from approximating return distributions, and non-smooth update dynamics. We present the first non-asymptotic analysis for QTD in both synchronous (generative model) and asynchronous (single Markovian trajectory) settings. We formulate QTD as a nonlinear stochastic approximation scheme for a quantile Bellman equation and establish an alignment property: the expected update direction is a descent direction for the ℓ∞ error relative to the true return quantiles whenever the error dominates quantile-discretization and support-excursion terms. We then derive finite-time bounds on the expected squared ℓ∞ error of the last iterate, uniformly over states and quantile levels, for both the synchronous setting and the asynchronous setting. We obtain finite-time bounds on the expected supremum 1-Wasserstein distance between the learned and true return distributions and perform sample complexity analysis. These results advance the theoretical foundation of distributional RL.

Multimodal data provide complementary views of the same subjects and can reveal population structures that are difficult to detect from any single source. Effective integration, however, requires more than pooling features because modalities may differ in signal strength, noise level, and relevance while containing both shared and modality-specific information. This talk presents MUSIC (Multimodal Spectral Integration and Clustering), an adaptive framework that extracts a low-dimensional singular subspace from each modality and decomposes it into common and modality-specific components. MUSIC iteratively estimates the common subspace and reweights modalities according to their agreement with the evolving common structure, thereby downweighting heterogeneous or uninformative sources while preserving modality-specific variation. The resulting spectral embeddings recover a coarse clustering shared across modalities together with finer, nested modality-specific refinements. Under a general low-rank model, we establish finite-sample guarantees for common and modality-specific subspace estimation and derive corresponding misclustering bounds. An application to multimodal molecular data from The Cancer Genome Atlas shows that MUSIC identifies clinically meaningful glioma subtypes and interpretable modality-specific refinements. The framework offers a principled approach to learning what information should be shared and how strongly each modality should be trusted.

Large-scale functional MRI studies generate subject-specific brain connectivity networks for tens of thousands of participants, creating high-dimensional matrix datasets that strain standard vector-based statistical methods. To address this challenge, we propose a manifold-based latent factor model (MLFM) that decomposes each connectivity matrix into a shared loading matrix on the Stiefel manifold, subject-specific symmetric cores capturing individual variation, and an explicit isotropic noise term. This noise separation is absent from conventional principal component analysis competitors, a feature that sharpens eigenvalue gaps and reduces subspace estimation bias.

We develop two complementary estimation frameworks, profiled likelihood and a generalized method of moments, solved via Stiefel-manifold optimization, alongside a manifold-adapted Bayesian information criterion that consistently selects the true latent dimension. For the loading matrix, we establish root-n consistency and asymptotic normality on the Grassmann manifold, characterizing their joint distribution via the Riemannian logarithmic map to enable principled, coordinate-free inference for latent network structures.

Applied to resting-state fMRI data from 37,794 UK Biobank subjects across 360 brain regions, MLFM identifies eight heritable functional networks, with two exceeding a 0.35 heritability threshold. A subsequent genome-wide association study yields 108 significant genetic loci across 27 phenotypes, providing a dimension-reduced pathway for large-scale neuroimaging genetics.

Joint work with: Wenlu Tang, Ke Zhang, Linglong Kong, and Tengfei Li

Understanding why training succeeds in deep neural networks remains a central theoretical challenge, particularly when both the network activations and the loss function are nonsmooth. This talk considers sufficiently wide deep ReLU networks trained directly with hinge loss for classification. Under suitable conditions on the data and network width, full-batch training reaches exactly zero hinge loss on the training data after finitely many updates, with high probability over Gaussian initialization. The key idea is geometric: a progress argument for a linear approximation of the network can be transferred to the actual nonlinear training process. The talk will explain this connection, discuss extensions to other classification and regression losses, and present numerical experiments illustrating finite-step termination and the role of network width.

Modern data science and AI increasingly raise uncertainty quantification challenges that go beyond the classical statistical inference framework, especially those involving discrete, non-numerical, or non-Euclidean parameters, non-numerical or non-Euclidean data, and complex data-generating mechanisms. This talk introduces the Repro Samples method, a general, likelihood-free, and principled approach to statistical inference in such settings. The method utilizes synthetic data, or “repro samples,” that mimic the observed data and applies Fisher inversion directly to the data-generating mechanism or an optimization algorithm. It accommodates inference problems involving discrete, non-numerical, or non-Euclidean parameters, as well as continuous parameters, while providing finite-sample or asymptotic coverage guarantees under appropriate conditions. I will first introduce the basic ideas and then illustrate them through change-point detection in image data, where we jointly quantify uncertainty in the unknown number and locations of change-points. Numerical and real-data examples demonstrate the practical utility and broad applicability of the approach, including uncertainty quantification beyond conventional point estimation and asymptotic approximations.

