ACO Student Seminar
Fall 2016


Description

The Georgia Tech ACO Student Seminar is run by students in the ACO program. The objective of the seminar is to give students and postdocs a forum to share their research results or present something of general interest. There will also be occasional survey talks by ACO faculty. The seminar currently meets on Fridays from 1pm to 2pm in Skiles 005, unless noted below, and some form of food/drinks will be provided.

Scheduled Talks

September 16: Sarah Cannon, A Markov Chain Algorithm for Compression in Self-Organizing Particle Systems

Abstract: I will present work on a new application of Markov chains to distributed computing. Motivated by programmable matter and the behavior of biological distributed systems such as ant colonies, the geometric amoebot model abstracts these processes as self-organizing particle systems where particles with limited computational power move on the triangular lattice. Previous algorithms developed in this setting have relied heavily on leader election, tree structures that are not robust to failures, and persistent memory. We developed a distributed algorithm for the compression problem, where all particles want to gather together as tightly as possible, that is based on a Markov chain and is simple, robust, and oblivious. Tools from Markov chain analysis enable rigorous proofs about its behavior, and we show compression will occur with high probability. This joint work with Joshua J. Daymude, Dana Randall, and Andrea Richa appeared at PODC 2016. I will also present some more recent extensions of this approach to other problems, which is joint work with Marta Andres Arroyo as well.

September 23: Richard Peng, Parallel Graph Algorithms

Abstract: Parallel algorithms study ways of speeding up sequential algorithms by splitting work onto multiple processors. Theoretical studies of parallel algorithms often focus on performing a small number of operations, but assume more generous models of communication. Recent progresses led to parallel algorithms for many graph optimization problems that have proven to be difficult to parallelize. In this talk I will survey routines at the core of these results: low diameter decompositions, random sampling, and iterative methods.

October 14: Matthew Fahrbach, Approximately Sampling Elements with Fixed Rank in Graded Posets

Abstract: Graded posets are partially ordered sets equipped with a unique rank function that respects the partial order and such that neighboring elements in the Hasse diagram have ranks that differ by one. We frequently find them throughout combinatorics, including the canonical partial order on Young diagrams and plane partitions, where their respective rank functions are the area and volume under the configuration. We ask when it is possible to efficiently sample elements with a fixed rank in a graded poset. We show that for certain classes of posets, a biased Markov chain that connects elements in the Hasse diagram allows us to approximately generate samples from any fixed rank in expected polynomial time. While varying a bias parameter to increase the likelihood of a sample of a desired size is common in statistical physics, one typically needs properties such as log-concavity in the number of elements of each size to generate desired samples with sufficiently high probability. Here we do not even require unimodality in order to guarantee that the algorithm succeeds in generating samples of the desired rank efficiently. This joint work with Prateek Bhakta, Ben Cousins, and Dana Randall will appear at SODA 2017.

October 28: Kevin Lai, Agnostic Estimation of Mean and Covariance

Abstract: We consider the problem of estimating the mean and covariance of a distribution from iid samples in R^n in the presence of an η fraction of malicious noise; this is in contrast to much recent work where the noise itself is assumed to be from a distribution of known type. This agnostic learning problem includes many interesting special cases, e.g., learning the parameters of a single Gaussian (or finding the best-fit Gaussian) when η fraction of data is adversarially corrupted, agnostically learning a mixture of Gaussians, agnostic ICA, etc. We present polynomial-time algorithms to estimate the mean and covariance with error guarantees in terms of information-theoretic lower bounds. We also give an agnostic algorithm for estimating the 2-norm of the covariance matrix of a Gaussian. This joint work with Santosh Vempala and Anup Rao appeared in FOCS 2016.

November 4: Aurko Roy, Hierarchical clustering via spreading metrics

Abstract: We study the cost function for hierarchical clusterings introduced by Dasgupta where hierarchies are treated as first-class objects rather than deriving their cost from projections into flat clusters. It was also shown that a top-down algorithm returns a hierarchical clustering of cost at most O (α_n log n) times the cost of the optimal hierarchical clustering, where α_n is the approximation ratio of the Sparsest Cut subroutine used. Thus using the best known approximation algorithm for Sparsest Cut due to Arora-Rao-Vazirani, the top down algorithm returns a hierarchical clustering of cost at most O(log^{3/2} n) times the cost of the optimal solution. We improve this by giving an O(log n)- approximation algorithm for this problem. Our main technical ingredients are a combinatorial characterization of ultrametrics induced by this cost function, deriving an Integer Linear Programming (ILP) formulation for this family of ultrametrics, and showing how to iteratively round an LP relaxation of this formulation by using the idea of sphere growing which has been extensively used in the context of graph partitioning. We also prove that our algorithm returns an O(log n)-approximate hierarchical clustering for a generalization of this cost function also studied in Dasgupta. This joint work with Sebastian Pokutta is to appear in NIPS 2016 (oral presentation).

November 11: Chi Ho Yuen, Geometric Bijections between the Jacobian and Bases of a Regular Matroid via Orientations

Abstract:The Jacobian (or sandpile group) of a graph is a well-studied group associated to the graph, known to biject with the set of spanning trees of the graph via a number of classical combinatorial mappings. The algebraic definition of a Jacobian extends to regular matroids, but without the notion of vertices, many such combinatorial bijections fail to generalize. In this talk, I will discuss how orientations provide a way to overcome such obstacle. We give a novel, effectively computable bijection scheme between the Jacobian and the set of bases of a regular matroid, in which polyhedral geometry plays an important role; along the way we also obtain new enumerative results related to the Tutte polynomial. This is joint work with Spencer Backman and Matt Baker.

November 18: Tim Duff, Problems, Algorithms, and Complexity in Algebraic Geometry.

Abstract: At the intersection of computability and algebraic geometry, the following question arises: does an integral polynomial system of equations have any integral solutions? Famously, the combined work of Robinson, Davis, Putnam, and Matiyasevich answers this in the negative. Nonetheless, algorithms have played in increasing role in the development of algebraic geometry and its many applications. I address some research related to this general theme and some outstanding questions.

December 2: Daniel Zink, Lazifying Conditional Gradient Algorithms

Abstract: Conditional gradient algorithms (also often called Frank-Wolfe algorithms) are popular due to their simplicity of only requiring a linear optimization oracle and more recently they also gained significant traction for online learning. While simple in principle, in many cases the actual implementation of the linear optimization oracle is costly. We show a general method to lazify various conditional gradient algorithms, which in actual computations leads to several orders of magnitude of speedup in wall-clock time. This is achieved by using a faster separation oracle instead of a linear optimization oracle, relying only on few linear optimization oracle calls.


Contact

If you are interested in giving a talk at the seminar, you can contact any of the organizers: Digvijay Boob, Marcel Celaya, or David Durfee.

Other Semesters

Fall 2016; Spring 2016; Fall 2015; Spring 2015; Fall 2014