S. A. Goldman and H. D. Mathias. 1996. Teaching a smarter learner. Journal of Computer and System Sciences, 52(2):255--267.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....oracles, one can turn every text learner into a conservative learner, thus one knows that every class from is learnable from good examples with a suciently powerful learner. So good examples are a variant of nite learning having the advantage of covering all classes in . Goldman and Mathias [11] de ned the same notion and addressed the role of a teacher (that is, the algorithm to compute F from e in the de nition below) in learning concrete classes like Horn formulas and decision lists. De nition 5.5 [11, 17] A class L is learnable from good examples if and only if there are a ....

....learning having the advantage of covering all classes in . Goldman and Mathias [11] de ned the same notion and addressed the role of a teacher (that is, the algorithm to compute F from e in the de nition below) in learning concrete classes like Horn formulas and decision lists. De nition 5. 5 [11, 17] A class L is learnable from good examples if and only if there are a partial learner M and a partial function such that, for every e with W e 2 L, e) is the canonical index of a nite subset D (e) of W e such that, for all nite sets D d with D (e) D d W e , M(d) is de ned and an index for ....

Sally Goldman and David Mathias. Teaching a smarter learner. Journal of Computer and System Sciences, 52:255-267, 1996.

....We note S = fuj(u; 1) 2 Sg and S = fuj(u; 0) 2 Sg. The size of a sample S (noted jjSjj) is the sum of the length of all the words in it.Gold showed that the class of regular languages is polynomially learnable from given data [Gol78] Goldman and Mathias introduced a learning model with teacher [GM96] that De la Higuera extended to languages and showed equivalent to the learning model from given data [Hig97] To show that the REG class, represented by DFA, is polynomially learnable from given data is equivalent to show that there exists two algorithms T and L such that for any regular language ....

S. A. Goldman and H. D. Mathias. Teaching a smarter learner. Journal of Computer and System Sciences, 52(2):255-267, 1996.

....most k literals and k is a constant, are probably approximately correct (PAC) learnable in Valiant s model [39] This has largely extended the classes of Boolean functions which are known to be learnable. In the sequel, decision lists have been studied extensively in the learning field, see e.g. [19, 8, 17, 9]. However, while it is known that decision lists generalize some classes of Boolean functions [34] their relationships to other classes such as Horn functions, read once functions, threshold functions, or 2monotonic functions, which are widely used in the literature, were only partially known ....

....problem amounts to the unique extension problem knowing that some extension exists; in general, this additional knowledge could be utilized for faster learning. Alternative teaching models have been considered, in which the sample given by the teacher does not precisely describe a single function [17]. However, identification of the target function is still possible, 3 since the teacher knows how the learner proceeds, and vice versa, the learner knows how the teacher generates his sample, called a teaching set in [17] To prevent collusion between the two sides (the target could be simply ....

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S. A. Goldman and H. D. Mathias. Teaching a Smarter Learner. Journal of Computer and System Sciences, 52:255--267, 1996.

....also be explicitly obtained using a trick used in [JS97, CJLZ97] We do not know at present whether we can do this for class preserving finite identification from good examples. 1 we provide a solution to this question. A model similar to the one studied here is also studied in the PAC setting by [GM96]. In the case of learning indexed families of recursive languages, the hypothesis space chosen is also an indexed family of recursive languages. The effective generation of the good examples is with respect to the hypothesis space. Two situations are usually considered: class preserving (when the ....

S. A. Goldman and H. D. Mathias. Teaching a smarter learner. Journal of Computer and System Sciences, 52:255--267, 1996.

....number of negative examples. The negative examples are not required to be computable and, additionally, the learning strategy is provided with all positive examples. On the other hand, our Theorem 17 was inspired by Theorem 31 in Baliga, Case and Jain [2] The approach in Goldman and Mathias [9] is essentially the same as in [5] 6] and in the present paper. For some formal definition of unfair coding tricks , there called collusion, it is formally proved in [9] that this approach avoids collusion. Finally, note that in Lange and Wiehagen [11] we proved the learnability of a special ....