Joint work with: Junyi Li (Rutgers) and Hao Chen (UC Davis)

For decades, statistical inference has largely been developed one problem at a time. Given a scientific target, such as a treatment effect or a regression function, statisticians design a problem-specific estimator together with a procedure for quantifying its uncertainty. This paper proposes a different paradigm. We focus on a classical problem in statistical inference, confidence interval construction, and develop TabCon, an amortized inference system built on a tabular foundation model that produces confidence intervals for new datasets through a simple forward pass. The key methodological ingredients of TabCon are a sparse mixture-of-experts architecture and reinforcement-learning-based post-training that calibrate the resulting confidence intervals to a desired coverage level. Across a wide range of benchmark datasets, TabCon attains near-nominal coverage while producing short confidence intervals. At inference time, it also offers considerably greater computational efficiency, running 50 times faster than the classical bootstrap procedure, even when the latter uses only 50 bootstrap samples.

Distribution-valued responses arise naturally in many scientific applications, where their relationships with predictors may exhibit structural changes affecting location, variability, and shape. We develop a piecewise Fréchet regression framework under the Wasserstein metric that accommodates unknown breakpoints corresponding to either continuous changes or discontinuities in the regression relationship. Exploiting the exact quantile representation of the Wasserstein distance for univariate distributions, we construct regression estimators and estimate breakpoint locations through a profiled Wasserstein prediction criterion. We establish consistency and investigate the asymptotic properties of the breakpoint estimators, revealing distinct convergence behaviors for continuous and jump breakpoints. Simulation studies assess breakpoint localization and distributional prediction performance, including comparisons with functional principal component approaches. Applications to maternal-age distributions and U.S. metropolitan housing-value distributions illustrate how the proposed framework can characterize structural changes across different parts of the response distribution.

Riemannian flow matching (RFM) extends flow-based generative modeling to data supported on manifolds by learning a time-dependent tangent vector field whose flow-ODE transports a simple base distribution to the data law. We develop a nonasymptotic Total Variation (TV) convergence analysis for RFM samplers that use a learned vector field together with Euler discretization on manifolds. Our key technical ingredient is a differential inequality governing the evolution of TV between two manifold ODE flows, which expresses the time-derivative of TV through the divergence of the vector-field mismatch and the score of the reference flow; controlling these terms requires establishing new bounds that explicitly account for parallel transport and curvature. Under smoothness assumptions on the population and learned flow-matching field, together with mean-square approximation guarantees for the learned field, we obtain explicit bounds with specific instantiations which yield explicit polynomial iteration complexities on the hypersphere and on the Hadamard manifolds (for e.g., SPD manifolds) under mild moment conditions.

Understanding population aging requires a framework that derives age structure from demographic first principles rather than arbitrary chronological thresholds. The Aging Equilibria (AE) model provides a non-arbitrary framework for defining stages of old age by shifting attention from fixed chronological cutoffs to the intrinsic geometry of life tables. AE derives aging structure by recursively extending the stationary population identity, in which the distribution of years lived equals the distribution of years remaining. Applied iteratively, this single symmetry generates a nested sequence of mortality-calibrated age tiers, each representing a structurally deeper stage of survival and preserving the same theoretical logic from the primary population to all secondary populations. Analysis of life tables from 100 countries shows that, although the chronological ages defining each tier rise with increasing life expectancy, the proportions of the stationary population contained within successive tiers remain remarkably stable across diverse mortality regimes. In particular, Tier 3 consistently marks the structural onset of old age, encompassing approximately one-eighth of the stationary population. By replacing arbitrary age thresholds with population-calibrated tiers, AE enables demographically coherent metrics of aging, including adaptive dependency ratios. The framework generalizes beyond human populations, offering a unified theoretical foundation for aging across demography, biodemography, and actuarial science.

