His research interests are in theory and applications of machine learning and data analysis. Some of his well-known work includes widely used Laplacian Eigenmaps, Graph Regularization and Manifold Regularization algorithms, which brought ideas from classical differential geometry and spectral analysis to data science. His recent work has been concerned with understanding remarkable mathematical and statistical phenomena observed in deep learning. This empirical evidence necessitated revisiting some of the basic concepts in statistics and optimization. One of his key recent findings is the “double descent” risk curve that extends the textbook U-shaped bias-variance trade-off curve beyond the point of interpolation.