K-Subspaces Algorithm Results at ICML

I’m excited that our results for the K-Subspaces algorithm were accepted to ICML. My postdoc Peng Wang will be presenting his excellent work; you may read the paper here or attend his session if you are interested. K-Subspaces (KSS) is a natural generalization of K-Means to higher dimensional centers, originally proposed by Bradley and Mangasarian in 2000. Peng not only showed that KSS converges locally, but that a simple spectral initialization guarantees a close-enough initialization in the case of data drawn randomly from arbitrary subspaces. This makes a giant step in a line of questioning that has been open for more than 20 years. Great work Peng!

HePPCAT in TSP

Our work on heteroscedastic PCA continues with our article “HePPCAT: Probabilistic PCA for Data with Heteroscedastic Noise,” published in IEEE Transactions on Signal Processing. In this paper we developed novel ascent algorithms to maximize the heteroscedastic PCA likelihood, simultaneously estimating the principal components and the heteroscedastic noise variances. We show a compelling application to air quality data, where it is common to have data both from sensors that are high-quality EPA instruments and others that are consumer grade. Code for the paper experiments is available at https://gitlab.com/heppcat-group, and the HePPCAT method is available as a registered Julia package. Congratulations to my student Kyle Gilman, former student David Hong, and colleague Jeff Fessler.

Congratulations Dr. Bower!

Last fall, my PhD student Amanda Bower defended her thesis titled “Dealing with Intransitivity, Non-Convexity, and Algorithmic Bias in Preference Learning.” Amanda was in the Applied Interdisciplinary Math program, co-advised by Martin Strauss. She will now be moving on to work with Twitter’s ML Ethics, Transparency, and Accountability (META) group. We are so proud that she is going to go make her mark on the world. Congratulations Dr. Bower!

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Preference Learning with Salient Features

I am excited that Amanda Bower will have the opportunity to discuss our new work in preference learning, “Preference Modeling with Context-Dependent Salient Features“, at ICML next week. In this work, we propose a new model for preference learning that takes into account the fact that when making pairwise comparisons, certain features may play an outside role in the comparison, making the pairwise comparison result inconsistent with a general preference order. We look forward to hearing people’s questions and feedback! Update post-conference: Her presentation can be viewed here.

Online Tensor Completion and Tracking

Kyle Gilman and I have a preprint out describing a new algorithm for online tensor completion and tracking. We derive and demonstrate an algorithm that operates on streaming tensor data, such as hyperspectral video collected over time, or chemo-sensing experiments in space and time. Kyle presented his work at the first fully virtual ICASSP, which you can view here. Anyone can register for free to this year’s virtual ICASSP and watch the videos, post questions, and join the discussion. Kyle’s code is also available here. We think this algorithm will have a major impact in speeding up low-rank tensor processing, especially with time-varying data, and we welcome questions and feedback.

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Congratulations Dejiao and David!

SPADA lab is so proud of Dr. Dejiao Zhang and Dr. David Hong. They both successfully defended their PhD dissertations this spring. Dejiao is going to Amazon Web Services next, and David is going to a postdoc at the University of Pennsylvania. We expect you both to go off and do great things! Congratulations!

NSF CAREER Award

I am honored to have received the NSF CAREER award for a proposal on optimization methods and theory for the joint formulation of dimension reduction and clustering. You can read about the award here in the UM press release and also here on the NSF website. Dimension reduction and clustering are arguably the two most critical problems in unsupervised machine learning; they are used universally for data exploration and understanding. Often dimension reduction is used before clustering (or vice versa) to lend tractability to the modeling algorithm. It’s more typical in real data to see clusters each with their own low-dimensional structure, and so a joint formulation is of great interest. I look forward to working toward this end in the next stage of my career.

Army Young Investigator

I am very excited that my project “Mathematics for Learning Nonlinear Generalizations of Subspace Models in High Dimensions” has won the Army Young Investigator award! Subspace models are widely used due to simplicity and ease of analysis. However, while these linear models are very powerful in many high-dimensional data contexts, they also often miss out on important nonlinearities in real data. This project aims to extend recent advances in signal processing to the single-index model and the nonlinear variety model. Read the department’s announcement here.

Postdoc Opportunity at the University of Michigan

to begin in spring 2019.

 

Please email Laura Balzano <girasole@umich.edu> with the subject “Joining the Balzano lab — postdoc 2019” if you are interested.

We are seeking a postdoc who is interested in applying machine learning techniques to real-time dynamic data analysis. While machine learning has advanced significantly over the last decade, its application to dynamic time-varying data is still in its infancy. This project will focus on three ML areas: online learning, stochastic gradient methods, and streaming PCA. We will work on theory to understand how the standard approaches behave when the data are time-varying, develop appropriate models for time-varying data, and develop novel approaches along with convergence theory. Our main applications focus will be power systems engineering and computer vision. In power systems, we will develop methodologies to infer the real-time behavior of aggregations of distributed energy resources from hierarchical, heterogeneous, and incomplete measurements of power system quantities. In computer vision, we will develop real-time algorithms for object tracking and activity recognition in video.

Optimally Weighted PCA for High-dimensional Heteroscedastic Data

Today I had the opportunity to speak about very recent results by my student David Hong (joint work also with Jeff Fessler) in analyzing asymptotic recovery guarantees for weighted PCA for high-dimensional heteroscedastic data. In the paper we recently posted online, we have asymptotic analysis (as both the number of samples and dimension of the problem grow to infinity, but converge to a fixed constant) of the recovery for weighted PCA components, amplitudes, and scores. Those recovery expressions allow us to find weights that give optimal recovery, and the weights turn out to be a very simple expression involving only the noise variance and the PCA amplitudes. To learn more, watch my talk here, and let us know if you have any questions!

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