CAM Colloquium: Short Research Presentations by Assistant Professors Christina Lee Yu (ORIE), Jamol Pender (ORIE), and Dmitry Savransky (MAE)
Frank H. T. Rhodes Hall 655
Christina Lee Yu, Assistant Professor, ORIE
Collaborative filtering for sparse tensor estimation
We consider the task of tensor estimation, i.e. estimating a low-rank 3-order tensor from noisy observations of a sparse subset of the entries. In the context of matrix (2-order tensor) estimation, a variety of algorithms have been proposed and analyzed in the literature including the popular collaborative filtering algorithm that is extremely well utilized in practice. We introduce a generalization of the collaborative filtering algorithm for the setting of tensor estimation and argue that it achieves sample complexity that (nearly) matches a conjectured lower bound on the sample complexity of polynomial time algorithms. Our generalization uses the matrix obtained from the "flattened" tensor to compute similarity via an associated bipartite graph. The sample complexity threshold corresponds to the connectivity threshold for the graph.
Jamol Pender, Assistant Professor, ORIE
Queueing theory in the information age
Many queueing systems provide real-time information to their customers with the goal of reducing the customers’ anxiety of the unknown. However, in reality, the information might be given in the form of an update. To understand the impact of updates, we prove fluid limit theorems for a state-dependent queueing model where customers choose which queue to join by a generalized multinomial logit choice model. In the choice model, the information about the queue length is updated periodically in increments of size ∆. We show that the fluid limit is given by a system of functional differential equations with a non-stationary time delay. Using the fluid limit, we derive an exact formula for the critical updating size that partitions the system in stable and unstable regions. In the case of multiple updates, we uncover a novel connection between our updating queueing model and Auto-Regressive (AR) time series models. To this end, we show that the stability of our updating queueing model is equivalent to analyzing the stationarity of a subsequent AR time series model. Finally, we show, using real waiting time data from Disneyland, that giving customers information might not be a smart decision.
Dmitry Savransky, Assistant Professor, MAE
Engineering the search for other worlds
The Space Imaging and Optical Systems laboratory (SIOSlab) supports a broad range of activities related to the science case of direct imaging of extrasolar planets. In addition to instrumentation and control of optical systems, our work includes the creation and analysis of advanced post-processing algorithms for weak signal extraction from imaging data along with the optimization of astrophysical surveys and space missions. Both of these require leveraging advanced tools from statistical modeling and optimization. Here, I will briefly describe our recent work on common spatial pattern filtering for 2D imaging data analysis, dynamic programming solutions for space mission scheduling, and prospects for the future.