## Seminars and Colloquia by Series

Friday, November 16, 2018 - 13:05 , Location: Skiles 005 , , Math, University of Michigan , , Organizer: He Guo
Consider  a  linear  combination  of  independent  identically  distributed  random variables $X_1, . . . , X_n$ with fixed weights $a_1, . . . a_n$.  If the random variablesare continuous, the sum is almost surely non-zero.  However, for discrete random variables an exact cancelation may occur with a positive probability.  Thisprobability depends on the arithmetic nature of the sequence $a_1, . . . a_n$.  We will discuss how to measure the relevant arithmetic properties and how to evaluate the probability of the exact and approximate cancelation.
Friday, November 9, 2018 - 13:05 , Location: Skiles 005 , , School of Computer Science, Georgia Tech , , Organizer: He Guo
Often the popular press talks about the power of quantum computing coming from its ability to perform several computations simultaneously. We’ve already had a similar capability from probabilistic machines. This talk will explore the relationship between quantum and randomized computation, how they are similar and how they differ, and why quantum can work exponentially faster on some but far from all computational problems. We’ll talk about some open problems in quantum complexity that can help shed light on the similarities and differences between randomness and “quantumness”.  This talk will not assume any previous knowledge of quantum information or quantum computing.
Friday, November 2, 2018 - 12:20 , Location: Skiles 005 , , ISyE/ECE, Georgia Tech , , Organizer: He Guo
Abstract In this talk, I will present a popular distributed method, namely, distributed consensus-based gradient (DCG) method, for solving optimal learning problems over a network of agents. Such problems arise in many applications such as, finding optimal parameters over a large dataset distributed among a network of processors or seeking an optimal policy for coverage control problems in robotic networks. The focus is to present our recent results, where we study the performance of DCG when the agents are only allowed to exchange their quantized values due to their finite communication bandwidth. In particular, we develop a novel quantization method, which we refer to as adaptive quantization. The main idea of our approach is to quantize the nodes' estimates based on the progress of the algorithm, which helps to eliminate the quantized errors. Under the adaptive quantization, we then derive the bounds on the convergence rates of the proposed method as a function of the bandwidths and the underlying network topology, for both convex and strongly convex objective functions. Our results suggest that under the adaptive quantization, the rate of convergence of DCG with and without quantization are the same, except for a factor which captures the number of quantization bits. To the best of the authors’ knowledge, the results in this paper are considered better than any existing results for DCG under quantization. This is based on a joint work with Siva Theja Maguluri and Justin Romberg. Bio Thinh T. Doan is a TRIAD postdoctoral fellow at Georgia Institute of Technology, joint between the School of Industrial and Systems Engineering and the School of Electrical and Computer Engineering (ECE). He was born in Vietnam, where he got his Bachelor degree in Automatic Control at Hanoi University of Science and Technology in 2008. He obtained his Master and Ph.D. degrees both in ECE from the University of Oklahoma in 2013 and the University of Illinois at Urbana-Champaign in 2018, respectively. His research interests lie at the intersection of control theory, optimization, distributed algorithms, and applied probability, with the main applications in machine learning, reinforcement learning, power networks, and multi-agent systems.
Friday, October 26, 2018 - 13:05 , Location: Skiles 005 , , CS, Duke University , , Organizer: He Guo
We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with dimension-independent error guarantees for several families of structured distributions.  In this work, we give the first nearly-linear time algorithms for high-dimensional robust mean estimation. Specifically, we focus on distributions with (i) known covariance and sub-gaussian tails, and (ii) unknown bounded covariance. Given $N$ samples on $R^d$, an $\epsilon$-fraction of which may be arbitrarily corrupted, our algorithms run in time $\tilde{O}(Nd)/poly(\epsilon)$ and approximate the true mean within the information-theoretically optimal error, up to constant factors. Previous robust algorithms with comparable error guarantees have running times $\tilde{\Omega}(N d^2)$. Our algorithms rely on a natural family of SDPs parameterized by our current guess $\nu$ for the unknown mean $\mu^\star$. We give a win-win analysis establishing the following: either a near-optimal solution to the primal SDP yields a good candidate for $\mu^\star$ -- independent of our current guess $\nu$ -- or the dual SDP yields a new guess $\nu'$ whose distance from $\mu^\star$ is smaller by a constant factor. We exploit the special structure of the corresponding SDPs to show that they are approximately solvable in nearly-linear time. Our approach is quite general, and we believe it can also be applied to obtain nearly-linear time algorithms for other high-dimensional robust learning problems. This is a joint work with Ilias Diakonikolas and Rong Ge.
Friday, October 19, 2018 - 13:05 , Location: Skiles 005 , , CS, Georgia Tech , , Organizer: He Guo
We investigate whether the standard dimensionality reduction techniques inadvertently produce data representations with different fidelity for two different populations. We show on several real-world datasets, PCA has higher reconstruction error on population A than B (for example, women versus men or lower versus higher-educated individuals). This can happen even when the dataset has similar number of samples from A and B . This motivates our study of dimensionality reduction techniques which maintain similar fidelity for A as B . We give an efficient algorithm for finding a projection which is nearly-optimal with respect to this measure, and evaluate it on several datasets. This is a joint work with Uthaipon Tantipongpipat, Jamie Morgenstern, Mohit Singh, and Santosh Vempala.
