My work explores computational methods for extracting information from data. I aim to provide quantitatively precise and rigorous guarantees for computational inference procedures. These strong guarantees are critical for engineers, statisticians, and others in data-intensive sciences who need to design systems or analyze experimental results. I approach these problems by exploring relationships between optimization, geometry, probability, and statistics.
News and updates
March 28, 2014: Our paper From Steiner formulas for cones to concentration of intrinsic volumes has been accepted to Discrete and Computational Geometry.
January 9, 2014: My paper Sharp recovery bounds for convex demixing, with applications has been accepted to JoFoCM.
January 7, 2014: Want to plot your own phase transitions? Try out my statistical dimension code!
November 1, 2013: We have a new tutorial article on convex methods for signal separation: Convexity in source separation: Models, geometry, and algorithms.
September 30, 2013: A new result on the limits of convex methods for demixing signals: The achievable performance of convex demixing.
August 26, 2013: Our latest paper is now available: From Steiner formulas for cones to concentration of intrinsic volumes.
June 14, 2013: I recieved the W.P. Carey & Co. Inc. Prize in Applied & Computational Mathematics for an outstanding doctoral dissertation.
May 23, 2013: My thesis is now available: A geometric analysis of convex demixing.
May 13, 2013: I successfully defended my Ph.D. thesis! The final copy will be available on this page soon.
March 26, 2013: Another one out: D. Amelunxen, M. Lotz, M.B. McCoy, and J.A. Tropp, Living on the edge: A geometric theory of phase transitions in convex optimization [arXiv:1303.6672]
May 8, 2012: Our deconvolution paper is available! M.B. McCoy and J.A. Tropp, Sharp bounds for convex deconvolution, with applications. 2012. preprint.
February 23, 2012: Our newest paper is out in the wild! Check it out. G. Lerman, M. McCoy, J.A. Tropp, and T. Zhang, Robust computation of linear models, or How to find a needle in a haystack . 2012. preprint.
September 14, 2011: Our paper "Two Proposals for Robust PCA using Semidefinite Programming" will appear in the Electronic Journal of Statistics (open-access).
August 11, 2011: I've updated my robust PCA code to reflect a revision in the paper. See here.
June 27—30, 2011: I'm attending SPARS'11 in Edinburgh, Scotland, where I'm presenting a talk titled "Two Proposals for Robust PCA" based on the pre-print here. The code associated with our work is here, and the slides are available here.
September 13—December 17, 2010: I'm spending much of my time at UCLA for the Modern Trends in Optimization and Its Application workshop.
June 7, 2010: Added a section about teaching since a couple of us are running a self-taught algebraic geometry course.
April 5, 2010: I added a makefile for LaTeX files to my code directory that I've been using for some time in case anyone else finds it useful.