Probabilistic language learning under monotonicity constraints

Meyer, Léa

doi:10.1016/s0304-3975(97)00017-0

Cited by 8 publications

(4 citation statements)

References 17 publications

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“…Probabilistic language learning [18] in the limit is the most interesting among those. Other recently studied models are probabilistic language learning with monotonicity restrictions [27] and probabilistic learning up to a small set of errors [22].…”

Section: Conclusion and Related Workmentioning

confidence: 99%

Probabilistic inductive inference: a survey

Ambainis

2001

Theoretical Computer Science

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Section: Conclusion and Related Workmentioning

confidence: 99%

Probabilistic inductive inference: a survey

Ambainis

2001

Theoretical Computer Science

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“…Furthermore, most concepts have a break-even point at some probability c < 1 in the sense that whenever such concepts are learnable with probability c, they are already learnable by a deterministic machine [1]. Meyer [12] showed that exact monotonic and exact conservative learning with any probability c < 1 is more powerful than deterministic learning; still in the case c = 1, the probabilistic and deterministic variants are again the same. In [8], the notions of effective measure and category are used to discuss the relative sizes of inferable sets and their complements.…”

Section: Introductionmentioning

confidence: 99%

Absolute versus probabilistic classification in a logical setting

Jain

Martin

Stephan

2008

Theoretical Computer Science

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Suppose we are given a set W of logical structures, or possible worlds, a set of logical formulas called possible data and a logical formula ϕ. We then consider the classification problem of determining in the limit and almost always correctly whether a possible world M satisfies ϕ, from a complete enumeration of the possible data that are true in M. One interpretation of almost always correctly is that the classification might be wrong on a set of possible worlds of measure 0, with respect to some natural probability distribution over the set of possible worlds. Another interpretation is that the classifier is only required to classify a set W of possible worlds of measure 1, without having to produce any claim in the limit on the truth of ϕ for the members of the complement of W in W. We compare these notions with absolute classification of W with respect to a formula that is almost always equivalent to ϕ in W, hence we investigate whether the set of possible worlds on which the classification is correct is definable. We mainly work with the probability distribution that corresponds to the standard measure on the Cantor space, but we also consider an alternative probability distribution proposed by Solomonoff and contrast it with the former. Finally, in the spirit of the kind of computations considered in Logic programming, we address the issue of computing almost correctly in the limit witnesses to leading existentially quantified variables in existential formulas.

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“…[ 141). In these cases, the learning power of probabilistic machines increases even if the probability has to be close to 1.…”

Section: Introductionmentioning

confidence: 99%

“…Previous work in this field (cf. [ 141) established that the probabilistic hierarchy in the case of proper probabilistic learning is dense, i.e., there is a dense set of rational numbers D C [0, l] such that for each p E D there is an indexed family C, which is conservatively learnable with probability p but not with probability q > p. In the case of class preserving conservative learning, we proved that for each p 2 l/2, there is an indexed family which is conservatively identifiable with a probability 1 > plL > p but not with probability (1 > pn . Thus, conservative probabilistic learning is much stronger than conservative deterministic learning provided the machines are restricted to proper or class preserving hypothesis spaces.…”

Section: Introductionmentioning

confidence: 99%