Date/Time : 04 Feb 2026 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Minwoo Chae, Pohang University of Science and Technology

In recent years, diffusion-based deep generative models have achieved remarkable success in various applications. In this talk, we present statistical theories for diffusion models within the framework of nonparametric structured density estimation. To address the curse of dimensionality in nonparametric density estimation, we assume that the underlying density function factorizes into several low-dimensional components. Such factorizable densities are common in important examples, such as Bayesian networks and Markov random fields. We prove that an implicit density estimator constructed from diffusion models achieves the minimax optimal convergence rate with respect to total variation. Technically, we design a novel network architecture, which includes convolutional neural networks as a special case, to construct a minimax optimal estimator.

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Date/Time : 19 Jan 2026 16:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Jasper Lee, University of California, Davis

Mean estimation is perhaps the most fundamental task in statistics, yet there is a divide between the standard theory and practice. The standard theory recommends taking the sample mean, but whose brittleness forces users to apply ad-hoc outlier removal techniques in practice, leading to documented cases of wrong experimental conclusions. On the other hand, theoretical algorithms designed specifically to mitigate such brittleness (e.g. median-of-means and high-dimensional generalizations) have poor empirical performance that they cannot/should not be adopted either.

In this talk, I’ll discuss our efforts to fully resolve the mean estimation problem, achieving (minimax) estimation error that is sharp even in the leading multiplicative constant. I will present a new multivariate mean estimator that has sharp estimation error in any (small) constant dimensions (in preparation), generalizing our previous 1-dimensional mean estimator (FOCS 2021, ICML 2025). I will also discuss a very simple multivariate mean estimator that achieves sharp error guarantees in the “very high-dimensional” regime (ITCS 2022).

The constant-dimensional mean estimator is joint work with Suraj Mathashery, Paul Valiant and Kun Wang, in preparation. The very high-dimensional mean estimator is joint work with Paul Valiant, which appeared in ITCS 2022.

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Date/Time : 16 Dec 2025 14:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Yongchun Li, The Chinese University of Hong Kong

The low-rank constrained optimization arises in various machine learning and operations research problems. It minimizes a linear objective function subject to multiple two-sided linear inequalities and a low-rank domain set. Although the low-rank constrained optimization is generally NP-hard, a viable approach is to convexify the domain set (i.e., replace the domain set with its convex hull), known as “partial convexification.” Partial convexification often leads to a tractable convex relaxation; however, its solution quality lacks theoretical guarantees. To fill this gap, (i) we establish the necessary and sufficient condition under which the partial convexification matches the original low-rank constrained optimization; and (ii) we derive an upper bound on the minimum rank among all the optimal solutions of the partial convexification and prove its tightness. To efficiently solve the partial convexification, we develop a column generation algorithm combined with a rank-reduction algorithm. This combination ensures that the output solution satisfies the theoretical guarantees. Finally, our numerical experiments validate the strength of the partial convexification and the effectiveness of the proposed algorithms.

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Date/Time : 10 Dec 2025 15:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Heikki Kälviäinen, Lappeenranta-Lahti University of Technology

The presentation considers computer vision and machine learning in plankton image recognition and animal re-identification, especially from a point of view of applications. Digital image processing and analysis with machine learning methods could enable efficient solutions for various areas of useful data-centric engineering applications. Challenges with imbalance of datasets, domain adaptation, active learning, open set classification, and metric learning of similarities are considered and related examples are given in plankton recognition and animal re-identification, based on the research of LUT Computer Vision and Pattern Recognition Laboratory (CVPRL).

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Date/Time : 24 Nov 2025 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Wang, Chao, Southern University of Science and Technology

Variational Bayesian inference offers a powerful framework for tackling key challenges in tensor analysis and image restoration, which are critical problems in machine learning and computer vision. This talk presents innovative approaches to address these challenges by integrating Bayesian principles, variational inference, and physical modeling. First, we introduce a Bayesian framework for Tensor Robust Principal Component Analysis (TRPCA) to recover low-rank structures and characterize sparse noise in mixed-noise scenarios. By embedding a low-rank tensor nuclear norm prior and a generalized sparsity-inducing prior within a Bayesian framework, our method learns the optimal tensor nuclear norm and balances low-rank and sparse components automatically. Second, we propose a novel physics-informed optimization framework for jointly solving depth estimation and image restoration from a single defocused image. By modeling the defocused image as a function of a depth map and an all-in-focus (AiF) image based on optical physics, the framework leverages their intrinsic connections. The depth map guides AiF image recovery, while the AiF image regularizes the depth map reconstruction via reconstruction error. A variational inference algorithm, parameterized with deep neural networks, ensures flexibility and high performance.

