We typically have seminars on Wednesday at noon in Malone 228. All seminar announcements will be sent to the theory mailing list.

Speaker: Karthik Abinav Sankararaman

Affiliation: University of Maryland

Title: Adversarial Bandits with Knapsacks

Abstract: In this talk we will discuss the multi-armed bandits problem with resource constraints under the adversarial setting. In this problem, we have an interactive and repeated game between the algorithm and an adversary. Given T time-steps, d resources, m actions and budgets B1, B2, .. Bd, the algorithm chooses one of the m actions at each time-step. An adversary then reveals a reward and consumption for each of the d resources corresponding to this action. The time-step at which the algorithm runs out of the d resources (i.e., the total consumption for resource j > Bj), the game stops and the total reward is the sum of rewards obtained until the stopping time. The goal is to maximize the competitive ratio; the ratio of the total reward of the algorithm to the expected reward of a fixed distribution that knows all the rewards and consumption ahead of time. We give an algorithm for this problem whose competitive ratio is tight (matches the lower-bound). Moreover the algorithmic tools extends in an (almost) black-box fashion to also give an algorithm for the stochastic setting thus giving a “best-of-both-worlds” algorithm where the algorithm need not know a-priori if the input is adversarial or i.i.d. Finally we conclude with applications and special cases including the Dynamic Pricing problem.

This talk is based on a recent working paper with Nicole Immorlica, Rob Schapire and Alex Slivkins.

Speaker: Nithin Varma

Affiliation: Boston University

Title: Separating erasures and errors in property testing using local list decoding

Abstract:

Corruption in data can be in the form of erasures (missing data) or errors (wrong data). Erasure-resilient property testing (Dixit, Raskhodnikova, Thakurta, Varma ’16) and tolerant property testing (Parnas, Ron, Rubinfeld ’06) are two formal models of sublinear algorithms that account for the presence of erasures and errors in input data, respectively.

We first show that there exists a property P that has an erasure-resilient tester whose query complexity is independent of the input size n, whereas every tolerant tester for P has query complexity that depends on n. We obtain this result by designing a local list decoder for the Hadamard code that works in the presence of erasures, thereby proving an analog of the famous Goldreich-Levin Theorem. We also show a strengthened separation by proving that there exists another property R such that R has a constant-query erasure-resilient tester, whereas every tolerant tester for R requires n^{Omega(1)} queries. The main tool used in proving the strengthened separation is an approximate variant of a locally list decodable code that works against erasures.

Joint work with Sofya Raskhodnikova and Noga Ron-Zewi.

Speaker: Jalaj Upadhyay

Affiliation: JHU

Title: Differentially Private Spectral Sparsification of Graphs

Abstract:

In this talk, we will discuss differentially private spectral sparsification of graphs. We argue that traditional spectral sparsification where the output graph is a subgraph of the input graph is not possible with differential privacy. This motivates us to define a relaxed version of spectral sparsification of graphs.

We consider edge-level privacy, i.e., neighboring graphs differs in one edge with weight one. We give efficient $(\alpha,\beta)$-differentially private algorithms that, on input a dense graph G, construct a spectral sparsification of G. Our output graphs has $ O(n/\eps^2)$ weighted edges, which matches the best known non-private algorithms.

We can use our private sparse graph to solve various combinatorial and learning problems on graphs efficiently while preserving differential privacy. Some examples include all possible cut queries, Max-Cut, Sparse-Cut, Edge-Expansion, Laplacian eigenmaps, etc.

This talk is based on a joint work with Raman Arora and Vladimir Braverman.

Speaker: Ke Wu

Affiliation: Johns Hopkins University

Title: Synchronization Strings: Efficient and Fast Deterministic Constructions over Small Alphabets

Abstract:

Synchronization strings are recently introduced by Haeupler and Shahrasbi (STOC 2017) in the study of codes for correcting insertion and deletion errors (insdel codes). They showed that for any parameter ε>0, synchronization strings of arbitrary length exist over an alphabet whose size depends only on ε. Specifically, they obtained an alphabet size of O(ε^{−4}), which left an open question on where the minimal size of such alphabets lies between Ω(ε^{1}) and O(ε^{−4}). In this work, we partially bridge this gap by providing an improved lower bound of Ω(ε^{−3/2}), and an improved upper bound of O(ε^{−2}). We also provide fast explicit constructions of synchronization strings over small alphabets.

Further, along the lines of previous work on similar combinatorial objects, we study the extremal question of the smallest possible alphabet size over which synchronization strings can exist for some constant ε<1. We show that one can construct ε-synchronization strings over alphabets of size four while no such string exists over binary alphabets. This reduces the extremal question to whether synchronization strings exist over ternary alphabets.

Speaker: Sami Davies

Affiliation: University of Washington

Title: A Tale of Santa Claus, Hypergraphs, and Matroids

Abstract:

A well-known problem in scheduling and approximation algorithms is the Santa Claus problem. Suppose that Santa Claus has a set of gifts, and he wants to distribute them among a set of children so that the least happy child is made as happy as possible. Here, the value that a child i has for a present j is of the form p_{ij} \in \{0,p_j\}. A polynomial time algorithm by Annamalai et al. gives a 12.33-approximation algorithm and is based on a modification of Haxell’s hypergraph matching argument.

