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Summary

My research focuses on mathematics and computation for data science. In particular, I design, analyze, and implement algorithms and models for large-scale problems in machine learning, statistics, data analysis, data mining, and scientific computing. My mathematical tools are drawn from: convex optimization, nonlinear programming, statistics, computer science, signal processing, differential geometry, {convex, functional, harmonic, matrix, and numerical} analysis. My work also involves special functions, experimental mathematics, polynomials, noncommutative algebra, metric geometry, quantum information theory, operator inequalities, optimization under uncertainty (robust, stochastic), distributed and parallel computation, economics, time-series analysis, healthcare informatics, and more.


Topics

Geometric Optimization

This is a new area of research that I am extremely interested in. Please visit this page to find out more, and join us in advancing this new research direction! I am looking for mathematically inclined, motivated students to work in this area.

Machine Learning, Statistics, Optimization

My main project interests lie in (algorithms, theory, implementations for):
  • Stochastic optimization, algorithms and theory
  • Large-scale convex optimization
  • Large-scale nonconvex optimization
  • Parallel and distributed methods
  • Optimization algorithms on novel hardware
  • Optimization and theory for deep-learning
  • Statistics on manifolds, and metric spaces
  • Optimization problems in computational statistics

Pure and Applied Mathematics

I enjoy spending some of my time thinking about selected problems in: matrix analysis, probability theory, algebra, convex analysis, geometry, algebraic combinatorics, graph theory, and an ecelectic selection of problems from other mathematical areas. I hope to apply some of the ideas from different math areas to find unexpected connections with problems in data science and computation!

Data Mining, IR, Web, Computer Vision

I am greatly interested in search and retrieval of structured data (videos, images, sequences, signals, etc.), both in the offline as well as real-time streaming data settings. Hashing, nearest-neighbors, distributed databases, metric learning, similarity functions, clustering, regression, top-k problems, and more.

Applications in Engineering, Science, Healthcare

Currently, I'm looking at some applications in: healthcare, wireless engineering, image processing, .... I am always open to more applications, as long as I have something new to contribute.