....the other hand, our Theorem 17 was inspired by Theorem 31 in Baliga, Case and Jain [2] The approach in Goldman and Mathias [9] is essentially the same as in [5] 6] and in the present paper. For some formal definition of unfair coding tricks , there called collusion, it is formally proved in [9] that this approach avoids collusion. Finally, note that in Lange and Wiehagen [11] we proved the learnability of a special indexable family, namely the family of all pattern languages, from polynomially many good text examples in polynomial time. A similar result for learning finite automata from ....

S.A. Goldman and H.D. Mathias, Teaching a smarter learner, in: Proc. 6th Annual ACM Conference on Computational Learning Theory (ACM Press, New York, 1993) pp. 67--76.

....by their parents. And completely incorrect utterances are rarely observed. We think that membership queries should be restricted in some way in order to be used in a positive learning framework. We may impose a teaching set to be present in every current sample (Gold, 1978) Angluin, 1987) (Goldman and Mathias, 1996). We mainly study here the learning model of Goldman and Mathias. If the teaching set may contain negative examples, the class REG is eciently exactly learnable in this model (Goldman and Mathias, 1996) Oncina and Garcia, 1992) But if the teaching set must be composed of positive examples only, ....

....may impose a teaching set to be present in every current sample (Gold, 1978) Angluin, 1987) Goldman and Mathias, 1996) We mainly study here the learning model of Goldman and Mathias. If the teaching set may contain negative examples, the class REG is eciently exactly learnable in this model (Goldman and Mathias, 1996), Oncina and Garcia, 1992) But if the teaching set must be composed of positive examples only, it is easy to show that REG is not learnable. In PAC framework, the class of allowed distributions can be restricted (Li and Vit anyi, 1991) Denis et al. 1996) Denis and Gilleron, 1997a) ....

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Goldman, S. A. and Mathias, H. D. (1996). Teaching a smarter learner. Journal of Computer and System Sciences, 52(2):255-267.

.... Applied Sciences Harvard University Cambridge, MA 02138 rocco deas.harvard.edu Keywords: computational learning theory, machine learning, teaching dimension 1 Introduction In recent years a number of researchers in learning theory have developed and analyzed computational models of teaching [8, 9, 10, 13, 16, 17, 18]. One motivation for this work is the hope that stronger and more realistic positive results might be achievable in a setting where labeled examples are provided by a helpful teacher rather than an omniscient adversary or a worst case probability distribution as is usually assumed in learning ....

....is the hope that stronger and more realistic positive results might be achievable in a setting where labeled examples are provided by a helpful teacher rather than an omniscient adversary or a worst case probability distribution as is usually assumed in learning theory. However, as discussed in [8, 9, 13, 16], any reasonable teaching model must disallow teacher learner collusion which trivializes the learning process for instance, it should not be possible for the teacher to simply encode a representation of the target concept in the instances it chooses for the learner according to a prearranged ....

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S.A. Goldman and H.D. Mathias. Teaching a smarter learner, J. Comput. Syst. Sci., 52, 1996, 255-267.

.... under the simple PAC model (Castro Guijarro, 1998) An analysis of the relationship between the PACS and simple PAC learning models and other popular models for learning in helpful environments such as learning from example based queries (Angluin, 1988) learning from polynomial teaching sets (Goldman Mathias, 1993; Gold, 1978) and mistake bounded learning (Littlestone, 1988) appears in (Parekh Honavar, 1999) A related question of interest has to do with the nature of environments that can be modeled by simple distributions. In particular, if Kolmogorov complexity is an appropriate measure of the ....

Goldman, S., & Mathias, H. (1993). Teaching a Smarter Learner. Pages 67--76 of: Proceedings of the Workshop on Computational Learning Theory (COLT'93). A. C. M. Press.

