TY - GEN

T1 - Testing probability distributions underlying aggregated data

AU - Canonne, Clément

AU - Rubinfeld, Ronitt

PY - 2014

Y1 - 2014

N2 - In this paper, we analyze and study a hybrid model for testing and learning probability distributions. Here, in addition to samples, the testing algorithm is provided with one of two different types of oracles to the unknown distribution D over [n]. More precisely, we consider both the dual and cumulative dual access models, in which the algorithm A can both sample from D and respectively, for any i ∈ [n], - query the probability mass D(i) (query access); or - get the total mass of {1,...,i}, i.e. Σj=1 i D(j) (cumulative access) In these two models, we bypass the strong lower bounds established in both of the previously studied sampling and query oracle settings for a number of problems, giving constant-query algorithms for most of them. Finally, we show that while the testing algorithms can be in most cases strictly more efficient, some tasks remain hard even with this additional power.

AB - In this paper, we analyze and study a hybrid model for testing and learning probability distributions. Here, in addition to samples, the testing algorithm is provided with one of two different types of oracles to the unknown distribution D over [n]. More precisely, we consider both the dual and cumulative dual access models, in which the algorithm A can both sample from D and respectively, for any i ∈ [n], - query the probability mass D(i) (query access); or - get the total mass of {1,...,i}, i.e. Σj=1 i D(j) (cumulative access) In these two models, we bypass the strong lower bounds established in both of the previously studied sampling and query oracle settings for a number of problems, giving constant-query algorithms for most of them. Finally, we show that while the testing algorithms can be in most cases strictly more efficient, some tasks remain hard even with this additional power.

UR - http://www.scopus.com/inward/record.url?scp=84904164512&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-43948-7_24

DO - 10.1007/978-3-662-43948-7_24

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AN - SCOPUS:84904164512

SN - 9783662439470

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 283

EP - 295

BT - Automata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Proceedings

PB - Springer Verlag

T2 - 41st International Colloquium on Automata, Languages, and Programming, ICALP 2014

Y2 - 8 July 2014 through 11 July 2014

ER -