September 10th

Beatrix Wen

• Title: GNN Explainability

• Abstract: The interpretability of deep learning models has drawn more and more attention over the past few years. In this presentation, I will introduce some popular algorithms that explain how Graph Neural Network (GNN) models work. GNN, as its name indicates, is one specific type of deep learning model that takes graphical data as its input.  

Sehee Park

• Title: What Causal Inference people are doing now:  Combining Observational Data and RCT

• Abstract: This lightning talk is on a hot area of ‘causal inference’. You may have heard of the expression ‘correlation is not causation’. Although we should approach with caution when inferring causal effects from the observational data, it is not impossible. To utilize the rich amount of observational data, the causal inference community nowadays is working on ‘how to incorporate Observational data with Randomized Control Trial(RCT) data’. This talk will introduce the key challenge of the problem, current literature, and some future directions of research.

September 17th

Thabo Samakhoana

• Title: Conic Programming and Smoothness

• Abstract: I will give an introduction to the concept of smoothness for sets. Then I will explain how smoothness can be leveraged to improve constrained optimization, focusing conic programming.

Zekun (Bill) Wang

• Title: Conference Network Analysis

• Abstract: In this presentation, we propose a large-scale conference network data by scraping and cleaning data from EcoSta and CFE-CMStatistics conferences. In this exploration of conference data, we dissect temporal patterns, geographical distributions, attendee demographics, as well as summary statistics such as graphical centrality. Additionally, we focus on the co-presentation at invited sessions to explore the pattern in terms of academic collaboration and social relationships among researchers, institutions and countries. Spectral embedding methods based on graph Laplacian are applied for a low-dimensional representation of such relationship among entities.

September 24th

Eleanor Belkin

• Title: Explainable ML models

• Abstract: This talk will discuss Generalized Additive Models (GAM), their principles and advantages over other learning models.

Parik Chalise, slides

• Title: 1 little idea; 4 big problems

• Abstract: When can you perfectly tile a graph (usually large) using copies of smaller graphs? We give an insight into Dr. G's novel method of solving graph tiling problems using properties of polynomial rings. 

October 1st

George Kevrekidis

• Title: Some recent work with Conformal Autoencoders

• Abstract: We will introduce the conformal autoencoder (neural network) architecture and discuss applications to dimension reduction, disentanglement, and computing invariants. This will be from a geometric perspective. Time permitting, we will discuss applications to some equivalence problems.

October 8th

Aaron Zoll

• Title: An Optimal Method for Minimizing Heterogeneously Smooth and Convex Compositions

• Abstract:  In this talk we propose a universal, optimal algorithm for convex minimization problems of the composite form f(x) + h(g1(x), ...,  gm(x)). We allow each gi to independently range from being nonsmooth Lipschitz to smooth and from convex to strongly convex, described by notions of Holder continuous gradients and uniform convexity. Note although the objective is built from a heterogeneous combination of components, it does not necessarily possess any smoothness, Lipschitzness, or any favorable convexity properties. Regardless, we show that our proposed sliding accelerated gradient method converges at an optimal rate guarantees in terms of oracle access to (sub)gradients of each gi. 

As a key application, fixing h as a nonpositive indicator function, this model readily captures functionally constrained minimization: f(x) subject to gi(x) ≤ 0. Our algorithm and analysis are directly inspired by the smooth constrained minimization method of Zhe Zhang and George Lan and their associated Q-analysis technique. Our theory recovers their accelerated guarantees and extends them to benefit from heterogeneously smooth and convex constraints.

October 15th

Ian McPherson

• Title: Wasserstein Barycenters: Riemannian Optimization Perspective

• Abstract: In this talk, I will introduce the notion of a manifold isometrically embedded in 2-Wasserstein space, which a concrete special case may be a class of images for example. Given n sample measures/images, can one recover their intrinsic average without explicit access to the manifold. We will highlight a graph based algorithm, taking inspiration from ISOMAP and Riemannian SGD. After presenting promising numerical results on a toy example, we will slightly shift gears and turn towards proofs of local convergence rates. Through this, we will highlight how we may lift intuitions from the Euclidean setting to this much more interesting metric space. Along the way, we will highlight theoretical intuitions and bottlenecks when using tools from Optimal Transport, Riemannian Optimization, and Convex Analysis for these proofs. Time permitting, I will also show pictures of my dogs.

