Naman Agarwal

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A k-lift of an n-vertex base-graph G is a graph H on n × k vertices, where each vertex of G is replaced by k vertices and each edge (u, v) in G is replaced by a matching representing a bijection π uv so that the edges of H are of the form (u, i), (v, π uv (i)). H is a (uniformly) random lift of G if for every edge (u, v) the bijection π uv is chosen(More)
We consider the problem of identifying underlying community-like structures in graphs. Towards this end we study the Stochastic Block Model (SBM) on k-clusters: a random model on n = km vertices, partitioned in k equal sized clusters, with edges sampled independently across clusters with probability q and within clusters with probability p, p > q. The goal(More)
First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to efficient per-iteration complexity. Second-order methods, while able to provide faster convergence, have been much less explored due to the high cost of computing the second-order information. In this paper we develop second-order stochastic methods(More)
We design a non-convex second-order optimization algorithm that is guaranteed to return an approximate local minimum in time which is linear in the input representation. The previously fastest methods run in time proportional to matrix inversion or worse. The time complexity of our algorithm to find a local minimum is even faster than that of gradient(More)
In this paper, we investigate the validity of the Unique Games Conjecture when the constraint graph is the boolean hypercube. We construct an almost optimal integrality gap instance on the Hypercube for the Goemans-Williamson semidefinite program (SDP) for Max-2-LIN(Z 2). We conjecture that adding triangle inequalities to the SDP provides a polynomial time(More)
— The Indian Retail Market is witnessing a revolution. The growth of internet has enabled the new retail format of the virtual retailer to emerge and forced the existing retailers to consider e-tailing model of retailing as well. A large number of consumers frequently use the Internet for shopping purposes but its' not clear what drives them to shop online.(More)
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