Elements of information theory
Elements of information theory
Self-testing/correcting with applications to numerical problems
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
Designing programs that check their work
Journal of the ACM (JACM)
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
On the rate of multivariate Poisson convergence
Journal of Multivariate Analysis
Towards estimation error guarantees for distinct values
PODS '00 Proceedings of the nineteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Average Case Analysis of Algorithms on Sequences
Average Case Analysis of Algorithms on Sequences
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
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
Three theorems regarding testing graph properties
Random Structures & Algorithms
A study of statistical zero-knowledge proofs
A study of statistical zero-knowledge proofs
Testing properties of distributions
Testing properties of distributions
Tight Lower Bounds for the Distinct Elements Problem
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Sublinear algorithms for testing monotone and unimodal distributions
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
The Complexity of Approximating the Entropy
SIAM Journal on Computing
Testing k-wise and almost k-wise independence
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Approximating entropy from sublinear samples
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Declaring independence via the sketching of sketches
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Testing symmetric properties of distributions
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Sublinear estimation of entropy and information distances
ACM Transactions on Algorithms (TALG)
A Combinatorial Characterization of the Testable Graph Properties: It's All About Regularity
SIAM Journal on Computing
Strong Lower Bounds for Approximating Distribution Support Size and the Distinct Elements Problem
SIAM Journal on Computing
A near-optimal algorithm for estimating the entropy of a stream
ACM Transactions on Algorithms (TALG)
Proceedings of the forty-third annual ACM symposium on Theory of computing
The Power of Linear Estimators
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Quantum Algorithms for Testing Properties of Distributions
IEEE Transactions on Information Theory
Taming big probability distributions
XRDS: Crossroads, The ACM Magazine for Students - Big Data
New analysis and algorithm for learning with drifting distributions
ALT'12 Proceedings of the 23rd international conference on Algorithmic Learning Theory
On the power of conditional samples in distribution testing
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
On Approximating the Number of Relevant Variables in a Function
ACM Transactions on Computation Theory (TOCT)
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We introduce the notion of a canonical tester for a class of properties on distributions, that is, a tester strong and general enough that “a distribution property in the class is testable if and only if the canonical tester tests it.” We construct a canonical tester for the class of properties of one or two distributions that are symmetric and satisfy a certain weak continuity condition. Analyzing the performance of the canonical tester on specific properties resolves two open problems, establishing lower bounds that match known upper bounds: we show that distinguishing between entropy $\beta$ on distributions over $[n]$ requires $n^{\alpha/\beta- o(1)}$ samples, and distinguishing whether a pair of distributions has statistical distance $\beta$ requires $n^{1- o(1)}$ samples. Our techniques also resolve a conjecture about a property that our canonical tester does not apply to: distinguishing identical distributions from those with statistical distance $\frac{1}{2}$ requires $\Omega(n^{2/3})$ samples.