Joint work with: Arni Rao, Laboratory for Theory and Mathematical Modeling, Division of Infectious Diseases, Department of Mathematics, Augusta University, Georgia, GA, USA

Neural network-based methods for conditional density estimation have recently gained substantial attention, as various neural density estimators have outperformed classical approaches in real-data experiments. Despite these empirical successes, implementation can be challenging due to the need to ensure non-negativity and unit-mass constraints, and theoretical understanding remains limited. In particular, it is unclear whether such estimators can adaptively achieve faster convergence rates when the underlying density exhibits a low-dimensional structure. This paper addresses these gaps by proposing a structure-agnostic neural density estimator, called the classification-induced neural density estimator and simulator (CINDES) that is straightforward to implement and provably adaptive, attaining faster rates when the true density admits a low-dimensional composition structure. Another key contribution of our work is to show that the proposed estimator integrates naturally into generative sampling pipelines, most notably score-based diffusion models, where it achieves provably faster convergence when the underlying density is structured. We validate its performance through extensive simulations and a real-data application. We also prove the optimality of score-based diffusion models for density estimation when the target density admits a factorizable, low-dimensional, nonparametric structure in a separate work. The main challenge is that the low-dimensional, factorizable structure no longer holds for most diffused timesteps, and it is very difficult to show that these diffused score functions can be well approximated without a significant increase in the number of network parameters.

Joint work with: Yihong Gu, Dehao Dai, Mukherjee, and Ximing Li

Parameter growth in artificial intelligence strains memory and data movement. A looped architecture repeatedly applies one fitted update function, sharing its parameters across iterations; a conventional untied network uses separate parameters at each iteration. We ask whether this reuse also improves statistical accuracy under a common budget on distinct trainable coefficients. For likelihood models, we establish an upper bound on the squared Hellinger risk of looped sieve maximum likelihood and a minimax lower bound for the corresponding untied family, even when its width and depth are jointly tuned. The bounds reveal a parameter–iteration–accuracy tradeoff: additional iterations tighten the approximation bound without adding parameters, while increasing computation and the estimation bound. For targets of known Hölder smoothness, looped residual feedforward networks and a specified post-layer-normalized Transformer attain the minimax polynomial rate, up to logarithmic factors, with a fixed number of bounded real coefficients. At a sufficiently large fixed budget, looped worst-case risk vanishes as sample size grows, whereas the optimal worst-case untied risk remains positive. A risk separation also holds under specified growing-budget schedules. The fixed-count result permits increasing coefficient precision. Gaussian and Laplace regression, binary response, and energy-based generative models illustrate the theory.

Joint work with: Xinyu Tian, University of Minnesota

We present a general framework for future prediction via online aggregation under changing distribution. Our setting is generic in the sense we do not impose any distributional assumptions such as stationarity or structured non-stationarity. The innovation aspect of our approach is to insert a memory hedging mechanism in the online aggregation, which trades off between the adaptiveness to the change and the stability of the prediction. For point prediction, the proposed MELO generates a pool of memory specified expert predictors based on the base experts via a penalized exponentially weighted least-squares scheme. For interval prediction, the new ARIA constructs the memory specified experts based on the sliding-window empirical quantiles of a appropriately specified score sequence. Both MELO and ARIA are adaptive automatically to the changes of the underlying distribution as well as the time-varying speed of the changes. We evaluate both MELO and ARIA on French national electricity-load forecasting through the COVID-19 lockdown using no regime indicators, lockdown dates, or policy covariates. The resulting improvement over the state-of-arts forecasting methods is substantial. They also outperform some newly developed DNN and foundation models. A noticeable fact is that the MELO based on some frozen models trained using the data from a pre-evaluation period, which is economic in computing, provides more accurate prediction than those of the online-updated DNN and foundation models.

Joint work with: Yutong Wang (DRW London) and Yannig Goude (EDF Paris)

Deep learning models can perform remarkable tasks, yet understanding how they arrive at their predictions remains challenging. In this talk, I will discuss recent work developing scalable methods to discover and quantify important feature interactions, from neural circuits in transformers to efficient interaction attribution. These tools (CD-T and SPEX/ProxySPEX) reveal structure hidden within complex models and provide a new lens for interpreting, analyzing, and ultimately understanding deep learning.

This talk discusses the estimation of the regression operator in function-on-function regression models. While traditional research has predominantly focused on linear models or their immediate nonlinear extensions, we propose a neural operator approach to accommodate general regression operators under mild assumptions. Operator learning has emerged as an active area of machine learning, particularly for solving physical models governed by partial differential equations. Using this paradigm, our methodology introduces the separable neural operator, a neural-operator architecture that represents the regression operator through input-dependent coefficient functions and output-dependent basis functions. Beyond adapting this architecture to the regression operator estimation problem, we establish the consistency of the estimator under relatively mild smoothness and sampling conditions, allowing functional data to be observed on dense, possibly irregular, discrete grids. We also apply the proposed approach to the BGC Argo data and demonstrate its potential for oceanographic research.