October 22nd

Lowen Peng

• Title: Spontaneous Stochasticity in Fluid Systems

• Abstract: In this talk I give a quick introduction to a type of theoretical critical phenomenon (spontaneous stochasticity) that gives physical meaning to nonunique weak solutions to PDEs. In this phenomenon there remains nontrivial stochasticity in a vanishing noise regime, supported exactly on the plurality of solutions to said PDE, showing the (1) physical meaningfulness of such solutions and (2) presence of something akin to symmetry breaking for stochasticity. I discuss evidence for this phenomenon, our contribution (a related proof in the case of fluid systems with molecular noise), and if time permits, future work and applications. Keywords: mathematical physics, PDEs, stochastic calculus, fluid dynamics.

October 29th

Abdel

• Title:  Preconditioning for over parameterized composite optimization

• Abstract: Composite optimization problems involve minimizing a composition of a smooth map with a convex function. Such objectives arise from numerous applications in data science and signal processing, including phase retrieval, matrix sensing, and tensor recovery. Iterative methods like subgradient descent are known to converge linearly for certain problems when the smooth map is well-conditioned and exactly parameterized. However, when either of these conditions fails, which is common in large-scale applications, subgradient descent exhibits much slower sublinear convergence or in certain nonconvex problems, fail to converge. To overcome this limitation, we introduce a new preconditioned variant of subgradient descent that, under mild conditions, converges linearly at a rate independent of the conditioning regardless of whether the smooth map is overparameterized. We further demonstrate that these conditions hold for several problems of interest, including square-variable formulations, symmetric and asymmetric low-rank matrix recovery problems, and tensor factorization.

November 5th

Dapeng Yao

• Title: A Domain Knowledge-guided Reinforcement Learning Approach for Optimizing Antiretroviral Therapy in People with HIV

• Abstract: Despite the success of antiretroviral therapy (ART) in achieving viral suppression in people with HIV (PWH), numerous ART-related adverse effects have been reported. Effective HIV management should prioritize viral suppression while simultaneously minimizing adverse effects, with regimens tailored to the specific characteristics of each individual. However, there is a lack of individualized approaches that leverage real-world evidence to assist with ART selection in clinical practice, particularly for treatment-experienced PWH. To address this, we developed HIV-AICare, a data-driven artificial intelligence (AI) tool for personalized ART selection. Leveraging reinforcement learning and clinical guidelines, HIV-AICare streamlines the complex process of selecting ART regimens, optimizing both treatment efficacy and long-term patient outcomes. Applied to the MACS/WIHS Combined Cohort Study data, HIV- AICare effectively navigates HIV treatment complexities. Its recommendations align with current clinical practice, offering tailored, guideline-compliant treatment options, highlighting the potential of a data-driven and domain knowledge-guided approach to enhance clinical decision-making.

November 12th

Alan Luner, slides

• Title: Performance Estimation for Smooth and Strongly Convex Sets

• Abstract: Given an optimization algorithm, the study of its worst-case convergence guarantees over some family of problem instances can be framed as a meta-optimization problem, called the Performance Estimation Problem (PEP). Through PEP we can obtain tight numerical (and sometimes analytical) convergence rates for various algorithms. Past work in Performance Estimation focused on structured functions; we extend the theory to apply to algorithms over structured sets. In this talk, I will show how we build our PEP for structured sets. I will then show how it can be applied to various constrained optimization algorithms (with a focus on Frank-Wolfe) for tight numerical convergence rates, step size improvement, and insights into acceleration.

November 19th

Wilson Gregory, slides

• Title:  Robust Emulator for Compressible Navier-Stokes using Equivariant Geometric Convolutions

• Abstract: Recent methods to simulate complex fluid dynamics problems have replaced computationally expensive and slow numerical integrators with surrogate models learned from data. However, while the laws of physics are relationships between scalars, vectors, and tensors that hold regardless of the frame of reference or chosen coordinate system, surrogate machine learning models are not coordinate-free by default. We enforce coordinate freedom by using geometric convolutions in three model architectures: a ResNet, a Dilated ResNet, and a UNet. In numerical experiments emulating 2D compressible Navier-Stokes, we see better accuracy and improved stability compared to baseline surrogate models in almost all cases. The ease of enforcing coordinate freedom without making major changes to the model architecture provides an exciting recipe for any CNN-based method applied on an appropriate class of problems.

November 26th

Thanksgiving break!

December 3rd

Zan Ahmad

• Title: Enforcing Symmetries in Diffeomorphic Mapping Operator Learning of PDEs

• Abstract: Using known symmetries of certain differential operators on a particular family of domains and exploiting them in a novel operator learning approach that diffeomorphically maps solutions to a canonical space where a latent operator is learned and then pulled back to target domains to be evaluated. The representation of the solutions in this canonical space (dimension and complexity) is related to the chosed domain itself and the transformation used to push PDE solutions to that space, which may affects how well the network can learn the overall solution. This talk describes the problem in detail and presents some toy examples to motivate further investigation.