Controlling Epidemic Spread using Probabilistic Diffusion Models on Networks

The spread of an epidemic is often modeled by an SIR random process on a social network graph. The MinINF problem for optimal social distancing involves minimizing the expected number of infections, when we are allowed to break at most $B$ edges; similarly the MinINFNode problem involves removing at most $B$ vertices. These are fundamental problems in epidemiology and network science. While a number of heuristics have been considered, the complexity of these problems remains generally open. In this paper, we present two bicriteria approximation algorithms for MinINF, which give the first non-trivial approximations for this problem. The first is based on the cut sparsification result of Karger \cite{karger:mathor99}, and works when the transmission probabilities are not too small. The second is a Sample Average Approximation (SAA) based algorithm, which we analyze for the Chung-Lu random graph model. We also extend some of our results to tackle the MinINFNode problem.

Deploying Vaccine Distribution Sites for Improved Accessibility and Equity to Support Pandemic Response

In response to COVID-19, many countries have mandated social distancing and banned large group gatherings in order to slow down the spread of SARS-CoV-2. These social interventions along with vaccines remain the best way forward to reduce the spread of SARS CoV-2. In order to increase vaccine accessibility, states such as Virginia have deployed mobile vaccination centers to distribute vaccines across the state. When choosing where to place these sites, there are two important factors to take into account: accessibility and equity. We formulate a combinatorial problem that captures these factors and then develop efficient algorithms with theoretical guarantees on both of these aspects. Furthermore, we study the inherent hardness of the problem, and demonstrate strong impossibility results. Finally, we run computational experiments on real-world data to show the efficacy of our methods.

Differentially Private Community Detection for Stochastic Block Models

The goal of community detection over graphs is to recover underlying labels/attributes of users (e.g., political affiliation) given the connectivity between users (represented by adjacency matrix of a graph). There has been significant recent progress on understanding the fundamental limits of community detection when the graph is generated from a stochastic block model (SBM). Specifically, sharp information theoretic limits and efficient algorithms have been obtained for SBMs as a function of $p$ and $q$, which represent the intra-community and inter-community connection probabilities. In this paper, we study the community detection problem while preserving the privacy of the individual connections (edges) between the vertices. Focusing on the notion of $(\epsilon, \delta)$-edge differential privacy (DP), we seek to understand the fundamental tradeoffs between $(p, q)$, DP budget $(\epsilon, \delta)$, and computational efficiency for exact recovery of the community labels. To this end, we present and analyze the associated information-theoretic tradeoffs for three broad classes of differentially private community recovery mechanisms: a) stability based mechanism; b) sampling based mechanisms; and c) graph perturbation mechanisms. Our main findings are that stability and sampling based mechanisms lead to a superior tradeoff between $(p,q)$ and the privacy budget $(\epsilon, \delta)$; however this comes at the expense of higher computational complexity. On the other hand, albeit low complexity, graph perturbation mechanisms require the privacy budget $\epsilon$ to scale as $\Omega(\log(n))$ for exact recovery. To the best of our knowledge, this is the first work to study the impact of privacy constraints on the fundamental limits for community detection.

Differentially Private Densest Subgraph Detection

Densest subgraph detection is a fundamental graph mining problem, with a large number of applications. There has been a lot of work on efficient algorithms for finding the densest subgraph in massive networks. However, in many domains, the network is private, and returning a densest subgraph can reveal information about the network. Differential privacy is a powerful framework to handle such settings. We study the densest subgraph problem in the edge privacy model, in which the edges of the graph are private. We present the first sequential and parallel differentially private algorithms for this problem. We show that our algorithms have an additive approximation guarantee. We evaluate our algorithms on a large number of real-world networks, and observe a good privacy-accuracy tradeoff when the network has high density.

Fair Disaster Containment via Graph-Cut Problems

Graph cut problems form a fundamental problem type in combinatorial optimization, and are a central object of study in both theory and practice. In addition, the study of fairness in Algorithmic Design and Machine Learning has recently received significant attention, with many different notions proposed and analyzed in a variety of contexts. In this paper we initiate the study of fairness for graph cut problems by giving the first fair definitions for them, and subsequently we demonstrate appropriate algorithmic techniques that yield a rigorous theoretical analysis. Specifically, we incorporate two different definitions of fairness, namely demographic and probabilistic individual fairness, in a particular cut problem modeling disaster containment scenarios. Our results include a variety of approximation algorithms with provable theoretical guarantees.

Parallel Algorithms for Densest Subgraph Discovery Using Shared Memory Model

The problem of finding dense components of a graph is a widely explored area in data analysis, with diverse applications in fields and branches of study including community mining, spam detection, computer security and bioinformatics. This research project explores previously available algorithms in order to study them and identify potential modifications that could result in an improved version with considerable performance and efficiency leap. Furthermore, efforts were also steered towards devising a novel algorithm for the problem of densest subgraph discovery. This paper presents an improved implementation of a widely used densest subgraph discovery algorithm and a novel parallel algorithm which produces better results than a 2-approximation.

Mapping Network States Using Connectivity Queries

Can we infer all the failed components of an infrastructure network, given a sample of reachable nodes from supply nodes? One of the most critical post-disruption processes after a natural disaster is to quickly determine the damage or failure states of critical infrastructure components. However, this is non-trivial, considering that often only a fraction of components may be accessible or observable after a disruptive event. Past work has looked into inferring failed components given point probes, i.e. with a direct sample of failed components. In contrast, we study the harder problem of inferring failed components given partial information of some `serviceable' reachable nodes and a small sample of point probes, being the first often more practical to obtain. We formulate this novel problem using the Minimum Description Length (MDL) principle, and then present a greedy algorithm that minimizes MDL cost effectively. We evaluate our algorithm on domain-expert simulations of real networks in the aftermath of an earthquake. Our algorithm successfully identify failed components, especially the critical ones affecting the overall system performance.

PAC-Learning for Strategic Classification

Machine learning (ML) algorithms may be susceptible to being gamed by individuals with knowledge of the algorithm (a.k.a. Goodhart's law). Such concerns have motivated a surge of recent work on strategic classification where each data point is a self-interested agent and may strategically manipulate his features to induce a more desirable classification outcome for himself. Previous works assume agents have homogeneous preferences and all equally prefer the positive label. This paper generalizes strategic classification to settings where different data points may have different preferences over the classification outcomes. Besides a richer model, this generalization allows us to include evasion attacks in adversarial ML also as a special case of our model where positive [resp. negative] data points prefer the negative [resp. positive] label, and thus for the first time allows strategic and adversarial learning to be studied under the same framework. We introduce the strategic VC-dimension (SVC), which captures the PAC-learnability of a hypothesis class in our general strategic setup. SVC generalizes the notion of adversarial VC-dimension (AVC) introduced recently by Cullina et al. arXiv:1806.01471. We then instantiate our framework for arguably the most basic hypothesis class, i.e., linear classifiers. We fully characterize the statistical learnability of linear classifiers by pinning down its SVC and the computational tractability by pinning down the complexity of the empirical risk minimization problem. Our bound of SVC for linear classifiers also strictly generalizes the AVC bound for linear classifiers in arXiv:1806.01471. Finally, we briefly study the power of randomization in our strategic classification setup. We show that randomization may strictly increase the accuracy in general, but will not help in the special case of adversarial classification under evasion attacks.