Deep Learning in Statistics

Abstract: Sampling from high-dimensional, multimodal distributions is a computationally challenging and fundamental task. This talk will focus on a family of random instances of such problems described by random quadratic potentials on the hypercube known as the Sherrington-Kirkpatrick model. I will describe an efficient sampling algorithm for the high temperature regime, and explain why chaos implies a form of hardness at low temperature. Our algorithm combines the technologies of stochastic localization and approximate message passing. Based on joint work with Ahmed El Alaoui and Andrea Montanari.

Abstract: AI and ML are revolutionizing drug discovery, particularly in the area of de novo drug design. These tools can predict the properties of potential drug candidates and identify promising drug targets by analyzing large amounts of data from various sources. Using AI and ML, researchers can generate new chemical entities with optimized drug-like properties. De novo drug design using AI and ML has led to the discovery of new treatments for cancer, infectious diseases, and metabolic disorders. However, challenges remain, such as the need for high-quality data and the exploration of larger chemical spaces. Despite these challenges, AI and ML have the potential to transform the way new drugs are designed and developed, accelerating the drug discovery process and bringing new treatments to patients faster than ever before.

Abstract: We develop a new type of stochastic neural network (StoNet), which is formulated as a composition of many simple linear/logistic regression models and includes the conventional deep neural network as a limiting case. The StoNet falls into the framework of statistical modeling, which does not only allow us to address many fundamental issues in deep learning, such as structure interpretability and uncertainty quantification,  but also provides with us a platform for transferring the theory and methods developed for linear models to deep learning. With the StoNet, we demonstrate the transferability of sparse learning theory from linear models to deep neural networks. We also showcase the integration of reproducing kernel methods into deep neural networks to enhance their training and prediction performance. Additionally, we show how to use the Stonet to handle some special types of data, such as those with missing values or measurement errors. Lastly, we demonstrate how to use the StoNet to perform nonlinear sufficient dimension reduction for high-dimensional data. This talk is based on the joint works with Yan Sun and Siqi Liang.