Ph.D. student, Electrical Engineering and Computer Sciences, UC Berkeley.
University of California, Berkeley 652 Sutardja Dai Hall Berkeley, CA 94720-1720 Email me at elalaoui at eecs dot berkeley dot edu
My research interests lie somewhere between mathematical statistics and optimization. I am generally interested in the design and analysis of algorithms that attempts to extract information from limited and corrupted data, and studying the various tradeoffs that may appear in the analysis of such algorithmic procedures, e.g. statistical accuracy vs. computational budget.
While advised by Alex Bayen (2013-2014):
(To be submitted to SIAM Journal of Matrix Analysis and Applications)
We present an algorithm (that we call ultralogdet) that exploits recent ideas on graph sparsification to compute the log-determinant of a SDD matrix in time quasi-linear in the number of its non-zero entries. The core idea is the simple identity: , for two matrices A and B. We show that if B is a good approximation to A (in the spectral sense), the second term can be approximated by a Monte Carlo procedure. Then, given such a good B, all we have do is compute its log-det, which can in turn be approximated in a similar way. Now, a remarkable fact (Spielman and Teng ’04) is that for an input SDD matrix A, such a chain of good approximations can be obtained by working on a graph underlying the matrix A, and incrementally sparsifying it, i.e. cutting its edges. The obtained (sequence of) graphs have fewer and fewer edges while retaining the spectral properties of their predecessors. Once the last graph of the chain is small enough, its log-det is computed by brute force, and the overall approximation is shown to be -accurate for a running time of . More on graph sparsification and related problems on Daniel Spielman's page.
(Submitted to the International Symposium on Transportation and Traffic Theory ’15)
We provide a tractable formulation for and solve the route assignment problem using novel techniques from convex optimization. Given origin-destination (OD) estimates for a region and link flow measurements at a number of links, we estimate the distribution of flows over a set of routes (the route flow). We propose a novel approach of using kernel methods from machine learning to estimate OD flows given aggregated counts of vehicles present on a part of the network (derived from the phones presence within each cell) for the current route flow estimate. We find a locally optimal solution for both OD flow and route flow by iterating between solving for each of these two problems.
I am a first year Ph.D. student in Electrical Engineering and Computer Science at the University of California at Berkeley. I did my master's at Ecole Normale Supérieure and my undergrad at Ecole Polytechnique. I wrote my master's dissertation on probabilistic record linkage while working at Ecole des Ponts with Guillaume Obozinski.
M.Sc. Mathématiques, Vision et Apprentissage, Ecole Normale Supérieure/Ecole des Ponts Paristech, 2013.
Eng.Deg. Applied math, Ecole Polytechnique, 2012.