Joint work with: Su-Yun Huang and Toshinari Morimoto, Institute of Statistical Science, Academia Sinica, Taipei, Taiwan

The talk introduces a test for determining whether conditional distributions are equal, with applications to causal inference, model diagnostics, and transfer learning. To address the loss of power caused by high-dimensional conditioning variables, the method uses generative models and combines observed data with synthetic samples. Sample splitting and studentization control estimation error. The resulting statistic is asymptotically normal under the null and has established local power under nearby alternatives. It requires only consistent estimation of the conditional distribution and performs well against kernel- and energy-based alternatives in empirical studies.

The rapid change in computational capabilities has made Big Data a major modern statistical challenge. Less well understood is the rise of Complex Data as a perhaps greater challenge. Object Oriented Data Analysis (OODA) is a framework for addressing this, in particular providing a general approach to the definition, representation, visualization and analysis of Complex Data. The notion of OODA generally guides data analysis, through providing a useful terminology for interdisciplinary discussion of the many choices typically needed in modern complex data analyses. The main ideas are illustrated through several OODA contexts, including shapes, trees (in the sense of graph theory), covariance matrices and nonnegative curves as data objects.

Fréchet means are among the most accessible descriptors for non-Euclidean data. On compact spaces, they can be nonunique and it turns out, this is just as generic as uniqueness—and at the boundary their asymptotic rates can be arbitrary slow. Such problems do not exist in spaces with curvatures bounded from above by zero, at the price that other problems may occur: vanishing asymptotic fluctuation. We give an overview and new results leaving some questions open.

We model spatially and temporally indexed point process data as a multi-level log-Gaussian Cox process where the log intensity function depends on a partially linear single-index structure of spatio-temporal covariates and three latent functional random effects representing the spatial and temporal random effects as well as their interactions. We assume that the latent functional effects are Gaussian processes with Karhunen-Loeve representations, and model the unknown link function of the single-index as well as the covariance functions of the latent functional effects as splines. We propose to estimate the partially linear coefficients and the single-index link function using a Poisson maximum likelihood method, and the covariance functions of the latent processes using maximum composite likelihood methods. We also propose approaches to predict the functional principal component scores. Under the multi-level dependence structure and allowing the spatio-temporal covariates to be non-stationary, the proposed estimators follow rather unconventional convergence rates which depend on both the number of locations and the number of repeated measures in time. We illustrate the proposed method through a simulation study and a real-data application in modeling bike-sharing events.

We study semi-supervised estimation of the best linear predictor under nonparametric regression models. A common imputation-based approach first estimates the regression function from the labeled data and then uses this estimator to impute responses for the unlabeled covariate vectors. We show that this approach may fail to achieve the parametric rate. The failure is driven by full-dimensional smoothing and is shown to occur when the covariate dimension is sufficiently large relative to the smoothness of the underlying regression function. To address this issue, we consider structured nonparametric smoothing and introduce target awareness for structured function classes, with the regression function projected onto these classes for use in imputation. We develop two target-aware approaches to estimating the best linear predictor. The first uses the original smooth backfitting algorithm, whereas the second employs a new constrained version of smooth backfitting. Under mild conditions, both resulting estimators achieve the parametric rate, and the second is asymptotically more efficient than both ordinary least squares and the first proposal. Simulation studies and real data applications show that the proposed estimators outperform existing methods.

Joint work with: Seung Hyun Moon, Seoul National University

This talk focuses on the integration of statistics, deep learning, and differential equations. In many scientific applications, data generation and evolution are governed by physical mechanisms that are often described by differential equations, while real-world complexity introduces additional effects that are better captured by data-driven tools such as deep learning. We study statistical modeling, estimation, and inference for such data-generating mechanisms. We first develop a framework for semiparametric M-estimation with overparameterized deep neural networks, establishing optimal convergence rates and parametric efficiency. We then introduce semiparametric differential equation models that combine interpretable mechanism-based components with flexible perturbation terms, together with a profiling-based estimation and inference procedure. Finally, we apply the proposed methodology to radiative transfer and atmospheric profile retrieval using FY-4B/GIIRS hyperspectral observations. The resulting hybrid model improves forward radiance reconstruction and enhances temperature profile retrieval accuracy, demonstrating the practical value of our framework.

