A new polynomial-time algorithm for linear programming
Combinatorica
SIAM Journal on Scientific and Statistical Computing
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Monotonicity testing over general poset domains
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
The complexity of approximating entropy
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Fast Approximate PCPs for Multidimensional Bin-Packing Problems
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
Improved Testing Algorithms for Monotonicity
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
Testing that distributions are close
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Testing Random Variables for Independence and Identity
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Testing monotone high-dimensional distributions
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Testing k-wise and almost k-wise independence
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Testing symmetric properties of distributions
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Property Testing: A Learning Theory Perspective
Foundations and Trends® in Machine Learning
Algorithmic and Analysis Techniques in Property Testing
Foundations and Trends® in Theoretical Computer Science
Measuring independence of datasets
Proceedings of the forty-second ACM symposium on Theory of computing
Testing monotone continuous distributions on high-dimensional real cubes
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Property testing and parameter testing for permutations
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Testing non-uniform k-wise independent distributions over product spaces
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Invariance in property testing
Property testing
Invariance in property testing
Property testing
Testing permutation properties through subpermutations
Theoretical Computer Science
Learning k-modal distributions via testing
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Approximating and testing k-histogram distributions in sub-linear time
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Taming big probability distributions
XRDS: Crossroads, The ACM Magazine for Students - Big Data
Testing Symmetric Properties of Distributions
SIAM Journal on Computing
On the power of conditional samples in distribution testing
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Testing Closeness of Discrete Distributions
Journal of the ACM (JACM)
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The complexity of testing properties of monotone and unimodal distributions, when given access only to samples of the distribution, is investigated. Two kinds of sublinear-time algorithms---those for testing monotonicity and those that take advantage of monotonicity---are provided. The first algorithm tests if a given distribution on [n] is monotone or far away from any monotone distribution in L1-norm; this algorithm uses O(√n) samples and is shown to be nearly optimal. The next algorithm, given a joint distribution on [n] x [n], tests if it is monotone or is far away from any monotone distribution in L1-norm; this algorithm uses O(n3/2) samples. The problems of testing if two monotone distributions are close in L1-norm and if two random variables with a monotone joint distribution are close to being independent in L1-norm are also considered. Algorithms for these problems that use only poly(log n) samples are presented. The closeness and independence testing algorithms for monotone distributions are significantly more efficient than the corresponding algorithms as well as the lower bounds for arbitrary distributions. Some of the above results are also extended to unimodal distributions.