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This paper presents a randomized scheduler for finding concurrency bugs. Like current stress-testing methods, it repeatedly runs a given test program with supplied inputs. However, it improves on stress-testing by finding buggy schedules more effectively and by quantifying the probability of missing concurrency bugs. Key to its design is the… (More)

- Prateek Jain, Pravesh Kothari, Abhradeep Thakurta
- COLT
- 2012

In this paper, we consider the problem of preserving privacy in the online learning setting. Online learning involves learning from the data in real-time, so that the learned model as well as its outputs are also continuously changing. This makes preserving privacy of each data point significantly more challenging as its effect on the learned model can be… (More)

- Deeparnab Chakrabarty, Prateek Jain, Pravesh Kothari
- NIPS
- 2014

Owing to several applications in large scale learning and vision problems, fast submodular function minimization (SFM) has become a critical problem. Theoretically, unconstrained SFM can be performed in polynomial time [10, 11]. However, these algorithms are typically not practical. In 1976, Wolfe [21] proposed an algorithm to find the minimum Euclidean… (More)

We show that all non-negative submodular functions have high noise-stability. As a consequence, we obtain a polynomial-time learning algorithm for this class with respect to any product distribution on {−1, 1} (for any constant accuracy parameter ). Our algorithm also succeeds in the agnostic setting. Previous work on learning submodular functions required… (More)

- Adam R. Klivans, Pravesh Kothari, Igor Carboni Oliveira
- Electronic Colloquium on Computational Complexity
- 2013

Fortnow and Klivans proved the following relationship between efficient learning algorithms and circuit lower bounds: if a class C ⊆ P/poly of Boolean circuits is exactly learnable with membership and equivalence queries in polynomial-time, then EXP * C (the class EXP was subsequently improved to EXP by Hitchcock and Harkins). In this paper, we improve on… (More)

- Vitaly Feldman, Pravesh Kothari, Jan Vondrák
- COLT
- 2013

We study the complexity of approximate representation and learning of submodular functions over the uniform distribution on the Boolean hypercube {0, 1}. Our main result is the following structural theorem: any submodular function is -close in `2 to a real-valued decision tree (DT) of depth O(1/ ). This immediately implies that any submodular function is… (More)

- Adam R. Klivans, Pravesh Kothari
- APPROX-RANDOM
- 2014

We give the first representation-independent hardness result for agnostically learning halfspaces with respect to the Gaussian distribution. We reduce from the problem of learning sparse parities with noise with respect to the uniform distribution on the hypercube (sparse LPN), a notoriously hard problem in theoretical computer science and show that any… (More)

- Vitaly Feldman, Pravesh Kothari
- COLT
- 2014

We study the problem of approximating and learning coverage functions. A function c : 2 → R is a coverage function, if there exists a universe U with non-negative weights w(u) for each u ∈ U and subsets A1, A2, . . . , An of U such that c(S) = ∑ u∈∪i∈SAi w(u). Alternatively, coverage functions can be described as non-negative linear combinations of monotone… (More)

- Pravesh Kothari, Ryuhei Mori, Ryan O'Donnell, David Witmer
- STOC
- 2017

Let <i>P</i>:{0,1}<sup><i>k</i></sup> â {0,1} be a nontrivial <i>k</i>-ary predicate. Consider a random instance of the constraint satisfaction problem (<i>P</i>) on <i>n</i> variables with Î <i>n</i> constraints, each being <i>P</i> applied to <i>k</i> randomly chosen literals. Provided the constraint density satisfies Î â« 1, such… (More)

- Boaz Barak, Siu On Chan, Pravesh Kothari
- STOC
- 2015

We prove that for every ε>0 and predicate P:{0,1}<sup>k</sup>-> {0,1} that supports a pairwise independent distribution, there exists an instance I of the Max P constraint satisfaction problem on n variables such that no assignment can satisfy more than a ~(|P<sup>-1</sup>(1)|)/(2<sup>k</sup>)+ε fraction of I's constraints but the degree… (More)