Testing probability distributions underlying aggregated data

Clément Canonne, Ronitt Rubinfeld

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageEnglish
Title of host publicationAutomata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Proceedings
PublisherSpringer Verlag
Number of pages13
EditionPART 1
ISBN (Print)9783662439470
StatePublished - 2014
Event41st International Colloquium on Automata, Languages, and Programming, ICALP 2014 - Copenhagen, Denmark
Duration: 8 Jul 201411 Jul 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume8572 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference41st International Colloquium on Automata, Languages, and Programming, ICALP 2014


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