Title: Dissecting tumor transcriptional heterogeneity from single-cell RNA-seq data by generalized binary covariance decomposition

Abstract: Profiling tumors with single-cell RNA sequencing has the potential to identify recurrent patterns of transcription variation related to cancer progression and to produce therapeutically relevant insights. However, strong inter-tumor heterogeneity can obscure more subtle patterns that are shared across tumors. 

In this talk, I will introduce a novel statistical method, generalized binary covariance decomposition (GBCD), to address this problem. GBCD can decompose transcriptional heterogeneity into interpretable components, including patient-specific, dataset-specific and shared components relevant to disease subtypes. In the presence of strong inter-tumor heterogeneity, it can produce more interpretable results than existing methods. 

Applied to data on pancreatic ductal adenocarcinoma, GBCD produced a refined characterization of existing tumor subtypes and identified a gene expression program prognostic of poor survival independent of tumor stage and subtype. The gene expression program is enriched for genes involved in stress responses,and suggests a role for the integrated stress response in pancreatic ductal adenocarcinoma.

Title: Evaluating LLMs When They Do Not Know the Answer: Statistical Evaluation of Mathematical Reasoning via Comparative Signals

Abstract: Evaluating mathematical reasoning in LLMs is constrained by limited benchmark sizes and inherent model stochasticity, yielding high-variance accuracy estimates and unstable rankings across platforms. On difficult problems, an LLM may fail to produce a correct final answer, yet still provide reliable pairwise comparison signals indicating which of two candidate solutions is better. We leverage this observation to design a statistically efficient evaluation framework that combines standard labeled outcomes with pairwise comparison signals obtained by having models judge auxiliary reasoning chains. 

Treating these comparison signals as control variates, we develop a semiparametric estimator based on the efficient influence function (EIF) for the setting where auxiliary reasoning chains are observed. This process yields a one-step estimator that achieves the semiparametric efficiency bound, guarantees strict variance reduction over naive sample averaging, and admits asymptotic normality for principled uncertainty quantification. 

Across simulations, our one-step estimator substantially improves ranking accuracy, with gains increasing as model output noise grows. Experiments on GPQA Diamond, AIME 2025, and GSM8K further demonstrate more precise performance estimation and more reliable model rankings, especially in small-sample regimes where conventional evaluation is pretty unstable.

Title: Adaptive designs: Methods and applications

Abstract: Adaptive designs for clinical trials were identified as a means to make the clinical development of therapies more efficient. Furthermore, adaptive designs can be used to make trials more robust against misspecifications in the planning phase. Focussing on confirmatory trials, an overview of adaptive design methodology will be provided. We start by considering nuisance-parameter-based sample size re-estimation, also known as internal pilot study designs. We demonstrate that re-estimating the sample size based on blinded (non-comparative) data has in most situations no practically relevant effect on the Type I error rate and maintains the power at a desired level for the planning alternative independent of the size of the nuisance parameter. In the second part of the presentation, adaptive seamless designs with treatment or subgroup selection are considered. We show how the Type I error rate can be controlled in very flexible designs. Practically relevant aspects such as the use of early outcomes to inform the interim decision on the adaptation while testing treatment effects on clinically relevant long-term outcomes are discussed. The methods will be motivated and illustrated using clinical trial examples.

Title: Several Studies in Label Shift

Abstract: We provide an introduction to label shift problems. In the context of discrete response, we study the importance weights confidence set problem by a paradigm shift from traditional inversion-based inference to a direct matrix constraint framework. We use this framework to characterize a joint confidence region and extract marginal intervals through linear programming, deriving provably tighter bounds for importance weights while maintaining exact finite-sample validity. In the context of continuous response, we study the estimation and inference of a general target population characteristic by developing doubly and singly robust estimators as well as the efficient estimator. Many ongoing and future developments will be discussed too.

Title: Multivariate Poisson Intensity Estimation via Low-Rank Tensor Decomposition

Abstract: In this work, we propose new matrix- and tensor-based methodologies for estimating multivariate intensity functions of inhomogeneous point processes. By viewing multivariate intensity functions as infinite-dimensional matrices or tensors within function spaces, our algorithms attain the optimal bias-variance trade-off, yielding rate-optimal estimation error with model complexity governed by matrix or tensor ranks. They substantially improve estimation accuracy while simultaneously reducing computational cost. 

To illustrate the adaptivity of the proposed framework, we show that many fundamental classes of multivariate functions, including additive and mean-field models, admit finite-rank tensor representations. We apply our method to a four-dimensional U.S. Geological Survey earthquake dataset, comprising such features as latitude, longitude, depth and magnitude. Our tensor estimator recovers localized seismicity patterns in California, Oklahoma, the Pacific Northwest and the north-central United States, whereas the kernel baseline ove-rsmooths them.

The paper is available here: https://arxiv.org/abs/2504.15879

Title: An Introduction to Extended Fiducial Inference: Theory, Computation, and Applications

Abstract: Extended fiducial inference provides a general paradigm for statistical inference in modern data science. Its defining feature is to formulate statistical inference as the problem of solving data-generating equations under uncertainty. EFI first constructs a fiducial law for the unobserved random errors underlying the observations and then propagates this law to the parameter space, either through an inverse mapping or, more generally, through a compatibility measure defined on the inverse fiber. 

This formulation enables EFI to address several difficulties encountered in Fisher’s original fiducial argument, including issues related to conditioning, marginalization, and non-invertibility. We develop general theoretical foundations for EFI that accommodate both single-valued and set-valued inverse mappings and apply in both low- and high-dimensional regimes. We also develop an adaptive stochastic-gradient MCMC computational framework for simulating the latent random errors and learning neural inverse mappings. The theory and computational methodology are illustrated through a variety of examples, including complex hypothesis testing, semi-supervised learning and uncertainty quantification for physics-informed neural networks.