On Teaching and Learning Intersection-Closed Concept Classes

Kuhlmann, Christian

doi:10.1007/3-540-49097-3_14

Cited by 15 publications

(23 citation statements)

References 6 publications

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“…However, [11] presents a family (C m ) m≥1 of concept classes such that VCD(C m ) = 2m but RTD(C m ) ≥ TD min (C m ) = 3m. This shows that RTD cannot generally be upper-bounded by the VC-dimension (but leaves open the possibility of an upper bound of the form O(VCD(C))).…”

Section: Recursive Teaching and Query Learningmentioning

confidence: 99%

“…As shown by Kuhlmann [11], TS min (C) ≤ I(C) holds for every intersection-closed concept class C. Kuhlmann's central argument (which occurred first in a proof of a related result in [8]) can be applied recursively so that the following is obtained:…”

Section: Recursive Teaching and Intersection-closed Classesmentioning

confidence: 99%

“…For every fixed constant d (e.g., d = 2), [11] presents a family (C m ) m≥1 of intersection-closed concept classes such that the following holds:…”

Section: Corollary 13 For Every Intersection-closed Class C Rtd(c) ≤mentioning

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: 99%

Section: Recursive Teaching and Intersection-closed Classesmentioning

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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“…Looking again at the class S n defined above, we directly see that TD(S n ) = n + n · 1 n + 1 < 2 for all n ≥ 2 and thus much smaller than the (worst case) teaching dimension TD(S n ) = n. Anthony, Brightwell and Shawe-Taylor [6] showed that the average teaching dimension for the class of linearly separable Boolean functions is O(n 2 ) and Kuhlmann [24] proved that all classes of VC-dimension 1 have an average teaching dimension of less than 2 and that balls of radius d in {0, 1} n have an average teaching dimension of at most 2d.…”

Section: The Average Teaching Dimensionmentioning

confidence: 90%

Recent Developments in Algorithmic Teaching

Balbach¹,

Zeugmann

2009

Language and Automata Theory and Applications

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Abstract. The present paper surveys recent developments in algorithmic teaching. First, the traditional teaching dimension model is recalled. Starting from the observation that the teaching dimension model sometimes leads to counterintuitive results, recently developed approaches are presented. Here, main emphasis is put on the following aspects derived from human teaching/learning behavior: the order in which examples are presented should matter; teaching should become harder when the memory size of the learners decreases; teaching should become easier if the learners provide feedback; and it should be possible to teach infinite concepts and/or finite and infinite concept classes. Recent developments in the algorithmic teaching achieving (some) of these aspects are presented and compared.

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“…So, instead of looking at the worst-case, one has also studied the average teaching dimension (cf., e.g., [3,4,15,16]). Nevertheless, the resulting model still does not allow to study interesting aspects of teaching such as teaching learners with limited memory or to investigate the difference to teach learners providing and not providing feedback, respectively (cf.…”

Section: Introductionmentioning

confidence: 99%

Teaching Memoryless Randomized Learners Without Feedback

Balbach

Zeugmann

2006

Lecture Notes in Computer Science

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Abstract. The present paper mainly studies the expected teaching time of memoryless randomized learners without feedback. First, a characterization of optimal randomized learners is provided and, based on it, optimal teaching teaching times for certain classes are established. Second, the problem of determining the optimal teaching time is shown to be NP-hard. Third, an algorithm for approximating the optimal teaching time is given. Finally, two heuristics for teaching are studied, i.e., cyclic teachers and greedy teachers.

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On Teaching and Learning Intersection-Closed Concept Classes

Cited by 15 publications

References 6 publications

Recursive Teaching Dimension, Learning Complexity, and Maximum Classes

Recursive Teaching Dimension, Learning Complexity, and Maximum Classes

Recent Developments in Algorithmic Teaching

Teaching Memoryless Randomized Learners Without Feedback

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