Associate Professor, Applied Mathematics University of Colorado at Boulder

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)

News

Call for papers: special issue on Big Scientific Data and Machine Learning in Science and Engineering, submission deadline Feb 1 2022

Group Research site

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

Yet another website is our 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 (updated infrequently though)

Current PhD students

• Liam Madden, Osman Malik, Richie Clancy, Erik Johnson, Akshay Seshadri, Kevin Doherty

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

Interested in undergrad research with our group? Here are some programs you can use to get funding

• For CU A&S students, see A&S student funding opportunities

• For CU engineering students, see CEAS student funding opportunities

Quick links

• Our new page on optimization classes and resources at CU

• The RCDS seminar website (for Robotics, Controls, and Dynamical Systems)

• Teachign (Spring 2021) graduate Convex Optimization, APPM 5630

• Teaching (Fall 2020) undergrad Numerical Analysis, APPM 4650

• Teaching (Spring 2020) 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

• 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 (on pause Fall ’20 Spring ’21 for COVID)

Recent News

A similar list of announcements is at the Announcements Page of our Google Site

• Summer internships for 2021

  • Richie will intern at Argonne national labs

  • Liam will intern for IBM Research Dublin again

  • Akshay will intern at NIST

  • Kevin… TBD

  • Erik and Osman will have graduated

• August 2020, Leo defends his PhD thesis

• Stephen will be speaking at the AIMS South Africa Spring School on Mathematics of Data Science in September 2019 (SIAM article describing AIMS)

• Summer internships for 2020

  • Liam is working for IBM Research Dublin

  • Osman is working for Fujitsu

  • Erik is working for Archer Dx

• Summer internships for 2019

  • Zhishen (Leo) Huang at Respond Software

  • Richie Clancy at Sensory, Inc

  • David Kozak at University of Genova working with Lorenzo Raso (MIT/Genova)

  • Osman Malik at IBM Research with Lior Horesh and Misha Kilmer

• April 2019, Matt Maierhofer and Marc Thomson defend their Masters theses

• April 2019, Jessica Gronski and Eric Kightley defend their PhD

• November 2018, Richard Border defends his Masters thesis

• October 2018, James defends his PhD. Congratulations James!

• June 2018, Stephen is a CCIMI Distinguished Visitor at Cambridge, giving a CCIMI short-course

• Summer internships for 2018

  • Jessica Gronski at Savvy Sherpa (now United Health Care)

  • Eric Kightley at Respond Software

  • Leo Huang at USC

• May 2018, Farhad departs to take a tenure-track position in CS at U. Mass Lowell

• January 2018, Stephen is one of four founding members of the Imaging Science IRT

• Spring 2017, Farhad Pourkamali-Anaraki gradautes with his PhD, staying with us for another year as a postdoc

• Spring 2017, Derek Driggs graduates with his MS, heads to Cambrdige in October

• January 2017, group member Derek Driggs (BS/MS) awarded a Cambridge Gates Fellowship (4 year fellowship to Cambridge for a PhD).

• Jan 2017, our group awarded a contract for signal processing algorithms with Northrop Grumman

• May 2016, our group awarded a gift from the Bloomberg data science program

• March 2016, Alex Gittens and Michael Mahoney visit

• March 2016, students have summer internship offers from the following companies:

  • Technicolor research (Bay Area), Farhad Pourkamali-Anaraki

  • Sandia National Lab with Tamara Kolda, Jessica Gronski

  • ICR, James Folberth

• July 12 2015, with Michael Grant and Emmanuel Candes, we have won the Beale-Orchard-Hays prize at ISMP 2015

• June 24 2015, selected for 2015 ICML Reviewer award

• Summer 2015, organizing the Workshop on Robust Subspace Learning and Computer Vision RSL-CV at ICCV 2015 (Santiago, Chile).

• Nov. ’14, we have free software available for our robust PCA algorithm at NIPS 2014 in Montreal.

• Sept. ’14, two papers accepted at NIPS

• Organizing NIPS 2014 “Out of the box: robustness in high dimension” workshop at NIPS 2014 in Montreal.

Interesting links, updated at least once per decade

• 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