The Data Science and Machine Learning Seminar as a regular seminar in the Department of Mathematics at the Florida State University. Beginning in Fall 2025, the seminar will collaborate with the Artificial Intelligence Seminar of the Department of Scientific Computing. Together, they will host two joint talks: one in the Department of Mathematics and one in the Department of Scientific Computing.
The organizers of the Data Science and Machine Learning Seminar are Martin Bauer and Tom Needham. Please contact one of the organizers if you have any questions and/or wish to give a talk in our seminar.
A schedule of the upcoming semester can be found below. Unless otherwise noted, all meeting will be held on Fridays at 1:20 p.m. in Love 106.
Fall 2025
08/29/2025
Organizational Meeting
09/05/2025 -- Remote
Speaker: Elias Döhrer (TU Chemnitz)
Title: Incorporating Self-Repulsion into Riemannian metrics
Abstract: Inspired by the work of Michor, Bauer, Bruveris, Maor et al. on the manifold of immersed curves, we propose a new strong Riemannian metric on the manifold of (parametrized) embedded curves of H^s regularity, s in (3/2,2). The construction is motivated by the concept of tangent-point energies, a family of self-avoiding functionals on curves and surfaces of arbitrary dimension. Their notion of self-repulsion allowed us to capture the topological property „embeddedness“ in a continuous way. This talk illustrates the impact of this metric and highlights its most important features, namely metric and geodesic completeness, relative compactness of bounded sets with respect to the weak H^s topology, and existence of length-minimizing geodesics between every pair of curves in the same knot class. https://arxiv.org/abs/2501.16647
09/12/2025
Speaker: Caroline Moosmüller (University of North Carolina at Chapel Hill)
Title: Learning in the space of probability measures
Abstract: Many datasets in modern applications - from cell gene expression and images to shapes and text documents - are naturally interpreted as probability measures, distributions, histograms, or point clouds. This perspective motivates the development of learning algorithms that operate directly in the space of probability measures. However, this space presents unique challenges: it is nonlinear and infinite-dimensional. Fortunately, it possesses a natural Riemannian-type geometry which enables meaningful learning algorithms. This talk will provide an introduction to the space of probability measures and present approaches to unsupervised, supervised, and manifold learning within this framework. We will examine temporal evolutions on this space, including flows involving stochastic gradient descent and trajectory inference, with applications to analyzing gene expression in single cells. The proposed algorithms are furthermore demonstrated in pattern recognition tasks in imaging and medical applications.
09/19/2025 -- Joint Seminar with the SC Artificial Intelligence Seminar
Speaker: Rocío Díaz Martín (FSU)
Title: The Barycentric Coding Model in Optimal Transport
Abstract: The context of this seminar will be the theory of Optimal Transport and its applications. We will consider the problem of estimating a point, either a distribution or a network, under the Barycentric Coding Model with respect to the Wasserstein (W) or Gromov-Wasserstein (GW) distance functions. Specifically, assuming that the target belongs to the set of W or GW barycenters of a finite collection of known templates, we aim to estimate the unknown barycentric coordinates with respect to those templates. In other words, the goal is to determine the right combination of templates (or barycentric coordinates) that best reconstructs the target. From the perspective of harmonic analysis, computing barycenters can be seen as a 'synthesis problem', whereas retrieving their coordinates corresponds to solving an 'analysis problem'. We will review the general theory for the classical case, i.e., using the Wasserstein metric, and then delve into the Gromov-Wasserstein case. For the latter, we focus on algorithms for finding barycentric coordinates (analysis), leveraging existing techniques for constructing barycenters (synthesis) that rely on fixed-point iteration (G. Peyré, M. Cuturi, and J. Solomon, 2016) and differentiation approaches via a blow-up method (S. Chowdhury and T. Needham, 2020). Applications will include covariance estimation, classification, compression, and data imputation.
09/26/2025
Speaker: Cagatay Ayhan (FSU)
Title: Equivalence of Landscape and Erosion Distances for Persistence Diagrams
Abstract: This talk is based on our recent work arXiv:2506.21488, which establishes connections between three of the most prominent metrics on persistence diagrams in topological data analysis: the bottleneck distance, Patel’s erosion distance, and Bubenik’s landscape distance. Our main result shows that the erosion and landscape distances are equal, thereby bridging the former's natural category-theoretic interpretation with the latter's computationally convenient structure. The proof utilizes the category with a flow framework of de Silva et al., and leads to additional insights into the structure of persistence landscapes. Our equivalence result is applied to prove several results on the geometry of the erosion distance. We show that the erosion distance is not a length metric, and that its intrinsic metric is the bottleneck distance. We also show that the erosion distance does not coarsely embed into any Hilbert space, even when restricted to persistence diagrams arising from degree-0 persistent homology. Moreover, we show that erosion distance agrees with bottleneck distance on this subspace, so that our non-embeddability theorem generalizes several results in the recent literature.
10/03/2025
Speaker: Ali Kara (FSU)
Title: Linear Function Approximations in Reinforcement Learning
Abstract: Control and learning of stochastic dynamical systems suffer from both the curse of dimensionality and the curse of history, since an optimal control generally depends on the entire history of observables. In this talk, I will talk about the standard approach of linear function approximation for learning in control. We will see that in this setting; the learning algorithms track the composition of an approximate Bellman operator with a projection operator. For policy evaluation, this composition can be shown to be contractive in L_2 norm of the stationary distribution of the finite-memory variables. Consequently, the learning method converges to an estimate that is sufficiently close to the true value of the policy under appropriate conditions.
However, for optimal value estimation, due to the mismatch between the exploration policy and the optimal policy, the learning algorithms, in general, may be unstable except in certain special cases. These special cases include: (i) when the basis functions are orthogonal, (ii) when the output of Bellman operator remains in the span of the basis functions.
10/10/2025
Speaker: Kun Meng (FSU Statistics)
Title: A Bridge Between Topological and Functional Data
Abstract: In the 21st century, we have seen a growing availability of shape-valued and imaging data, prompting the development of new statistical methods to analyze them. Importantly, bridging the new methods and existing frameworks is advisable. In this talk, I will introduce several statistical inference methods for shapes and images based on the Euler characteristic. These methods have applications in many fields, such as geometric morphometrics and radiomics. From a statistical perspective, these methods are naturally connected to functional data analysis. From a mathematical viewpoint, they are grounded in solid foundations, bridging various branches of mathematics: algebraic and tame topology, Euler calculus, functional analysis, and probability theory. I will also briefly discuss some of my ongoing and future research directions.
10/17/2025
Speaker:
10/24/2025 -- Joint Seminar with the SC Artificial Intelligence Seminar
!!!Special Location and time: 499 Dirac Science Library at 12:00pm!!!
Speaker: Gordon Erlebacher (FSU Scientific Computing)
Title: Latest Architectures, Hierarchical Reasoning Model
11/07/2025 -- Academic Job Market Discussion
Speakers: Rocío Díaz Martín (FSU), Ali Kara (FSU), Zhe Su (Auburn), Zezhong Zhang (Auburn)
11/14/2025
Speaker: Mao Nishino
11/21/2025
Speaker: Wenwen Li