Learning DNF by Statistical and Proper Distance Queries Under the Uniform Distribution

Lindner, Wolfgang

doi:10.1007/11564089_17

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Learning Dnf Formulas With Statistical Queries1

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2007

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“…Hence we can apply Lemma 35 with C = m-DNF n and γ = τ 0 to get an algorithm which uses γ −4 ln 2 ε −1 N 0 = n O(log(m/ε)) many queries under the protocol STAT τ,U to produce for any target f ∈ C a hypothesis h with error δ(f, h) ε. 2 We note that by applying more powerful boosting strategies, it can be shown [23] that m-term DNFs are ε-learnable from n O(log(m/ε)) statistical queries with tolerance (ε/m) instead of (ε 2 /m) as in Theorem 36.…”

Section: Learning Dnf Formulas With Statistical Queriesmentioning

confidence: 97%

A general dimension for query learning

Balcázar¹,

Castro²,

Guijarro³

et al. 2007

Journal of Computer and System Sciences

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We introduce a combinatorial dimension that characterizes the number of queries needed to exactly (or approximately) learn concept classes in various models. Our general dimension provides tight upper and lower bounds on the query complexity for all sorts of queries, not only for example-based queries as in previous works.As an application we show that for learning DNF formulas, unspecified attribute value membership and equivalence queries are not more powerful than standard membership and equivalence queries. Further, in the approximate learning setting, we use the general dimension to characterize the query complexity in the statistical query as well as the learning by distances model. Moreover, we derive close bounds on the number of statistical queries needed to approximately learn DNF formulas.

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Section: Learning Dnf Formulas With Statistical Queriesmentioning

confidence: 97%