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1
June 2018
STOC 2018: Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing
Publisher: ACM
Bibliometrics:
Citation Count: 1
Downloads (6 Weeks): 29, Downloads (12 Months): 118, Downloads (Overall): 118
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We propose a new secondorder method for geodesically convex optimization on the natural hyperbolic metric over positive definite matrices. 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, orbitclosure intersection, positive definite
2
June 2018
Computational Complexity: Volume 27 Issue 2, June 2018
Publisher: Birkhauser Verlag
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 boundeddegree 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
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The celebrated BrascampLieb (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:
BrascampLieb, 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
5
May 2016
CCC '16: Proceedings of the 31st Conference on Computational Complexity
Publisher: Schloss DagstuhlLeibnizZentrum fuer Informatik
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, subsetsum, algebraic complexity
6
May 2016
CCC '16: Proceedings of the 31st Conference on Computational Complexity
Publisher: Schloss DagstuhlLeibnizZentrum fuer Informatik
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 wellknown 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: SpringerVerlag New York, Inc.
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
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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 lowsensitivity functions is still a mystery. A wellknown conjecture states that every such Boolean function can ...
Keywords:
noise stability, boolean functions, sensitivity, selfcorrection, formula depth
9
January 2016
SODA '16: Proceedings of the twentyseventh annual ACMSIAM 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
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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
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
This paper establishes a statistical versus computational tradeoff for solving a basic highdimensional machine learning problem via a basic convex relaxation method. Specifically, we consider the Sparse Principal Component Analysis (Sparse PCA) problem, and the family of SumofSquares (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
In this work we study the quantitative relation between VCdimension 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 VCdimension. Let C be a binary concept class of size m and VCdimension d. Prior ...
13
June 2015
CCC '15: Proceedings of the 30th Conference on Computational Complexity
Publisher: Schloss DagstuhlLeibnizZentrum fuer Informatik
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 minentropy bound k = k ( n ), the seed length r = r ( n ), ...
Keywords:
AC0, bitfixing sources, multiplesource extraction, randomness extractors, block sources, general minentropy sources
14
June 2015
STOC '15: Proceedings of the fortyseventh annual ACM symposium on Theory of computing
Publisher: ACM
Bibliometrics:
Citation Count: 3
Downloads (6 Weeks): 5, Downloads (12 Months): 27, Downloads (Overall): 113
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This paper studies the parameters for which binary ReedMuller (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 multivariate GF(2) polynomials on random sets of inputs. ...
Keywords:
weight enumerator, channel capacity, reedmuller codes, multivariate polynomials.
15
June 2015
STOC '15: Proceedings of the fortyseventh annual ACM symposium on Theory of computing
Publisher: ACM
Bibliometrics:
Citation Count: 10
Downloads (6 Weeks): 5, Downloads (12 Months): 26, Downloads (Overall): 229
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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 polynomialtime algorithms only solve the problem for k = ...
16
May 2014
STOC '14: Proceedings of the fortysixth 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:
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We prove that 3query 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
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We initiate the study of the complexity of arithmetic circuits with division gates over noncommuting variables. Such circuits and formulas compute noncommutative 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, noncommutative rational function
18
June 2013
STOC '13: Proceedings of the fortyfifth annual ACM symposium on Theory of computing
Publisher: ACM
Bibliometrics:
Citation Count: 11
Downloads (6 Weeks): 0, Downloads (12 Months): 15, Downloads (Overall): 169
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We study interactive proofs with sublineartime 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
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
Foam problems are about how to best partition space into bubbles of minimal surface area. We investigate the case where one unitvolume 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 ...

