The complexity of approximating entropy
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Sublinear algorithms for testing monotone and unimodal distributions
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Testing monotone high-dimensional distributions
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Testing k-wise and almost k-wise independence
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Declaring independence via the sketching of sketches
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Testing symmetric properties of distributions
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Estimating PageRank on graph streams
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Property Testing: A Learning Theory Perspective
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Algorithmic and Analysis Techniques in Property Testing
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Measuring independence of datasets
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Efficient distributed random walks with applications
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Testing monotone continuous distributions on high-dimensional real cubes
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Testing non-uniform k-wise independent distributions over product spaces
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Estimating PageRank on graph streams
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Invariance in property testing
Property testing
Sublinear algorithms in the external memory model
Property testing
Property testing
Invariance in property testing
Property testing
Sublinear algorithms in the external memory model
Property testing
Property testing
On the complexity of computational problems regarding distributions
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Nearly tight bounds for testing function isomorphism
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Approximating and testing k-histogram distributions in sub-linear time
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Taming big probability distributions
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Testing Symmetric Properties of Distributions
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On the power of conditional samples in distribution testing
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Testing Closeness of Discrete Distributions
Journal of the ACM (JACM)
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Given access to independent samples of a distribution A over [n] 脳 [m], we show how to test whether the distributions formed by projecting A to each coordinate are independent, i.e., whether A is \varepsilon-close in the L1 norm to the product distribution A1 脳 A2 for some distributions A1 over [n] and A2 over [m]. The sample complexity of our test is \widetilde0(n^{{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3}} m^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} poly(\varepsilon ^{ - 1} )), assuming without loss of generality that m \leqslant n. We also give a matching lower bound, up to poly(\log n,\varepsilon ^{ - 1} ) factors.Furthermore, given access to samples of a distribution X over [n], we show how to test if X is \varepsilon-close in L1 norm to an explicitly specified distribution Y . Our test uses \widetilde0(n^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} poly(\varepsilon ^{ - 1} )) samples, which nearly matches the known tight bounds for the case when Y is uniform.