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We apply it to solve the operator scaling problem in time polynomial in the input size and logarithmic in the error. This is an exponential improvement over previous algorithms which were ... Keywords: capacity, geodesic convex, operator scaling, orbit-closure intersection, positive definite 2 June 2018 Computational Complexity: Volume 27 Issue 2, June 2018 Publisher: Birkhauser Verlag Bibliometrics: Citation Count: 0 A map $${f : \{0,1\}^{n} \to \{0,1\}^{n}}$$f:{0,1}nź{0,1}n has localityt if every output bit of f depends only on t input bits. Arora et al. (Colloquium on automata, languages and programming, ICALP, 2009) asked if there exist bounded-degree expander graphs on 2n nodes such that the neighbors of a node $${x\in\{0,1\}^{n}}$$xź{0,1}n ... Keywords: 68Q99, Cayley graph, Derandomization, Expander graph, Hardness amplification, Locality 3 June 2017 STOC 2017: Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing Publisher: ACM Bibliometrics: Citation Count: 2 Downloads (6 Weeks): 3,   Downloads (12 Months): 76,   Downloads (Overall): 143 Full text available: PDF The celebrated Brascamp-Lieb (BL) inequalities [BL76, Lie90], and their reverse form of Barthe [Bar98], are an important mathematical tool, unifying and generalizing numerous in- equalities in analysis, convex geometry and information theory, with many used in computer science. While their structural theory is very well understood, far less is known ... Keywords: Brascamp-Lieb, Inequalities, Operator Scaling, optimization 4 May 2017 Communications of the ACM: Volume 60 Issue 6, June 2017 Publisher: ACM Bibliometrics: Citation Count: 1 Downloads (6 Weeks): 3,   Downloads (12 Months): 90,   Downloads (Overall): 352 Full text available: Html  PDF 5 May 2016 CCC '16: Proceedings of the 31st Conference on Computational Complexity Publisher: Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik Bibliometrics: Citation Count: 1 We give upper and lower bounds on the power of subsystems of the Ideal Proof System (IPS), the algebraic proof system recently proposed by Grochow and Pitassi [26], where the circuits comprising the proof come from various restricted algebraic circuit classes. This mimics an established research direction in the boolean ... Keywords: proof complexity, nullstellensatz, subset-sum, algebraic complexity 6 May 2016 CCC '16: Proceedings of the 31st Conference on Computational Complexity Publisher: Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik Bibliometrics: Citation Count: 0 The sensitivity of a Boolean function f is the maximum, over all inputs x , of the number of sensitive coordinates of x (namely the number of Hamming neighbors of x with different f -value). The well-known sensitivity conjecture of Nisan (see also Nisan and Szegedy) states that every sensitivity- ... Keywords: fourier degree, boolean functions, sensitivity, decision trees 7 February 2016 Combinatorica: Volume 36 Issue 1, February 2016 Publisher: Springer-Verlag New York, Inc. Bibliometrics: Citation Count: 1 Coding theoretic and complexity theoretic considerations naturally lead to the question of generating symmetric, sparse, redundant linear systems. This paper provides a new way of construction with better parameters and new lower bounds. Low Density Parity Check (LDPC) codes are linear codes defined by short constraints (a property essential for ... Keywords: 05C25, 68Q01, 68P30 8 January 2016 ITCS '16: Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science Publisher: ACM Bibliometrics: Citation Count: 3 Downloads (6 Weeks): 5,   Downloads (12 Months): 47,   Downloads (Overall): 116 Full text available: PDF A natural measure of smoothness of a Boolean function is its sensitivity (the largest number of Hamming neighbors of a point which differ from it in function value). The structure of smooth or equivalently low-sensitivity functions is still a mystery. A well-known conjecture states that every such Boolean function can ... Keywords: noise stability, boolean functions, sensitivity, self-correction, formula depth 9 January 2016 SODA '16: Proceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms Publisher: Society for Industrial and Applied Mathematics Bibliometrics: Citation Count: 5 Downloads (6 Weeks): 1,   Downloads (12 Months): 5,   Downloads (Overall): 38 Full text available: PDF We study efficient, deterministic interactive coding schemes that simulate any interactive protocol both under random and adversarial errors, and can achieve a constant communication rate independent of the protocol length. For channels that flip bits independently with probability ε < 1/2, our coding scheme achieves a communication rate of 1 ... 10 January 2016 Machine Learning: Volume 102 Issue 1, January 2016 Publisher: Kluwer Academic Publishers Bibliometrics: Citation Count: 0 We study several problems in which an unknown distribution over an unknown population of vectors needs to be recovered from partial or noisy samples, each of which nearly completely erases or obliterates the original vector. For example, consider a distribution $$p$$p over a population $$V \subseteq \{0,1\}^n$$V⊆{0,1}n. A noisy sample ... Keywords: Partial information, Identification, Noise recovery 11 December 2015 NIPS'15: Proceedings of the 28th International Conference on Neural Information Processing Systems - Volume 1 Publisher: MIT Press Bibliometrics: Citation Count: 2 This paper establishes a statistical versus computational trade-off for solving a basic high-dimensional machine learning problem via a basic convex relaxation method. Specifically, we consider the Sparse Principal Component Analysis (Sparse PCA) problem, and the family of Sum-of-Squares (SoS, aka Lasserre/Parillo) convex relaxations. It was well known that in large ... 