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Date/Time : 21 Nov 2025 16:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Matthew Shunshi Zhang, University of Toronto

We introduce a new method for analyzing midpoint discretizations of stochastic differential equations (SDEs), which are frequently used in Markov chain Monte Carlo (MCMC) methods for sampling from a target measure π \propto exp(−V). Borrowing techniques from Malliavin calculus, we compute estimates for the Radon-Nikodym derivative for processes which may anticipate the Brownian motion, in the sense that they may not be adapted to the filtration at the same time. Applying these to various popular midpoint discretizations, we are able to improve the regularity and cross-regularity results in the literature on sampling methods. We also obtain a query complexity bound of O(d^{1/4}) for obtaining a ε^2-accurate sample in 𝖪𝖫 divergence, under log-concavity and strong smoothness assumptions for ∇^2 V.

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Date/Time : 19 Nov 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Srecko Durasinovic, Nanyang Technological University

Mixture models, such as Gaussian mixture models (GMMs), are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the mixture parameters. We study the problem of approximating a target measure, available only through finitely many of its moments, by a mixture of distributions from a parametric family (e.g., Gaussian, exponential, Poisson), with approximation quality measured by the 2-Wasserstein ($\was$) or the total variation ($\tv$) distance. Unlike many existing approaches, the parameter set is not assumed to be finite; it is modeled as a compact basic semi-algebraic set. We introduce a hierarchy of semidefinite relaxations with asymptotic convergence to the desired optimal value. In addition, when a certain rank condition is satisfied, the convergence is even finite and recovery of an optimal mixing measure is obtained. We also present an application to clustering, where our framework serves either as a stand-alone method or as a preprocessing step that yields both the number of clusters and strong initial parameter estimates, thereby accelerating convergence of standard (local) clustering algorithms.

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Date/Time : 15 Oct 2025 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Vladimir Spokoiny, Weierstrass Institute for Applied Analysis and Stochastics (WIAS)

The recent paper Gao et al. (2023) on estimation and inference for top-ranking problem in Bradley-Terry-Luce (BTL) model presented a surprising result: component-wise estimation and inference can be done under much weaker conditions on the number of comparison then it is required for the full dimensional estimation. The present paper revisits this finding from completely different viewpoint. Namely, we show how a theoretical study of estimation in sup-norm can be reduced to the analysis of plug-in semiparametric estimation. For the latter, we adopt and extend the general approach from Spokoiny (2025b) to high-dimensional estimation and inference. The main tool of the analysis is a theory of perturbed marginal optimization when an objective function depends on a low-dimensional target parameter along with a high-dimensional nuisance parameter. A particular focus of the study is the critical dimension condition. Full-dimensional estimation requires in general the condition n ≫ p between the effective parameter dimension p and the effective sample size corresponding to the smallest eigenvalue of the Fisher information matrix . Inference on the estimated parameter is even more demanding: the condition n ≫ p^2 cannot be generally avoided; see Spokoiny (2025b). However, for the sup-norm estimation, the critical dimension condition can be reduced to n ≥ C log p.

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Date/Time : 30 Sep 2025 10:00
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Haiyun He, Hong Kong University of Science and Technology, Guangzhou

Watermarking has become a critical technique for distinguishing AI-generated text from human-authored content. In this talk, we introduce a novel theoretical framework for both zero-bit and multi-bit watermarking for Large Language Models (LLMs), aiming to jointly optimize both the watermarking scheme and the detection process. Our approach rigorously characterizes the fundamental trade-offs between watermark detectability, text quality, and information embedding rate. We establish the concept of distributional information embedding, where watermarking actively modifies the token generation process rather than embedding signals into a pre-existing text. Our theoretical analysis reveals that the maximum achievable watermarking rate is dictated by the entropy of the LLM’s output distribution and increases with higher allowable distortion.

Leveraging these insights, we propose an efficient, model-agnostic, and distribution-adaptive watermarking algorithm that optimally balances detectability and text quality while maintaining strict false alarm control. Our method employs a surrogate model along with the Gumbel-max trick to achieve superior detection performance. Empirical evaluations on LLaMA2-13B and Mistral-8×7B demonstrate the effectiveness of our approach. Additionally, we explore robustness considerations, paving the way for watermarking systems that can withstand adversarial attacks more effectively.

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