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Statements

Subject Item: dbr:Uniform_convergence_(combinatorics)
dbo:wikiPageWikiLink: dbr:Uniform_convergence_in_probability
dbo:wikiPageRedirects: dbr:Uniform_convergence_in_probability

Subject Item: dbr:Extremum_estimator
dbo:wikiPageWikiLink: dbr:Uniform_convergence_in_probability

Subject Item: dbr:Uniform_convergence
dbo:wikiPageWikiLink: dbr:Uniform_convergence_in_probability

Subject Item: dbr:Growth_function
dbo:wikiPageWikiLink: dbr:Uniform_convergence_in_probability

Subject Item: dbr:Uniform_convergence_in_probability
rdfs:label: Uniform convergence in probability
rdfs:comment: Uniform convergence in probability is a form of convergence in probability in statistical asymptotic theory and probability theory. It means that, under certain conditions, the empirical frequencies of all events in a certain event-family converge to their theoretical probabilities. Uniform convergence in probability has applications to statistics as well as machine learning as part of statistical learning theory.
dct:subject: dbc:Combinatorics dbc:Articles_containing_proofs dbc:Probability_theorems dbc:Machine_learning
dbo:wikiPageID: 22999791
dbo:wikiPageRevisionID: 1011632869
dbo:wikiPageWikiLink: dbc:Combinatorics dbr:Law_of_large_numbers dbr:Statistical_learning_theory dbr:Sauer–Shelah_lemma dbc:Articles_containing_proofs dbr:Concept_class dbr:Vapnik–Chervonenkis_dimension dbr:Expected_value dbr:Machine_learning dbc:Probability_theorems dbr:Chebyshev's_inequality dbr:VC_dimension dbr:Asymptotic_theory_(statistics) dbr:Probability_theory dbr:Predicate_(mathematical_logic) dbr:Shattering_number dbr:Statistics dbr:With_high_probability dbc:Machine_learning dbr:Growth_function dbr:VC_Dimension dbr:Hoeffding's_inequality dbr:Convergence_in_probability
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dbo:abstract: Uniform convergence in probability is a form of convergence in probability in statistical asymptotic theory and probability theory. It means that, under certain conditions, the empirical frequencies of all events in a certain event-family converge to their theoretical probabilities. Uniform convergence in probability has applications to statistics as well as machine learning as part of statistical learning theory. The law of large numbers says that, for each single event , its empirical frequency in a sequence of independent trials converges (with high probability) to its theoretical probability. In many application however, the need arises to judge simultaneously the probabilities of events of an entire class from one and the same sample. Moreover it, is required that the relative frequency of the events converge to the probability uniformly over the entire class of events The Uniform Convergence Theorem gives a sufficient condition for this convergence to hold. Roughly, if the event-family is sufficiently simple (its VC dimension is sufficiently small) then uniform convergence holds.
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Subject Item: dbr:Outline_of_machine_learning
dbo:wikiPageWikiLink: dbr:Uniform_convergence_in_probability

Subject Item: dbr:Uniform_convergence_to_probability
dbo:wikiPageWikiLink: dbr:Uniform_convergence_in_probability
dbo:wikiPageRedirects: dbr:Uniform_convergence_in_probability

Subject Item: dbr:Uniform_Convergence_(Machine_learning)
dbo:wikiPageWikiLink: dbr:Uniform_convergence_in_probability
dbo:wikiPageRedirects: dbr:Uniform_convergence_in_probability

Subject Item: dbr:Uniform_Convergence_Theorem_(Combinatorics)
dbo:wikiPageWikiLink: dbr:Uniform_convergence_in_probability
dbo:wikiPageRedirects: dbr:Uniform_convergence_in_probability

Subject Item: dbr:Uniform_convergence_(machine_learning)
dbo:wikiPageWikiLink: dbr:Uniform_convergence_in_probability
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Subject Item: wikipedia-en:Uniform_convergence_in_probability
foaf:primaryTopic: dbr:Uniform_convergence_in_probability