Congratulations David!

David Hong was awarded the Richard and Eleanor Towner Prize for Outstanding PhD Research at the Michigan Engineering Graduate Symposium. This is a prize awarded annually across the entire college of engineering to PhD students within about a year of graduation, and the criteria for selection are creativity, innovation, impact on society, and achievement. Congratulations David!

Data-Driven Discovery of Models

Jason Corso and I have been awarded a DARPA D3M grant. Our project is called SPIDER: Subspace Primitives that are Interpretable and DivERse. We will be contributing machine learning software primitives for a system that helps domain experts perform a wide variety of automated data analysis on their datasets. The project has 24 teams and is already off to a great start — We look forward to final system developed by this team over the next few years!

ICML Acceptances, SIAM OPT success

Congratulations to postdoc Greg Ongie, whose excellent work on Variety Models for Matrix Completion has been accepted to ICML. We’re very excited about the potential applications and open problems that we posed in this work. Congratulations also to John Lipor, whose work on Active Subspace Clustering has also been accepted to ICML — I’ve spoken about this work before at the Simons Institute workshop on Interactive Learning. It achieves state of the art clustering error on several benchmark datasets using very few pairwise cluster queries. (Edit: See here for Greg’s talk and here for John’s talk at ICML!)

We also just finished a week at the SIAM Optimization conference, where our mini-symposium on Non-convex Optimization in Data Analysis was a huge hit. We had a full room for each session and 12 outstanding talks. Thanks to my co-organizers Stephen Wright, Rebecca Willett, and Rob Nowak, and thanks to all the speakers and participants.

MIDAS seminar and new results

Last Friday I gave the MIDAS weekly seminar. You can find the description here, along with the link directly to the recording. I talked about two recent problems I have been working on: First I talked about my work with Ravi Ganti and Rebecca Willett on learning a low-rank matrix that is observed through a monotonic function from partial measurements. This is common in calibration and quantization problems. Follow up work with Nikhil Rao and Rob Nowak in addition generalized this to learning structured single index models. Second, I talked about the work of my student David Hong, co-advised by Jeff Fessler, on the asymptotic performance of PCA with heteroscedastic data. This is common in problems like sensor networks or medical imaging, where different measurements of the same phenomenon are taken with different quality sensing (eg high or low radiation). David has recently posted his paper on arxiv showing predictions of the asymptotic performance; exploiting the structure of these expressions we also showed that asymptotic recovery for a fixed average noise variance is maximized when the noise variances are equal (i.e., when the noise is in fact homoscedastic). Average noise variance is often a practically convenient measure for the overall quality of data, but our results show that it gives an overly optimistic estimate of the performance of PCA for heteroscedastic data.

AAAI and Simons

This week I head to the bay area for two presentations: My collaborator Ravi Ganti will be presenting our work on estimating high dimensional structured single index models.  The week following I’ll be at the Simons workshop on Interactive Learning presenting my work with student John Lipor on active labeling from union of subspace data. I’m looking forward to sharing our work and hearing about all the other interesting work going on in these areas! (Edit: See here for my Simons talk on active labeling for union of subspace data.)

Fall 2016 DSP Projects

The link to all the awesome projects in my fall DSP class is up — Every year the projects get more creative and more technically interesting as well. Great work everyone!

Student accomplishments

Congratulations to John Lipor for passing his proposal defense!

Congratulations to David Hong for winning both the session award for (SIC) Signal and Image Processing, Computer Vision at the University of Michigan Engineering Graduate Symposium and the award for Most Interesting Methodological Advancement in the Michigan MIDAS Symposium for his work on heteroscedastic PCA.

Congratulations to Chenlan Wang for winning the Rackham International Student Fellowship.

Nice work team!


Three papers online

My students and I have posted three very exciting papers in the last few months!

Towards a Theoretical Analysis of PCA for Heteroscedastic Data” with David Hong and Jeff Fessler studies the behavior of PCA with data points that have different noise variances. We published that work at the Allerton conference.

Convergence of a Grassmannian Gradient Descent Algorithm for Subspace Estimation From Undersampled Data” with Dejiao Zhang proves expected convergence rates for incremental gradient subspace estimation constrained to the Grassmannian. Despite this being a non-convex problem, our results show locally linear convergence rates when the observed vectors have either missing data or compressively sampled data.

Leveraging Union of Subspace Structure to Improve Constrained Clustering” with John Lipor demonstrates how the assumption of subspace structure can dramatically help active clustering algorithms. By querying users intelligently for pairwise clustering constraints, we drive clustering error on several benchmark datasets down near zero.

Productive spring

This spring I’ve had a couple opportunities to share work with Ravi Sastry Ganti and Rebecca Willett on Matrix completion under monotonic single index model observations that we had at NIPS last December. In a week I’ll be at AI stats with my student Dejiao Zhang presenting our work on Global convergence of a Grassmannian gradient descent algorithm for subspace learning — we now have a proof that the GROUSE subspace learning algorithm converges globally from any random initialization to the global minimizer, or to a ball around the generating subspace in the case of noisy data. And last but never least, I had a great set of grad students in my Estimation, Detection, and Filtering class this year; they did some great projects on data science and statistical inference and did very well in the class overall.

Fall 2015 DSP Projects

The link to all the awesome projects in my fall DSP class is up — Once again the students impressed me with their creative ideas and excitement about advanced topics in signal processing. Great work everyone!