Measuring teachability using variants of the teaching dimension

Balbach, Frank J.

doi:10.1016/j.tcs.2008.02.025

Cited by 22 publications

(39 citation statements)

References 29 publications

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“…The largest number of examples required at any stage is the recursive teaching dimension (RTD) of C. The RTD significantly improves on bounds for previous teaching models. It lower-bounds not only the complexity of the "classical" teaching model [6,19] but also the complexity of iterated optimal teaching [2], which is often significantly below the classical teaching dimension.…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

Recursive Teaching Dimension, Learning Complexity, and Maximum Classes

Doliwa

Simon

Zilles

2010

Lecture Notes in Computer Science

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“…Another recent direction assumes a helpful and powerful teacher who provides a minimal set of examples necessary for learning a concept, so the learner can eliminate competing concepts based on the size of the teaching set [3,28]. Naturally, the strange behavior of the learner on the contradictory concept also vanishes in this model (and in fact, this concept has a teaching set of size O(1)), but only under the troublesome assumption that the learner "knows" the optimal size of teaching sets-troublesome because Servedio [25] showed that the optimal size of teaching sets (in the traditional sense) is NP-hard to compute, so it is doubtful that these more sophisticated notions of teaching dimension could be computed easily.…”

Section: Existing Models Of Teachingmentioning

confidence: 99%

Massive online teaching to bounded learners

Juba

Williams

2013

Proceedings of the 4th Conference on Innovations in Theoretical Computer Science

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We consider a model of teaching in which the learners are consistent and have bounded state, but are otherwise arbitrary. The teacher is non-interactive and "massively open": the teacher broadcasts a sequence of examples of an arbitrary target concept, intended for every possible on-line learning algorithm to learn from. We focus on the problem of designing interesting teachers: efficient sequences of examples that lead all capable and consistent learners to learn concepts, regardless of the underlying algorithm used by the learner. We use two measures of teaching efficiency: the number of mistakes made by the worst-case learner, and the maximum length of the example sequence needed for the worst-case learner. Our results are summarized as follows:• Given a uniform random sequence of examples of an nbit concept function, learners (capable of consistently learning the concept) with s(n) bits of state are guaranteed to make only O(n · s(n)) mistakes and exactly learn the concept, with high probability. This theorem has interesting corollaries; for instance, every concept c has a sequence of examples can teach c to all capable consistent on-line learners implementable with s(n)-size circuits, such that every learner makes onlyÕ(s(n) 2 ) mistakes. That is, all resourcebounded algorithms capable of consistently learning a concept can be simultaneously taught that concept with few mistakes, on a single example sequence.We also show how to efficiently generate such a sequence of examples on-line: using Nisan's pseudorandom generator, each example in the sequence can be generated with polynomial-time overhead per example, with an O(n · s(n))-bit initial seed.• To justify our use of randomness, we prove that any non-trivial derandomization of our sequences would imply new circuit lower bounds. For instance, if there is a deterministic 2 n O(1) time algorithm that generates a sequence of examples, such that all consistent and capable polynomialsize circuit learners learn the all-zeroes concept with less than 2 n mistakes, then EXP ⊂ P/poly.• We present examples illustrating that the key differences in our model -our focus on mistakes rather than the total number of examples, and our use of a state bound -must be considered together to obtain our results.• We show that for every consistent s(n)-state bounded learner A, and every n-bit concept that A is capable of learning, there is a custom "tutoring" sequence of only O(n · s(n)) examples that teaches A the concept. That is, in principle, there are no slow learners, only bad teachers: if a statebounded learner is capable of learning a concept at all, then it can always be taught that concept quickly via some short sequence of examples.

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“…One such model (see Balbach [7,8]) assumes the learner picks hypotheses that are not only consistent but of minimal complexity. This model is inspired by the Occam's razor principle.…”

Section: Further Directionsmentioning

confidence: 99%

“…Another variant devised by Balbach [8] assumes that the learners know the teaching dimensions of all concepts in the class and choose their hypotheses only from the consistent ones with a teaching dimension at least as large as the sample given by the teacher. In other words, they assume the teacher does not give more examples than necessary for the concept to be taught.…”

Section: Further Directionsmentioning

confidence: 99%

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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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Measuring teachability using variants of the teaching dimension

Cited by 22 publications

References 29 publications

Recursive Teaching Dimension, Learning Complexity, and Maximum Classes

Recursive Teaching Dimension, Learning Complexity, and Maximum Classes

Massive online teaching to bounded learners

Recent Developments in Algorithmic Teaching

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