Huy L. Nguyen

Learn More
An oblivious subspace embedding (OSE) given some parameters &#x03B5;, d is a distribution D over matrices &#x03A0; &#x2208; R<sup>m&#x00D7;n</sup> such that for any linear subspace W &#x2286; R<sup>n</sup> with dim(W) = d, P<sub>&#x03A0;~D</sub>(&#x2200;x &#x2208; W ||&#x03A0;x||<sub>2</sub> &#x2208; (1 &#x00B1; &#x03B5;)||x||<sub>2</sub>) &gt; 2/3. We show(More)
In the turnstile model of data streams, an underlying vector <i>x</i> &#8712; {--<i>m</i>,--<i>m</i>+1,..., <i>m</i>--1,<i>m</i>}<sup><i>n</i></sup> is presented as a long sequence of positive and negative integer updates to its coordinates. A randomized algorithm seeks to approximate a function <i>f</i>(<i>x</i>) with constant probability while only making(More)
We present a new data structure for the c-approximate near neighbor problem (ANN) in the Euclidean space. For n points in R, our algorithm achieves Oc(n + d logn) query time and Oc(n + d logn) space, where ρ ≤ 7/(8c2) + O(1/c3) + oc(1). This is the first improvement over the result by Andoni and Indyk (FOCS 2006) and the first data structure that bypasses a(More)
We study convergence of the following discrete-time non-linear dynamical system: $n$ agents are located in R<sup>d</sup> and at every time step, each moves synchronously to the average location of all agents within a unit distance of it. This popularly studied system was introduced by Krause to model the dynamics of opinion formation and is often referred(More)
<lb>Sketching is a prominent algorithmic tool for processing<lb>large data. In this paper, we study the problem of sketching<lb>matrix norms. We consider two sketching models. The first<lb>is bilinear sketching, in which there is a distribution over<lb>pairs of r×n matrices S and n× s matrices T such that for<lb>any fixed n×n matrix A, from S ·A ·T one can(More)
In this work, we present a new algorithm for maximizing a non-monotone submodular function subject to a general constraint. Our algorithm finds an approximate fractional solution for maximizing the multilinear extension of the function over a down-closed polytope. The approximation guarantee is 0.372 and it is the first improvement over the 1/e(More)
We explore the connection between dimensionality and communication cost in distributed learning problems. Specifically we study the problem of estimating the mean ~ ✓ of an unknown d dimensional gaussian distribution in the distributed setting. In this problem, the samples from the unknown distribution are distributed among m different machines. The goal is(More)
The selective detection of ultratrace amounts of aflatoxin M1 (AFM1) is extremely important for food safety since it is the most toxic mycotoxin class that is allowed to be present on cow milk with strictly low regulatory levels. In this work, Fe3O4 incorporated polyaniline (Fe3O4/PANi) film has been polymerized on interdigitated electrode (IDE) as(More)
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. Unfortunately, the resulting submodular optimization problems are often too large to be solved on a single machine. We develop a simple distributed algorithm that is(More)