Stephen Becker

Assistant Professor, Applied Mathematics
University of Colorado at Boulder
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I joined the department of Applied Math in fall 2014. Previously I was a Herman Goldstine Postdoctoral fellow in Mathematical Sciences at IBM Research in Yorktown Heights, NY, and a postdoctoral fellow via the Fondation Sciences Mathématiques de Paris at Paris 6. Until 2011, I was at Caltech where I did my doctoral work under Emmanuel Candès.

Our group thanks:

Proud member of the Math Alliance

Contact

stephen.jezejfdbecker@colorado.edu
Office telephone: (303) 492 0662
Office: 338 ECOT (Engineering center, office tower). I moved offices July 2019 (I am no longer on the 2nd floor ECOT)

Group Research site

Please note: this website (amath.colorado.edu/faculty/becker) is being (slowly) deprecated in favor of a more homogenous faculty website.

Our most up-to-date website is the research group website with public information about our research activities as well as our group's internal collaboration tools.

My CV is on my CU Experts Profile page.

Research interests

Broadly speaking, our group is interested in information extraction from various types of datasets. We are part of a hybrid field combining applied math with computer science and signal processing techniques. Some specific topics we research are:

Optimization: first-order methods, quasi-Newton methods, primal-dual algorithms, convex analysis
Numerical linear algebra: randomization and its interplay with optimization methods
Sampling theory: how to make the best use of your resources when confronted with big data
Mathematical applications: compressed sensing and variants, matrix completion and variants (robust PCA…), non-negative matrix factorization and end-member detection, sparse SVM
Physical applications: radar ADC using compressed sensing, quantum tomography, MRI, medical imaging, IMRT, renewable energy, big-data

Students interested in working with our group: If you are not currently a student, please apply to our undergraduate or graduate program and your application will receive full consideration.

Here's a somewhat more cohesive summary of our research:

“The Becker group focuses on optimization, signal processing, machine learning, and numerical methods. One main thrust is collaboration with engineering groups to design signal recovery algorithms for imaging devices (microscopes, ultrasound, MRI, photoacoustic imaging, brain imaging via MEG) and remote sensing (radar, visible and hyperspectral imaging from satellites). Another main area is matrix and tensor factorizations designed for streaming data, used for machine learning or scientific computation. Finally, a common factor in much of our research is optimization, linear algebra, and randomized methods. Sometimes we study these methods on their own, and sometimes we use these methods for applications. For example, we look at convergence of new stochastic optimization methods, either in terms of optimization error or (for machine learning) generalization error. Some recent optimization work considers the case when we cannot find a derivative easily, with applications to shape optimization and other PDE-constrained optimization. Other recent work uses optimization to design statistical estimators with rigorous confidence intervals for use in quantum tomography.”

Collaborators at CU and nearby (2020 and recent years)

Svenja Knappe (CU Mechanical Engineering; see Faculty Spotlight on Svenja Knappe) on OPM-MEG (i.e., wearable brain scanners)
Todd Murray (CU Mechanical Engineering) on blind structured-illumination photoacoustics (i.e., our joint NSF grant)
Carol Cogswell (CU Electrical Engineering) on super-resolution flourescence microscopy (i.e., our joint paper Achieving superresolution with illumination-enhanced sparsity )
Alireza Doostan (CU Aerospace Engineering) and Luis Tenorio (Colorado School of Mines) on derivative-free optimization (i.e., our preprint Stochastic Subspace Descent )
Manuel Lladser (CU Applied Math) on computational bio (i.e., our paper Resolvability of Hamming Graphs).
Will Kleiber (CU Applied Math) on spatial statistics (i.e., our paper Penalized basis models for very large spatial datasets).

Specific research projects, 2018

See a high-level overview of a few of our projects from a 30 minute colloquium talk I gave in 2018: Colloquium talk slides

To give you an idea of what we're up to in 2018:

Parametric and compressive estimation, for phase retrieval (Jessica) in x-ray imaging, and for discovering archaeological ruins (Abby) in radar imaging without creating a DEM
Theoretical machine learning: sub-sampling and sketching (Farhad, Eric)
Avoiding and analyzing saddle points in non-convex optimization: for biconvex programming in program analysis and controls (Jessica), and for dictionary learning and neural network learning (Leo)
Improving accuracy of sparse estimation using mixed-integer programming (Eric, Leo)
Efficient computation of the cross-ambiguity function (CAF) for signal processing, to estimate time-of-arrival of radar signals (James)
Randomized algorithms for numerical linear algebra and optimization (James, Derek)
Optimization algorithms in general, and ill-conditioning and pre-conditioning (James, Jessica, Osman)
Efficient algorithms for GPUs (James, Derek, Jessica)
Tensor decompositions (Osman, Derek)
Robust estimation (Richie)
Misc imaging applications (for optical super-resolution, with Carol Cogswell's group in ECEE; and for photo-acoustic super-resolution, with Todd Murray's group in Mech E)
Stochastic variance reduction methods for nonlinear inverse problems
Remote sensing of the Chesapeake bay (Cheryl)
Behavior genetics (Richard, Farhad)

Students

See our Group Members website

Current PhD students

Liam Madden, Osman Malik, Richie Clancy, Erik Johnson, Akshay Seshadri Current PmD students (Professional masters Degree)
Jacob Tiede (deep learning for genetics)

Alumni (PhD and Masters)

Farhad Pourkamali-Anaraki (PhD 2017), now assistant professor at U. Mass Lowell
Derek Driggs (MS 2017), now PhD student at Cambridge University
James Folberth (PhD 2018), now researcher at ICR, inc.
Eric Kightley (PhD 2019), now data scientist at Amazon
Jessica Gronski (PhD 2019), now data scientist at United Health Care
Richard Border (MS 2018; PhD in IBG 2019), now postdoc at UCSF/Harvard
Marc Thomson (MS 2019), now data scientist at Exxon Mobil research
David Kozak (co-advised; PhD 2020), now at Solea Energy
Zhishen (Leo) Huang (PhD 2020), now postdoc at Michigan State

Quick links

Our new page on optimization classes and resources at CU
The RCDS seminar website (for Robotics, Controls, and Dynamical Systems)
Teaching (Spring 202) Theory of Machine Learning special topics PhD class
Teaching (Fall 2019) APPM 5440 Applied Analysis (we no longer have a public website, only an internal Canvas website)
Teaching (Spring 2019) APPM 4720/5720 Special Topics: Randomized Algorithms (see also the permanent github site)
Teaching (Fall 2018): APPM 4720/5720 Special Topics: Advanced Topics in Convex Optimization (see the permanent github site)
Teaching (Fall 2018): 2 sections of APPM 2360 Differential Equations
Teaching (Spring 2018): APPM5450 Applied Analysis 2
Other teaching links at my department faculty website
Statistics, Optimization, Machine Learning seminar usually at 3:30 PM every Tuesday in Newton Lab

Interesting links

Good color schemes for scientific documents
CU Math department's DeLong lecture series
Google Scholar's classic papers
Machine Learning courses at CU
CS department colloquium
Simons Institute youtube channel for interesting talks on a range of subjects
MMDS Foundation youtube channel for talks on big-data topics
Gene Golub summer school, 2015 is on randomization in numerical linear algebra
Laura Grigori's reading group on randomized numerical linear algebra
Lieven Vandenberghe's “Optimization methods for large-scale systems”
Statistical Machine Learning in Paris