Georgia Institute of Technology College of Sciences

Partial identification provides an alternative to point identification: instead of pinning down a unique parameter estimate, the goal is to characterize a set guaranteed to contain the true parameter value. Many partial identification approaches take the form of linear optimization problems, which seek the "best- and worst-case scenarios" of a proposed model subject to the constraint that the model replicates correct observable information. However, such linear programs become intractable in settings with multivalued or continuous variables. This paper introduces a novel method to overcome this computational and statistical curse of cardinality: an entropy penalty transforms these potentially infinite-dimensional linear programs into general versions of multi-marginal Schrödinger bridges, enabling efficient approximation of their solutions. In the process, we establish novel statistical and mathematical properties of such multi-marginal Schrödinger bridges---including an analysis of the asymptotic distribution of entropic approximations to infinite-dimensional linear programs. We illustrate this approach by analyzing  instrumental variable models with continuous variables, a setting that has been out of reach for existing methods.

Particle physics research relies on making statistical statements about Nature. The field is one of the last bastions of classical statistics and certainly among its most rigorous users, relying on a worldwide computing grid to process zettabyte-scale data. Recent AI-enabled developments have reinvigorated research in classical statistics, particularly by removing the need for asymptotic approximations in many calculations.

In this talk, I will discuss how AI has allowed us to question core assumptions in our statistical inference techniques. Neural networks enable high-dimensional statistical inference, avoiding aggressive data reduction or the use of unnecessary assumptions. However, they also introduce new sources of systematic uncertainty that require novel uncertainty quantification tools. AI further enables more robust statistical inference by accelerating Neyman inversion and confidence-interval calibration. These advances allow the design of new test statistics that leverage Bayesian mathematical tools while still guaranteeing frequentist coverage, an approach that was previously considered computationally infeasible. These new techniques raise questions about practical methods for handling nuisance parameters, the definition of point estimators, and the computationally efficient implementation of mathematical solutions. If time permits, I will also introduce the emerging challenge of non-nestable hypothesis testing in particle physics.

My group is among the teams leading this revitalization of classical statistical research in particle physics, and I look forward to connecting with students and senior colleagues at Georgia Tech who are interested in contributing to this emerging field.

Bio: Aishik Ghosh is an assistant professor in the School of Physics at Georgia Tech with a focus on developing AI methods to accelerate fundamental physics and astrophysics. His group works on theoretical physics, statistical methods, and experiment design. For robust scientific applications, Dr. Ghosh focuses on uncertainty quantification, interpretability, and verifiability of AI algorithms, targeting publications in physics journals and ML conferences.

The bi-adjacency matrix of an Erdős–Rényi random bipartite graph with bounded aspect ratio is a rectangular random matrix with Bernoulli entries. Depending on the sparsity parameter $p$, its spectral behavior may either resemble that of a classical Wishart matrix or depart from this universal regime. In this talk, we study the extreme singular values at the critical density $np=c\log n$. We present the first quantitative characterization of the emergence of outlier singular values outside the Marčenko–Pastur law and determine their precise locations as functions of the largest and smallest degree vertices in the underlying random graph, which can be seen as an analogue of the Bai–Yin theorem in the sparse setting. These results uncover a clear mechanism by which combinatorial structures in sparse graphs generate spectral outliers. Joint work with Ioana Dumitriu, Haixiao Wang and Zhichao Wang.

Suppose that a continuous-time, stochastic diffusion (i.e., the Susceptible-Infected process) spreads on an unknown graph. We only observe the time at which the diffusion reaches each vertex, i.e., the set of infection times. What can be learned about the unknown graph from the infection times? While there is far too little information to learn individual edges in the graph, we show that certain high-level properties -- such as the number of vertices of sufficiently high degree, or super-spreaders -- can surprisingly be determined with certainty. To achieve this goal, we develop a suite of algorithms that can efficiently detect vertices of degree asymptotically greater than sqrt(n) from infection times, for a natural and general class of graphs with n vertices. To complement these results, we show that our algorithms are information-theoretically optimal: there exist graphs for which it is impossible to tell whether vertices of degree larger than n^{1/2 - \epsilon} exist from vertices' infection times, for any \epsilon > 0. Finally, we discuss the broader implications of our ideas for change-point detection in non-stationary point processes. This talk is based on joint work with Anna Brandenberger (MIT) and Elchanan Mossel (MIT).