Joint Statistics and DSI Colloquium: Mateo Díaz
11:30 am–12:30 pm DSI 105
Mateo Díaz
Assistant Professor
Department of Applied Mathematics and Statistics
Mathematical Institute for Data Science
Johns Hopkins University
Title: Leveraging Structure for Faster Algorithms in Optimization and Diffusion
Abstract: Large-scale iterative methods drive modern AI, yet their theoretical foundations often lag behind their empirical success. We argue that bridging this gap requires identifying the inherent problem structure that enables these algorithms to perform well. This talk instantiates this principle across two domains: optimization and generative modeling.
First, we derive new theoretical guarantees for the Levenberg–Morrison-Marquardt method. Although this method is ubiquitous in settings that demand highly accurate solutions—for instance, when training physics-informed neural networks for scientific discovery—classical guarantees do not explain its strong empirical performance in modern overparameterized, ill-conditioned regimes. By reframing it through the lens of composite optimization, we uncover geometric conditions that ensure fast convergence even in these challenging modern regimes.
Second, we introduce Proximal Diffusion Models (PDM). While standard diffusion models rely on score-matching and forward discretization, we demonstrate that a backward discretization using proximal maps offers significant theoretical and practical advantages. Under mild conditions, we prove that PDM achieves $\varepsilon$-accuracy in KL-divergence within $\widetilde{O}(d/\sqrt{\varepsilon})$ steps and empirically demonstrate that it outperforms conventional methods using fewer sampling iterations.
Joint Statistics and DSI Colloquium: Jiaqi Zhang
4:00–5:00 pm DSI 105
Jiaqi Zhang
PhD Candidate
Massachusetts Institute of Technology
Title: Modeling Large-Scale Interventions
Abstract: Complex causal mechanisms among genes govern cellular functions in health and disease. Understanding these mechanisms can accelerate therapeutic discovery but remains challenging due to the large number of genes and their intricate dependencies. Recent advances in experimental technologies are making this problem increasingly tractable: it is now possible to systematically intervene on individual genes or gene combinations in single cells and measure their downstream effects, enabling empirical identification and validation of causal relationships. However, interventional data are high-dimensional, making interpretation challenging, and costly to collect.
In this talk, I will present our work tackling these challenges from three aspects. First, we introduced causal representation theories and algorithms with identifiability guarantees to uncover latent variables behind high-dimensional data. Second, we developed a method to model interventional data that can predict the effects of novel interventions with high accuracy, incorporating both distributional shifts and prior domain knowledge. Finally, we showed how predictive intervention modeling can improve future experimental design, illustrated by an application where we predicted and validated previously unknown T-cell regulators with therapeutic potential for cancer immunotherapy.
Billingsley Lectures on Probability: Christophe Garban
5:00–6:00 pm Kent 120
Billingsley Lectures on Probability
Reception immediately following the lecture at 6:10 pm, in Jones 111, 5747 S Ellis Ave.
Christophe Garban
Université Lyon 1/Courant - NYU
Title: Continuous Symmetry and Phase Transitions in Lattice Spin Systems
Abstract: A central problem in statistical physics is to understand how spins placed on the lattice Z^d interact and collectively organize at different temperatures. When the spins take values in a discrete set — for instance in the celebrated Ising model, where \sigma_x\in\{−1,+1\} — the mechanisms governing phase transitions are by now relatively well understood.
The situation changes dramatically when the spins take values in a continuous space, such as the unit circle S^1 in the XY model or the unit sphere S^2 in the classical Heisenberg model. In this setting, new phenomena appear, and the behavior depends strongly on whether the underlying symmetry is Abelian or non-Abelian. In particular, the non-Abelian case remains far more mysterious.
In this talk, I will introduce the mathematics of spin systems with continuous symmetry, emphasizing their deep connections with analysis, including harmonic functions, harmonic maps, and geometric analysis. I will also describe some recent results and open problems in the area.
No prior background in statistical physics or probability will be assumed. Based on joint works with J. Aru, D. van Engelenburg, P. Dario, N. de Montgolfier, A. Sepúlveda and T. Spencer.
Reception immediately following the lecture at 6:10 pm, in Jones 111, 5747 S Ellis Ave.