In this paper, we introduce a matroid version of the Santa Claus problem. Our algorithm is also based on Haxell’s augmentation tree, but with the introduction of the matroid structure we solve a more general problem with cleaner methods. Our result can then be used as a blackbox to obtain a (4 +\varepsilon)-approximation for Santa Claus. This factor also compares against a natural, compact LP for Santa Claus.

Speaker: Jalaj Upadhyay

Affiliation: Johns Hopkins Universit

Title: Towards Robust and Scalable Private Data Analysis

Abstract:

In the current age of big data, we are constantly creating new data which is analyzed by various platforms to improve service and user’s experience. Given the sensitive and confidential nature of these data, there are obvious security and privacy concerns while storing and analyzing such data. In this talk, I will discuss the fundamental challenges in providing robust security and privacy guarantee while storing and analyzing large data. I will also give a brief overview of my contributions and future plans towards addressing these challenges.

To give a glimpse of these challenges in providing a robust privacy guarantee known as differential privacy, I will use spectral sparsification of graphs as an example. Given the ubiquitous nature of graphs, differentially private analysis on graphs has gained a lot of interest. However, existing algorithms for these analyses are tailored made for the task at hand making them infeasible in practice. In this talk, I will present a novel differentially private algorithm that outputs a spectral sparsification of the input graph. At the core of this algorithm is a method to privately estimate the importance of an edge in the graph. Prior to this work, there was no known privacy preserving method that provides such an estimate or spectral sparsification of graphs.

Since many graph properties are defined by the spectrum of the graph, this work has many analytical as well as learning theoretic applications. To demonstrate some applications, I will show more efficient and accurate analysis of various combinatorial problems on graphs and the first technique to perform privacy preserving manifold learning on graphs.

Speaker: Martin Farach-Colton

Affiliation: Rutgers University

Title: TBA

Abstract: TBA

Speaker: Xue Chen

Affiliation: Northwestern University

Title: Active Regression via Linear-Sample Sparsification

Abstract:

E[||X \wt{\beta} – X\beta^*||_2^2] \leq \eps ||X \beta^* – y||_2^2.

This improves on the best previous result of O(d \log d + d/\eps) from leverage score sampling. We also present results for the *inductive* setting, showing when \wt{\beta} will generalize to fresh samples; these apply to continuous settings such as polynomial regression. Finally, we show how the techniques yield improved results for the non-linear sparse Fourier transform setting.

Bio: Xue Chen is broadly interested in randomized algorithms and the use of randomness in computation. Specific areas include Fourier transform, learning theory and optimization, and pseudorandomness. He obtained his Ph.D. at the University of Texas at Austin, under the supervision of David Zuckerman. Currently, he is a postdoctoral fellow in Northwestern University.

Speaker: Rediet Abebe

Affiliation: Cornell University

Title: Using Search Queries to Understand Health Information Needs in Africa

Abstract:

Access to healthcare and health information is of major global

concern. The stark inequality in the availability of health data by

country, demographic groups, and socioeconomic status impedes the

identification of major public health concerns and implementation of

effective interventions. This data gap ranges from basic disease

statistics, such as disease prevalence rates, to more nuanced

information, such as public attitudes. A key challenge is

understanding health information needs of under-served and

marginalized communities. Without understanding people’s everyday

needs, concerns, and misconceptions, health organizations lack the

ability to effectively target education and programming efforts.

In this presentation, we focus on the lack of comprehensive,

high-quality data about information needs of individuals in developing

nations. We propose an approach that uses search data to uncover

health information needs of individuals in all 54 nations in Africa.

We analyze Bing searches related to HIV/AIDS, malaria, and

tuberculosis; these searches reveal diverse health information needs

that vary by demographic groups and geographic regions. We also shed

light on discrepancies in the quality of content returned by search

engines.

We conclude with a discussion on computationally-informed

interventions both on- and off-line in health and related domains and

the Mechanism Design for Social Good research initiative.

Bio:

Rediet Abebe is a computer scientist with a strong interest in the

promotion of equality and justice. Her research focuses on algorithms,

AI, and their applications to social good. As part of this research

agenda, she co-founded and co-organizes Mechanism Design for Social

Good (MD4SG), an interdisciplinary, multi-institutional research

initiative with over 300 individuals. She is also a co-founder and

co-organizer of Black in AI, an international network of over 1000

individuals focused on increasing the presence and inclusion of Black

and African researchers in AI. Her research is deeply influenced by

her upbringing in her hometown of Addis Ababa, Ethiopia, where she

lived until moving to the U.S. in 2009. Her work has been generously

supported by fellowships and scholarships through Facebook, Google,

the Cornell Graduate School, and the Harvard-Cambridge Fellowship.