Maria Nareklishvili

Maria Nareklishvili, Nick Polson, Vadim Sokolov

Generative methods (Gen-AI) are reviewed with a particular goal of solving tasks in machine learning and Bayesian inference. Generative models require one to simulate a large training dataset and to use deep neural networks to solve a supervised learning problem. To do this, we require high-dimensional regression methods and tools for dimensionality reduction (a.k.a. feature selection). The main advantage of Gen-AI methods is their ability to be model-free and to use deep neural networks to estimate conditional densities or posterior quintiles of interest. To illustrate generative methods , we analyze the well-known Ebola data set. Finally, we conclude with directions for future research.

Maria Nareklishvili, Nicholas Polson, Vadim Sokolov

We present generative artificial intelligence (AI) to empirically validate fundamental laws of physics, focusing on the Stefan-Boltzmann law linking stellar temperature and luminosity. Our approach simulates counterfactual luminosities under hypothetical temperature regimes for each individual star and iteratively refines the temperature-luminosity relationship in a deep learning architecture. We use Gaia DR3 data and find that, on average, temperature's effect on luminosity increases with stellar radius and decreases with absolute magnitude, consistent with theoretical predictions. By framing physics laws as causal problems, our method offers a novel, data-driven approach to refine theoretical understanding and inform evidence-based policy and practice.