Friday, October 12, 2018 - 13:05 , Location: Skiles 005 , , ISyE, Georgia Tech , , Organizer: He Guo
At the heart of most algorithms today there is an optimization engine trying to learn online and provide the best decision, for e.g. rankings of objects, at any time with the partial information observed thus far in time. Often it becomes difficult to find near optimal solutions to many problems due to their inherent combinatorial structure that leads to certain computational bottlenecks. Submodularity is a discrete analogue of convexity and is a key property often exploited in tackling combinatorial optimization problems. In the first part of the talk, we will focus on computational bottlenecks that involve submodular functions: (a) convex function minimization over submodular base polytopes (for e.g. permutahedron) and (b) movement along a line inside submodular base polytopes. We give a conceptually simple and strongly polynomial algorithm Inc-Fix for the former, which is useful in computing Bregman projections in first-order projection-based methods like online mirror descent. For the latter, we will bound the iterations of the discrete Newton method which gives a running time improvement of at least n^6 over the state of the art. This is joint work with Michel Goemans and Patrick Jaillet. In the second part of the talk, we will consider the dual problem of (a), i.e. minimization of composite convex and submodular objectives. We will resolve Bach's conjecture from 2015 about the running time of a popular Kelley's cutting plane variant to minimize these composite objectives. This is joint work with Madeleine Udell and Song Zhou.
Friday, October 5, 2018 - 13:05 , Location: Skiles 005 , , ISyE, Georgia Tech , , Organizer: He Guo
Abstract: Queueing systems are studied in various asymptotic regimes because they are hard to study in general. One popular regime of study is the heavy-traffic regime, when the system is loaded very close to its capacity. Heavy-traffic behavior of queueing systems is traditionally studied using fluid and diffusion limits. In this talk, I will present a recently developed method called the 'Drift Method', which is much simpler, and is based on studying the drift of certain test functions. In addition to exactly characterizing the heavy-traffic behavior, the drift method can be used to obtain lower and upper bounds for all loads. In this talk, I will present the drift method, and its successful application in the context of data center networks to resolve a decade-old conjecture. I will also talk about ongoing work and some open problems.   Bio: Siva Theja Maguluri is an Assistant Professor in the School of Industrial and Systems Engineering at Georgia Tech. Before that, he was a Research Staff Member in the Mathematical Sciences Department at IBM T. J. Watson Research Center. He obtained his Ph.D. from the University of Illinois at Urbana-Champaign in Electrical and Computer Engineering where he worked on resource allocation algorithms for cloud computing and wireless networks. Earlier, he received an MS in ECE and an MS in Applied Math from UIUC and a B.Tech in Electrical Engineering from IIT Madras. His research interests include Stochastic Processes, Optimization, Cloud Computing, Data Centers, Resource Allocation and Scheduling Algorithms, Networks, and Game Theory. The current talk is based on a paper that received the best publication in applied probability award, presented by INFORMS Applied probability society.
Friday, September 28, 2018 - 13:15 , Location: Skiles 005 , , Math, Georgia Tech , , Organizer: He Guo
Given a finite partially ordered set (poset) of width $w$, Dilworth's theorem gives an existence and minimality of a chain partition of size $w$. First-Fit is an online algorithm for creating a chain partition of a poset. Given a linear ordering of the points of the poset, $v_1, \cdots, v_n$, First-Fit assigns the point $v_i$ to the first available chain in the chain partition of the points $v_1, \cdots, v_{i-1}$. It is a known fact that First-Fit has unbounded performance over the family of finite posets of width 2. We give a complete characterization of the family of finite posets in which First-Fit performs with subexponential efficiency in terms of width. We will also review what is currently known on the family of posets in which First-Fit performs with polynomial efficiency in terms of width. Joint work with Kevin Milans.
Friday, September 21, 2018 - 13:05 , Location: Skiles 005 , , CS, Georgia Tech , , Organizer: He Guo
As a generalization of many classic problems in combinatorial optimization, submodular optimization has found a wide range of applications in machine learning (e.g., in feature engineering and active learning).  For many large-scale optimization problems, we are often concerned with the adaptivity complexity of an algorithm, which quantifies the number of sequential rounds where polynomially-many independent function evaluations can be executed in parallel.  While low adaptivity is ideal, it is not sufficient for a (distributed) algorithm to be efficient, since in many practical applications of submodular optimization the number of function evaluations becomes prohibitively expensive.  Motivated by such applications, we study the adaptivity and query complexity of adaptive submodular optimization. Our main result is a distributed algorithm for maximizing a monotone submodular function with cardinality constraint $k$ that achieves a $(1-1/e-\varepsilon)$-approximation in expectation.  Furthermore, this algorithm runs in $O(\log(n))$ adaptive rounds and makes $O(n)$ calls to the function evaluation oracle in expectation.  All three of these guarantees are optimal, and the query complexity is substantially less than in previous works.  Finally, to show the generality of our simple algorithm and techniques, we extend our results to the submodular cover problem. Joint work with Vahab Mirrokni and Morteza Zadimoghaddam (arXiv:1807.07889).
Friday, September 14, 2018 - 13:05 , Location: Skiles 005 , , CS, Georgia Tech , , Organizer: He Guo
We study the dynamic graph connectivity problem in the massively parallel computation model. We give a data structure for maintaining a dynamic undirected graph that handles batches of updates and connectivity queries in constant rounds, as long as the queries fit on a single machine. This assumption corresponds to the gradual buildup of databases over time from sources such as log files and user interactions. Our techniques combine a distributed data structure for Euler Tour (ET) trees, a structural theorem about rapidly contracting graphs via sampling n^{\epsilon} random neighbors, as well as modifications to sketching based dynamic connectivity data structures. Joint work with David Durfee, Janardhan Kulkarni, Richard Peng and Xiaorui Sun.