12 October 2015 FOCS '15: Proceedings of the 2015 IEEE 56th Annual Symposium on Foundations of Computer Science (FOCS) Publisher: IEEE Computer Society Bibliometrics: Citation Count: 0 In this work we study the quantitative relation between VC-dimension and two other basic parameters related to learning and teaching. Namely, the quality of sample compression schemes and of teaching sets for classes of low VC-dimension. Let C be a binary concept class of size m and VC-dimension d. Prior ... 13 June 2015 CCC '15: Proceedings of the 30th Conference on Computational Complexity Publisher: Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik Bibliometrics: Citation Count: 1 We consider randomness extraction by AC 0 circuits. The main parameter, n , is the length of the source, and all other parameters are functions of it. The additional extraction parameters are the min-entropy bound k = k ( n ), the seed length r = r ( n ), ... Keywords: AC0, bit-fixing sources, multiple-source extraction, randomness extractors, block sources, general min-entropy sources 14 June 2015 STOC '15: Proceedings of the forty-seventh annual ACM symposium on Theory of computing Publisher: ACM Bibliometrics: Citation Count: 3 Downloads (6 Weeks): 5,   Downloads (12 Months): 27,   Downloads (Overall): 113 Full text available: PDF This paper studies the parameters for which binary Reed-Muller (RM) codes can be decoded successfully on the BEC and BSC, and in particular when can they achieve capacity for these two classical channels. Necessarily, the paper also studies properties of evaluations of multi-variate GF(2) polynomials on random sets of inputs. ... Keywords: weight enumerator, channel capacity, reed-muller codes, multivariate polynomials. 15 June 2015 STOC '15: Proceedings of the forty-seventh annual ACM symposium on Theory of computing Publisher: ACM Bibliometrics: Citation Count: 10 Downloads (6 Weeks): 5,   Downloads (12 Months): 26,   Downloads (Overall): 229 Full text available: PDF Finding cliques in random graphs and the closely related "planted" clique variant, where a clique of size k is planted in a random G(n,1/2) graph, have been the focus of substantial study in algorithm design. Despite much effort, the best known polynomial-time algorithms only solve the problem for k = ... 16 May 2014 STOC '14: Proceedings of the forty-sixth annual ACM symposium on Theory of computing Publisher: ACM Bibliometrics: Citation Count: 4 Downloads (6 Weeks): 1,   Downloads (12 Months): 9,   Downloads (Overall): 85 Full text available: PDF We prove that 3-query linear locally correctable codes over the Reals of dimension d require block length n > d 2+ λ for some fixed, positive λ > 0. Geometrically, this means that if n vectors in R d are such that each vector is spanned by a linear number ... Keywords: locally decodable codes, error correcting codes, locally correctable codes 17 January 2014 ITCS '14: Proceedings of the 5th conference on Innovations in theoretical computer science Publisher: ACM Bibliometrics: Citation Count: 2 Downloads (6 Weeks): 2,   Downloads (12 Months): 6,   Downloads (Overall): 99 Full text available: PDF We initiate the study of the complexity of arithmetic circuits with division gates over non-commuting variables. Such circuits and formulas compute non-commutative rational functions, which, despite their name, can no longer be expressed as ratios of polynomials. We prove some lower and upper bounds, completeness and simulation results, as follows. ... Keywords: arithmetic circuit complexity, free skew field, non-commutative rational function 18 June 2013 STOC '13: Proceedings of the forty-fifth annual ACM symposium on Theory of computing Publisher: ACM Bibliometrics: Citation Count: 11 Downloads (6 Weeks): 0,   Downloads (12 Months): 15,   Downloads (Overall): 169 Full text available: PDF We study interactive proofs with sublinear-time verifiers. These proof systems can be used to ensure approximate correctness for the results of computations delegated to an untrusted server. Following the literature on property testing, we seek proof systems where with high probability the verifier accepts every input in the language, and ... Keywords: interactive proofs, sublinear algorithms 19 October 2012 FOCS '12: Proceedings of the 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science Publisher: IEEE Computer Society Bibliometrics: Citation Count: 5 We study several problems in which an unknown distribution over an unknown population of vectors needs to be recovered from partial or noisy samples, each of which nearly completely erases or obliterates the original vector. For example, consider a distribution p over a population V subset of or equal to ... Keywords: information recovery, learning theory, noisy data 20 October 2012 Communications of the ACM: Volume 55 Issue 10, October 2012 Publisher: ACM Bibliometrics: Citation Count: 0 Downloads (6 Weeks): 10,   Downloads (12 Months): 76,   Downloads (Overall): 740 Full text available: Html  PDF Foam problems are about how to best partition space into bubbles of minimal surface area. We investigate the case where one unit-volume bubble is required to tile d -dimensional space in a periodic fashion according to the standard, cubical lattice. While a cube requires surface area 2 d , we ...