Statistics Seminar - Spring 2026

For questions about the seminar schedule, please contact Chenlu Shi and Yan Sun

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February 26

Dr. Chi-Kuang Yeh, Georgia State University

Single and multi-objective optimal designs for group testing experiments

Group testing, or pooled-sample testing, is widely used in large-scale screening and resource-constrained studies, yet principled design methodology for precise parameter estimation remains limited. This talk presents an optimal design framework for group testing that targets efficient estimation of key model parameters while accounting for cost constraints. Beyond classical criteria such as D-, D_s-, and A-optimality, a central novelty is the introduction of maximin design principles, including potentially non-differentiable criteria, into group testing procedures. These nondifferentiable criteria have not previously been explored in this context and yield designs with strong worst-case guarantees and improved robustness. The framework accommodates both large-sample settings through optimal approximate designs and small-sample studies through exact optimal designs, enabling systematic assessment of robustness to changes in criteria, statistical models, and cost structures. We demonstrate the practical impact of this approach through an application to Chlamydia screening using imperfect assays under budget constraints, and show that precise parameter estimation via optimal design is a foundational step that directly enables efficient and reliable sequential group-testing procedures.

This talk will be mainly based on the paper that is in revision, https://arxiv.org/abs/2508.08445, and the other two papers that are under review.

Homepage: https://chikuang.github.io/ 

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March 12

Dr. Aram-Alexandre Pooladian, Yale University

Blind denoising diffusion models and the blessings of dimensionality

We analyze, theoretically and empirically, the performance of generative diffusion models based on \emph{blind denoisers}, in which the denoiser is not given the noise amplitude in either the training or sampling processes. Assuming that the data distribution has low intrinsic dimensionality, we prove that blind denoising diffusion models (BDDMs), despite not having access to the noise amplitude, \emph{automatically} track a particular \emph{implicit} noise schedule along the reverse process. Our analysis shows that BDDMs can accurately sample from the data distribution in polynomially many steps as a function of the intrinsic dimension. Empirical results corroborate these mathematical findings on both synthetic and image data, demonstrating that the noise variance is accurately estimated from the noisy image. Remarkably, we observe that schedule-free BDDMs produce samples of higher quality compared to their non-blind counterparts. We provide evidence that this performance gain arises because BDDMs correct the mismatch between the true residual noise (of the image) and the noise assumed by the schedule used in non-blind diffusion models. This is joint work with Zahra Kadkhodaie, Sinho Chewi, and Eero Simoncelli.

Preprint available at https://arxiv.org/abs/2602.09639 

Homepage: https://arampooladian.com/ 

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April 2

Tareq Aldirawi, NJIT

Conformal Risk Control Under Non-Monotone Loss

Conformal risk control (CRC) provides distribution-free guarantees for controlling the expected loss at a user-specified level. Existing theory typically assumes that the loss decreases monotonically with a tuning parameter that governs the size of the prediction set. This assumption is often violated in practice, where losses may behave non-monotonically due to competing objectives such as coverage and efficiency. 

We study CRC under non-monotone loss functions when the tuning parameter is selected from a finite grid, a common scenario in thresholding or discretized decision rules. Revisiting a known counterexample, we show that the validity of CRC without monotonicity depends on the relationship between the calibration sample size and the grid resolution. In particular, risk control can still be achieved when the calibration sample is sufficiently large relative to the grid. 

We provide a finite-sample guarantee for bounded losses over a grid of size $m$, showing that the excess risk above the target level $\alpha$ is of order $\sqrt{\log(m)/n}$, where $n$ is the calibration sample size. A matching lower bound shows that this rate is minimax optimal. We also derive refined guarantees under additional structural conditions, including Lipschitz continuity and monotonicity, and extend the analysis to settings with distribution shift via importance weighting. 

Numerical experiments on synthetic multilabel classification and real object detection data illustrate the practical impact of non-monotonicity. Methods that account for finite-sample deviations achieve more stable risk control than approaches based on monotonicity transformations, while maintaining competitive prediction-set sizes.

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April 9

Dr. Xiang Li, University of Pennsylvania

What Can Statistics Offer to Language Models: Watermarking and Evaluation

Large language models (LLMs) have transformed how we generate and process information, yet two foundational challenges remain: ensuring the authenticity of their outputs and accurately evaluating their true capabilities. In this talk, I argue that both challenges are, at their core, statistical problems, and that statistical thinking can play an important role in advancing reliable and principled research on large language models. I will present two lines of work that approach these problems from a statistical perspective.

