The power of self-directed learning

Goldman, Sally A.; Sloan, Robert H.

doi:10.1007/bf00993977

Cited by 15 publications

(29 citation statements)

References 20 publications

(24 reference statements)

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“…According to Corollary 8, recursive teaching is an even more powerful model so that upper bounds on SDC apply to RTD as well, and lower bounds on RTD apply to SDC and LC-PARTIAL as well. The following result, which is partially known from [8,22], illustrates this: Proof. All upper bounds on SDC are from [8] and, as mentioned above, they apply to RTD as well.…”

Section: Recursive Teaching and Query Learningmentioning

confidence: 95%

“…Self-directed learners are very powerful; they yield a query complexity lower-bounding the one obtained from partial equivalence queries [8]. Even though the self-directed learning complexity can exceed the VC-dimension, existing results show some connection between these two complexity measures.…”

Section: Introductionmentioning

confidence: 97%

“…As demonstrated in [8], the model of self-directed learning is extremely powerful. According to Corollary 8, recursive teaching is an even more powerful model so that upper bounds on SDC apply to RTD as well, and lower bounds on RTD apply to SDC and LC-PARTIAL as well.…”

Section: Recursive Teaching and Query Learningmentioning

confidence: 99%

“…A query in the model of self-directed learning [7,8] consists of an instance x ∈ X and a label b ∈ {0, 1}, passed to an oracle. The latter returns the true label C * (x) assigned to x by the target concept C * .…”

Section: Learning Complexitymentioning

confidence: 99%

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Recursive Teaching Dimension, Learning Complexity, and Maximum Classes

Doliwa

Simon

Zilles

2010

Lecture Notes in Computer Science

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Abstract. This paper is concerned with the combinatorial structure of concept classes that can be learned from a small number of examples. We show that the recently introduced notion of recursive teaching dimension (RTD, reflecting the complexity of teaching a concept class) is a relevant parameter in this context. Comparing the RTD to self-directed learning, we establish new lower bounds on the query complexity for a variety of query learning models and thus connect teaching to query learning. For many general cases, the RTD is upper-bounded by the VC-dimension, e.g., classes of VC-dimension 1, (nested differences of) intersection-closed classes, "standard" boolean function classes, and finite maximum classes. The RTD thus is the first model to connect teaching to the VC-dimension. The combinatorial structure defined by the RTD has a remarkable resemblance to the structure exploited by sample compression schemes and hence connects teaching to sample compression. Sequences of teaching sets defining the RTD coincide with unlabeled compression schemes both (i) resulting from Rubinstein and Rubinstein's corner-peeling and (ii) resulting from Kuzmin and Warmuth's Tail Matching algorithm.

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Section: Recursive Teaching and Query Learningmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 97%

Section: Recursive Teaching and Query Learningmentioning

confidence: 99%

Section: Learning Complexitymentioning

confidence: 99%

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Recursive Teaching Dimension, Learning Complexity, and Maximum Classes

Doliwa

Simon

Zilles

2010

Lecture Notes in Computer Science

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“…Fundamental issues of adaptive versus nonadaptive learning in the mistake-bound model are studied in Ben-David, Kushilevitz, and Mansour (1997), cf. also Goldman and Sloan (1994).…”

Section: Related Workmentioning

confidence: 99%

Untitled

Damaschke

2000

Machine Learning

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Abstract.We study the complexity of learning arbitrary Boolean functions of n variables by membership queries, if at most r variables are relevant. Problems of this type have important applications in fault searching, e.g. logical circuit testing and generalized group testing. Previous literature concentrates on special classes of such Boolean functions and considers only adaptive strategies. First we give a straightforward adaptive algorithm using O(r 2 r log n) queries, but actually, most queries are asked nonadaptively. This leads to the problem of purely nonadaptive learning. We give a graph-theoretic characterization of nonadaptive learning families, called r -wise bipartite connected families. By the probabilistic method we show the existence of such families of size O(r 2 r log n + r 2 2 r ). This implies that nonadaptive attribute-efficient learning is not essentially more expensive than adaptive learning. We also sketch an explicit pseudopolynomial construction, though with a slightly worse bound. It uses the common derandomization technique of small-biased k-independent sample spaces. For the special case r = 2, we get roughly 2.275 log n adaptive queries, which is fairly close to the obvious lower bound of 2 log n. For the class of monotone functions, we prove that the optimal query number O(2 r + r log n) can be already achieved in O(r ) stages. On the other hand, (2 r log n) is a lower bound on nonadaptive queries.

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A Model of Interactive Teaching

Mathias

1997

Journal of Computer and System Sciences

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Previous teaching models in the learning theory community have been batch models. That is, in these models the teacher has generated a single set of helpful examples to present to the learner. In this paper we present an interactive model in which the learner has the ability to ask queries as in the query learning model of Angluin. We show that this model is at least as powerful as previous teaching models. We also show that anything learnable with queries, even by a randomized learner, is teachable in our model. In all previous teaching models, all classes shown to be teachable are known to be efficiently learnable. An important concept class that is not known to be learnable is DNF formulas. We demonstrate the power of our approach by providing a deterministic teacher and learner for the class of DNF formulas. The learner makes only equivalence queries and all hypotheses are also DNF formulas. ] 1997 Academic Press

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The power of self-directed learning

Cited by 15 publications

References 20 publications

Recursive Teaching Dimension, Learning Complexity, and Maximum Classes

Recursive Teaching Dimension, Learning Complexity, and Maximum Classes

Untitled

A Model of Interactive Teaching

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