The increasing use of machine learning technologies on publicly available datasets has also raised concerns about privacy and fairness. Creating synthetic observations that preserve the original information provides a viable alternative for resolving these issues. However, prior research has raised doubts about whether such data could remain effective, particularly when combined with other/future data sources. Conducting valid statistical inference places additional demands on data scientists who generate synthetic data. In our research, we propose adding a redundant synthetic component to make it easier to achieve the desired purposes. The synthetic component naturally provides a tuning mechanism to evaluate how effectively the targets are met. The resulting data-generation mechanism offers several advantages: it satisfies constraints such as privacy protection or fairness control, preserves information from the original data to enhance utility when combined with new data sources, increases statistical power in testing compared with existing methods, and is easy for researchers in other disciplines to use. The methods are developed in a non- and semi-parametric framework, reducing the burden of distributional assumptions for high-dimensional variables. We will discuss the theoretical guarantees and underlying principles. We illustrate the efficacy, quality, and practical applicability of the proposed procedures numerically.

Training on self-generated synthetic data has become increasingly common, yet its theoretical understanding remains limited. We study verified self-training in a linear regression model, where a pre-trained estimator generates synthetic covariate-response pairs, a verification rule keeps pairs whose generated-response error is at most δ, and post-training refits an active subset of coordinates while fixing the remaining coordinates at their pre-trained values. We derive nonasymptotic risk bounds in four regimes determined by the relative sizes of the verification threshold, the generation-noise scale, and the pre-training error scale. The bounds characterize when verified self-generated data improve prediction accuracy. Verification is most effective when generation noise exceeds the pre-training error, since it reduces the error in generated responses that pass verification while preserving informative covariate variation. When the pre-training error dominates, verification tends to retain samples already well fitted by the pre-trained estimator, and the inherited error persists under partial fine-tuning. A similar limitation appears when the generation-noise scale falls below the verification threshold, since acceptance is then governed primarily by the pre-training error term. We also quantify the variance increase caused by the reduced accepted sample size and extend the analysis to logistic regression.

Joint work with: Heejune Sheen, Yale University

We propose a unified approach to constructing confidence regions and conducting hypothesis tests for random objects in general metric spaces. The proposed method bases inference on the criterion used for estimation. Under regularity conditions, we establish asymptotically exact coverage and consistent rejection of fixed alternatives. Our method can be applied to inference for Fréchet means and medians, as well as global and local Fréchet regression. Our results also include two-sample comparisons of population centers and simultaneous confidence regions for global regression. We illustrate the proposed method through applications to several real-world datasets.

Joint work with: Yidong Zhou (University of Minnesota), Taisuke Otsu (London School of Economics), and Hans-Georg Mueller (University of California, Davis)

As medical imaging and clinical video technologies advance, analyzing dynamic behavioral data has become pivotal for precise diagnosis. However, raw clinical videos present high-dimensional, discrete pixel structures that resist classical imaging models. To unlock these complex datasets, we bridge the gap between medical computing and Functional Data Analysis (FDA)—demonstrating that statistical tools from the FDA community are indispensable assets for solving modern clinical imaging bottlenecks.

Grounded in the pioneering framework of Fréchet regression for random objects on non-Euclidean spaces developed by Petersen and Müller (2019), this talk introduces a novel approach to track anatomical landmarks across discrete video frames. We demonstrate how unstructured clinical video clips can be naturally transformed into continuous functional trajectories on a Riemannian manifold. Once mapped into this non-Euclidean domain, the complex dynamics of gait impairment become statistically transparent through the lens of metric-space regression. Utilizing intrinsic variance analysis, we unveil new empirical findings: Freezing of Gait (FoG) episodes in Parkinson’s disease are characterized by a sudden, measurable breakdown in the global synchrony of these functional movement curves. This work highlights the practical power of Müller’s Fréchet regression paradigm in enabling imaging scientists to transform irregular, high-dimensional observations into smooth, highly interpretable functional objects for real-time clinical applications.

Joint work with: Dr. Lorry Luo’s team at CityU HKSAR and Dr. Xu Zhang from South China Normal University

Under certain conditions, the largest eigenvalue of a sample covariance matrix undergoes a well-known phase transition when the sample size and data dimension diverge proportionally. In the subcritical regime, this eigenvalue has fluctuations of order n^{-2/3} that can be approximated by a Tracy-Widom distribution, while in the supercritical regime, it has fluctuations of order n^{-1/2} that can be approximated with a Gaussian distribution. However, the statistical problem of determining which regime underlies a given dataset is far from resolved. We develop a new testing framework and procedure to address this problem. In particular, we demonstrate that the procedure has an asymptotically controlled level, and that it is power consistent for certain alternatives. Also, this testing procedure enables the design of a new bootstrap method for approximating the distributions of functionals of the leading sample eigenvalues within the subcritical regime—which is the first such method that is supported by theoretical guarantees.

Joint work with: Nina Dörnemann