The first part introduces a statistical framework for language watermarks, which embed imperceptible signals into model-generated text for provenance verification. By formulating watermark detection as a hypothesis testing problem, this framework identifies pivotal statistics, provides rigorous Type I error control, and derives optimal detection rules that are both theoretically grounded and computationally efficient. It clarifies the theoretical limits of existing methods, such as the Gumbel-max watermark, and guides the design of more robust and powerful detectors. The second part focuses on language model evaluation, where I study how to quantify the unseen knowledge that models possess but may not reveal through limited queries. To that end, I introduce a statistical pipeline, based on the smoothed Good–Turing estimator, to estimate the total amount of a model’s knowledge beyond what is observed in benchmark datasets. The findings reveal that even advanced LLMs often articulate only a fraction of their internal knowledge, suggesting a new perspective on evaluation and model competence. Together, these projects represent an ongoing effort to develop statistical foundations for trustworthy and reliable language models, with applications ranging from watermark detection to model evaluation.

This talk is based on the following works:
https://arxiv.org/abs/2404.01245 
https://arxiv.org/abs/2506.02058 
and will briefly mention follow-up studies:
https://arxiv.org/abs/2411.13868 
https://arxiv.org/abs/2510.22007 

Homepage: https://lx10077.github.io/ 

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April 23

Dr. Yuchen Wu, Cornell University

Statistical Inference in an Interactive Learning Paradigm

The proliferation of generative artificial intelligence has given rise to an interactive learning paradigm, where model parameters are continuously updated using not only data generated by natural processes, but also synthetic outputs produced by other models. This paradigm introduces two major challenges: (1) training data are no longer drawn exclusively from the target population, undermining a core assumption of classical statistical learning theory, and (2) model training processes become inherently correlated, as models influence one another through repeated exposure to each other’s synthetic outputs. Establishing reliable statistical inference in such interactive environments therefore remains an important open problem. In particular, there is growing concern about model collapse, a phenomenon in which the performance of generative models progressively degrades as they are trained on synthetic data produced by earlier model generations.

In this work, we study the behavior of generative models under general interaction patterns. We formalize these interactions using directed graphs and show that the occurrence of model collapse depends critically on the graph’s topology. Within this framework, we derive an explicit necessary and sufficient condition characterizing when model collapse occurs. Our analysis covers both finite-sample results for linear regression and asymptotic guarantees for general M-estimators. We further validate our theoretical findings through extensive numerical experiments.

This is based on joint work with Kangjie Zhou and Weijie Su.

Homepage: https://wuyc0114.github.io/ 

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April 30

Dr. Amir Sagiv, NJIT Department of Mathematical Sciences

Sampling by Transport and the Approximation of Measures

Transportation of measure underlies many contemporary methods in machine learning and statistics. Sampling, which is a fundamental building block in computational science, can be done efficiently given an appropriate measure-transport map. We ask: what is the effect of using approximate maps in such algorithms? We propose a new framework to analyze the approximation power of measure transport. This framework applies to existing algorithms, but also suggests new ones. At the core of our analysis is the theory of optimal transport regularity, approximation theory, and an emerging class of inequalities, previously studied in the context of uncertainty quantification (UQ).

Homepage: https://asagivmath.github.io/ 

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May 7

Xiaotian Mu, NJIT Department of Mathematical Sciences

Learning Latent Structures from Single-Cell Data to Explain Bulk Gene Expression

Bulk RNA sequencing provides a robust and cost-effective way to measure gene expression at the tissue level, but it averages signals across many different cell types, which makes it difficult to understand the underlying cellular mechanisms. Single-cell RNA sequencing, on the other hand, offers much finer resolution by capturing variability across individual cells, although it is often noisy, sparse, and high-dimensional.

In this work, we explore how information from single-cell data can be used to better interpret bulk expression. Rather than relying on raw single-cell measurements or predefined cell-type averages, we first summarize the data into a low-dimensional representation that captures the main patterns of variation across cells. These components are then used as features in a simple regression framework to model bulk expression.

This provides a flexible, data-driven alternative to traditional deconvolution approaches, allowing bulk signals to be interpreted in terms of latent biological patterns instead of fixed cell types. More broadly, our framework can highlight how representation learning can serve as a bridge between cell-level and tissue-level transcriptomic data.

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Last updated: May 4, 2026