Learn More
When delegating computation to a service provider, as in the cloud computing paradigm, we seek some reassurance that the output is correct and complete. Yet recomputing the output as a check is inefficient and expensive, and it may not even be feasible to store all the data locally. We are therefore interested in what can be validated by a streaming(More)
When computation is outsourced, the data owner would like to be assured that the desired computation has been performed correctly by the service provider. In theory, proof systems can give the necessary assurance, but prior work is not sufficiently scalable or practical. In this paper, we develop new proof protocols for verifying computations which are(More)
The central goal of data stream algorithms is to process massive streams of data using <i>sublinear</i> storage space. Motivated by work in the database community on outsourcing database and data stream processing, we ask whether the space usage of such algorithms can be further reduced by enlisting a more powerful &#8220;helper&#8221; that can(More)
Several research teams have recently been working toward the development of practical general-purpose protocols for verifiable computation. These protocols enable a computationally weak verifier to offload computations to a powerful but untrusted prover, while providing the verifier with a guarantee that the prover performed the requested computations(More)
Motivated by the trend to outsource work to commercial cloud computing services, we consider a variation of the streaming paradigm where a streaming algorithm can be assisted by a powerful helper that can provide annotations to the data stream. We extend previous work on such annotation models by considering a number of graph streaming problems. Without(More)
The ε-approximate degree of a Boolean function f : {−1, 1} n → {−1, 1} is the minimum degree of a real polynomial that approximates f to within error ε in the ℓ ∞ norm. We prove several lower bounds on this important complexity measure by explicitly constructing solutions to the dual of an appropriate linear program. Our first result resolves the(More)
We give the first dimension-efficient algorithms for learning Rectified Linear Units (ReLUs), which are functions of the form x → max(0, w · x) with w ∈ S n−1. Our algorithm works in the challenging Reliable Agnostic learning model of Kalai, Kanade, and Mansour [18] where the learner is given access to a distribution D on labeled examples but the labeling(More)
The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Abstract. We study the problem of releasing k-way marginals of a database D ∈ ({0, 1} d) n , while preserving differential privacy. The answer to a k-way marginal query is the fraction of D's records x ∈ {0, 1} d with a given value in(More)
Variable selection for sparse linear regression is the problem of finding, given an m×p matrix B and a target vector y, a sparse vector x such that Bx approximately equals y. Assuming a standard complexity hypothesis, we show that no polynomial-time algorithm can find a k-sparse x with ||Bx − y|| 2 ≤ h(m, p), where k = k · 2 log 1−δ p and h(m, p) ≤ p C1 m(More)
The approximate degree of a Boolean function f : {−1, 1} n → {−1, 1} is the minimum degree of a real polynomial that approximates f to within error 1/3 in the ∞ norm. In an influential result, Aaronson and Shi (J. ACM 2004) proved tight˜Ω(n 1/3) and˜Ω(n 2/3) lower bounds on the approximate degree of the Collision and Element Distinctness functions,(More)