Georgia Institute of Technology College of Sciences

Spin glasses are disordered statistical physics system with both ferromagnetic and anti-ferromagnetic spin interactions. The Gibbs measure belongs to the exponential family with parameters, such as inverse temperature $\beta>0$ and external field $h\in R$.  A fundamental statistical problem is to estimate the system parameters from a single sample of the ground truth. In 2007, Chatterjee first proved that under reasonable conditions, for spin glass models with $h=0$, the maximum pseudo-likelihood estimator for $\beta$ is $\sqrt{N}$-consistent. This is in contrast to the existing estimation results for classical non-disordered models. However, Chatterjee's approach has been restricted to the single parameter estimation setting.  The joint parameter estimation of $(\beta,h)$ for spin glasses has remained open since then. In this talk, I will introduce a new idea to show that under some easily verifiable conditions,  the bi-variate maximum pseudo-likelihood estimator is jointly $\sqrt{N}$-consistent for a large collection of spin glasses, including the Sherrington-Kirkpatrick model and its diluted variants. Based on joint work with Wei-Kuo Chen, Arnab Sen. 

We study a broad class of space–time continuous directed polymers in a Gaussian environment that is white in time and spatially correlated (Itô sense). Under Dalang’s condition, we prove key properties of the partition function—positivity, stationarity, scaling, homogeneity, and a Chapman–Kolmogorov relation—and establish pathwise regularity of the polymer (Hölder continuity and quadratic variation). We give a sharp singularity criterion: the polymer measure is singular w.r.t. Wiener measure iff the spectral measure has infinite total mass. Finally, for d≥3, we prove diffusive large-time behavior in the high-temperature regime, providing a unified framework for polymers driven by singular Gaussian noise.

Joint work with Cheng Ouyang (UIC), Samy Tindel (Purdue), and Panqiu Xia (Cardiff).

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.