Testing problems with sub-learning sample complexity

Kearns, Michael; Ron, Dana

doi:10.1145/279943.279996

Cited by 30 publications

(45 citation statements)

References 15 publications

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“…2 Testing under non-uniform distributions (e.g., [HK03,AC06]) and testing with random examples (e.g., [KR00]) have been considered (and are discussed in this survey), but most of the work in property testing deals with testing under the uniform distributions and with queries.…”

Section: Property Testing and Hypothesis Testingmentioning

confidence: 99%

“…The only positive results we are aware of in this model are those presented by Kearns and Ron [KR00], and are described next. The functions studied in [KR00] are decision trees over [0, 1] d , and a special case of neural networks. We first extend the notion of property testing by allowing the relaxation of the rejection criteria.…”

Section: Testing From Random Examplesmentioning

confidence: 99%

“…This is a special case of decision trees (which are defined precisely in Subsection 5.2.2) and the study of this simple class gives some of the flavor of the other results in [KR00]. For any size s, the class of interval functions with at most s intervals, denoted INT s , is defined as follows.…”

Section: Interval Functionsmentioning

confidence: 99%

“…It is also proven in [KR00] that the dependence on √ s is unavoidable. Specifically, it is shown that distinguishing with probability at least 2/3 between a function selected randomly from a certain subclass of INT s and a completely random function over [0,1] requires Ω( √ s) examples.…”

Section: Interval Functionsmentioning

confidence: 99%

“…In fact, the relation between weak learning and a certain form of weak testing is formalized in [KR00] as described next.…”

Section: Testing and Weak Learningmentioning

confidence: 99%

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Property Testing: A Learning Theory Perspective

Ron

2007

FNT in Machine Learning

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Property testing deals with tasks where the goal is to distinguish between the case that an object (e.g., function or graph) has a prespecified property (e.g., the function is linear or the graph is bipartite) and the case that it differs significantly from any such object. The task should be performed by observing only a very small part of the object, in particular by querying the object, and the algorithm is allowed a small failure probability.One view of property testing is as a relaxation of learning the object (obtaining an approximate representation of the object). Thus property testing algorithms can serve as a preliminary step to learning. That is, they can be applied in order to select, very efficiently, what hypothesis class to use for learning. This survey takes the learning-theory point of view and focuses on results for testing properties of functions that are of interest to the learning theory community. In particular we cover results for testing algebraic properties of functions such as linearity, testing properties defined by concise representations, such as having a small DNF representation, and more.

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Section: Property Testing and Hypothesis Testingmentioning

confidence: 99%

Section: Testing From Random Examplesmentioning

confidence: 99%

Section: Interval Functionsmentioning

confidence: 99%

Section: Interval Functionsmentioning

confidence: 99%

“…In fact, the relation between weak learning and a certain form of weak testing is formalized in [KR00] as described next.…”

Section: Testing and Weak Learningmentioning

confidence: 99%

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Property Testing: A Learning Theory Perspective

Ron

2007

FNT in Machine Learning

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Testing the diameter of graphs

Parnas

Ron

2002

Random Struct Algorithms

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ABSTRACT:We propose a general model for testing graph properties, which extends and simplifies the bounded degree model of Goldreich and Ron [Property Testing in Bounded Degree Graphs, Proc. 31st Annual ACM Symposium on the Theory of Computing, 1997, pp. 406-415.] In this model, we present a family of algorithms that test whether the diameter of a graph is bounded by a given parameter D, or is -far from any graph with diameter at most β D . The function β D ranges between D + 4 and 4D + 2, depending on the algorithm. All our algorithms run in time polynomial in 1/ .

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