Anirudh Sridhar

Johannes Bäumler, Miklós Z. Rácz, Nathan Ross et al.

We introduce and study a new model of correlated uniform attachment (UA) trees, where correlation is sprinkled throughout the time evolution of the process. In this model, two UA trees are grown in parallel, and at each time step a new node is added to each tree, with an edge between it and a uniformly chosen existing vertex in the respective tree. The two choices of attachment are correlated: with probability $α$, the edges attach to nodes with the same time label in both trees, and with probability $1-α$, the choices are made independently. We study fundamental detection and estimation questions for this model, given two \emph{unlabeled} trees. In our main result, we construct a consistent estimator of the correlation parameter $α$, as the size of the trees goes to infinity. The construction of our statistic relies on two key ideas. First, we use Jordan centrality to identify subsets of vertices of each tree whose intersection has a sufficient number of common early vertices. The second idea is that, across multiple time scales, it is possible to approximately determine the labels of vertices that have attached to these early vertices, using the sizes of fringe subtrees. Our analysis includes novel quantitative bounds on the fraction of early vertices that remain central, which are of independent interest in the network archaeology literature.

Sérgio Machado, Anirudh Sridhar, Paulo Gil et al. · mit

We study the problem of graph structure identification, i.e., of recovering the graph of dependencies among time series. We model these time series data as components of the state of linear stochastic networked dynamical systems. We assume partial observability, where the state evolution of only a subset of nodes comprising the network is observed. We devise a new feature vector computed from the observed time series and prove that these features are linearly separable, i.e., there exists a hyperplane that separates the cluster of features associated with connected pairs of nodes from those associated with disconnected pairs. This renders the features amenable to train a variety of classifiers to perform causal inference. In particular, we use these features to train Convolutional Neural Networks (CNNs). The resulting causal inference mechanism outperforms state-of-the-art counterparts w.r.t. sample-complexity. The trained CNNs generalize well over structurally distinct networks (dense or sparse) and noise-level profiles. Remarkably, they also generalize well to real-world networks while trained over a synthetic network (realization of a random graph). Finally, the proposed method consistently reconstructs the graph in a pairwise manner, that is, by deciding if an edge or arrow is present or absent in each pair of nodes, from the corresponding time series of each pair. This fits the framework of large-scale systems, where observation or processing of all nodes in the network is prohibitive.

Miklós Z. Rácz, Anirudh Sridhar · mit

We consider the task of estimating the latent vertex correspondence between two edge-correlated random graphs with generic, inhomogeneous structure. We study the so-called \emph{$k$-core estimator}, which outputs a vertex correspondence that induces a large, common subgraph of both graphs which has minimum degree at least $k$. We derive sufficient conditions under which the $k$-core estimator exactly or partially recovers the latent vertex correspondence. Finally, we specialize our general framework to derive new results on exact and partial recovery in correlated stochastic block models, correlated Chung-Lu graphs, and correlated random geometric graphs.

Julia Gaudio, Miklos Z. Racz, Anirudh Sridhar

We consider the problem of learning latent community structure from multiple correlated networks. We study edge-correlated stochastic block models with two balanced communities, focusing on the regime where the average degree is logarithmic in the number of vertices. Our main result derives the precise information-theoretic threshold for exact community recovery using multiple correlated graphs. This threshold captures the interplay between the community recovery and graph matching tasks. In particular, we uncover and characterize a region of the parameter space where exact community recovery is possible using multiple correlated graphs, even though (1) this is information-theoretically impossible using a single graph and (2) exact graph matching is also information-theoretically impossible. In this regime, we develop a novel algorithm that carefully synthesizes algorithms from the community recovery and graph matching literatures.

Miklos Z. Racz, Anirudh Sridhar

We consider the task of learning latent community structure from multiple correlated networks. First, we study the problem of learning the latent vertex correspondence between two edge-correlated stochastic block models, focusing on the regime where the average degree is logarithmic in the number of vertices. We derive the precise information-theoretic threshold for exact recovery: above the threshold there exists an estimator that outputs the true correspondence with probability close to 1, while below it no estimator can recover the true correspondence with probability bounded away from 0. As an application of our results, we show how one can exactly recover the latent communities using multiple correlated graphs in parameter regimes where it is information-theoretically impossible to do so using just a single graph.

Jeremiah Blocki, Anirudh Sridhar

Offline attacks on passwords are increasingly commonplace and dangerous. An offline adversary is limited only by the amount of computational resources he or she is willing to invest to crack a user's password. The danger is compounded by the existence of authentication servers who fail to adopt proper password storage practices like key-stretching. Password managers can help mitigate these risks by adopting key stretching procedures like hash iteration or memory hard functions to derive site specific passwords from the user's master password on the client-side. While key stretching can reduce the offline adversary's success rate, these procedures also increase computational costs for a legitimate user. Motivated by the observation that most of the password guesses of the offline adversary will be incorrect, we propose a client side cost asymmetric secure hashing scheme (Client-CASH). Client-CASH randomizes the runtime of client-side key stretching procedure in a way that the expected computational cost of our key derivation function is greater when run with an incorrect master password. We make several contributions. First, we show how to introduce randomness into a client-side key stretching algorithms through the use of halting predicates which are selected randomly at the time of account creation. Second, we formalize the problem of finding the optimal running time distribution subject to certain cost constraints for the client and certain security constrains on the halting predicates. Finally, we demonstrate that Client-CASH can reduce the adversary's success rate by up to $21\%$. These results demonstrate the promise of the Client-CASH mechanism.