....how quickly learning problems may be completed. Models in which the environment is a helpful teacher are well suited to this task. However, traditional models of learning do not permit this. In recent years, several models of teaching have been introduced to the learning theory community [6, 7, 5, 13]. Within each model, theoretical results have been presented demonstrating their utility. However, there has been no research presented to demonstrate the real utility of such models. In other words, how do we know if these models are of use beyond the theoretical realm In this paper we present ....

S. Goldman and D. Mathias. Teaching a smarter learner. Journal of Computer and System Sciences, 52(2):255--267, April 1996.

....under helpful distributions. It is also proved that DFA are learnable under helpful distributions when the learner knows a bound on the number of states of the target DFA. We compare our model when restricted to exact learning with other models of teaching (for instance, the teaching model of (Goldman and Mathias, 1996) and the model of identification from given data of (Gold, 1978) Also, a PAC learning model with simple teacher (simplicity is based on program size complexity) is defined and the model is compared with previously defined simple PAC learning models ( Li and Vit anyi, 1991) and (Denis et al. ....

.... algorithm knows something about the underlying distribution ( Benedek and Itai, 1988) Denis et al. 1996) Kearns et al. 1987) Natarajan, 1987) Li and Vit anyi, 1991) a teaching set may be designed in order to help the learner ( Goldman and Kearns, 1995) Shinohara and Miyano, 1991) (Goldman and Mathias, 1996)) For instance, Goldman and Mathias assume that the teacher builds a teaching set related to the target concept and that an adversary adds new examples to this set in order to prevent collusion between the learner and the teacher. Then, the learner must identify exactly the target from this set ....

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Goldman, S. A. and Mathias, H. D. (1996). Teaching a smarter learner. Journal of Computer and System Sciences, 52(2):255--267.

....for establishing lower bounds on the number of examples required by a learning algorithm. Finally, as illustrated above, there are environments in which the learner and teacher speak different languages and thus, encoding or programming are impossible and learning must be used. Goldman and Mathias [11] (GM) extended T L pairs so that prevention of collusion does not reduce the model to teaching any consistent learner. In that model, the teacher prepares a teaching set a collection of labeled examples that allow the learner to infer the target concept. To prevent collusion, an adversary is ....

....a small amount of information. These trusted bits allow the teacher to communicate a stopping condition or a size parameter of the target. When trusted bits are allowed, they show that any class that is learnable is teachable in their model. Our model is derived from that of Goldman and Mathias [11]. They developed a model that pairs teachers and learners but prevents collusion without forcing the teacher to teach any consistent learner. In their model the teacher constructs a teaching set designed to teach optimally, to a particular learner, the target concept. To prevent collusion, an ....

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S. Goldman and D. Mathias. Teaching a smarter learner. In Proceedings of the Sixth Annual ACM Conference on Computational Learning Theory, pages 67--76. ACM Press, New York, NY, 1993. To appear, Journal of Computer and System Sciences.

....membership queries. See [Blum, Chalasani, Goldman, and Slonim, 1995] for a summary of several models introduced to address this situation. As one last example, there has been much work recently in exploring models of a helpful teacher, since teaching is often used to assist human learning (e.g. [Goldman and Mathias, 1996, Angluin and Krikis, 1997] Finally, there has been work to bridge the computational learning research with the research from other fields such as neural networks, natural language processing, DNA analysis, inductive logic programming, information retrieval, expert systems, and many others. 8 ....

Goldman, S. and Mathias, D. 1996. Teaching a smarter learner. J. of Comput. Syst. Sci. 52, 2 (April), 255--267.

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S. A. Goldman and H. D. Mathias. 1996. Teaching a smarter learner. Journal of Computer and System Sciences, 52(2):255--267.

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Goldman, S. A., and Mathias, H. D. 1996. Teaching a smarter learner. Journal of Computer and System Sciences 52(2):255--267.

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S. Goldman and H. Mathias. Teaching a smarter learner. Journal of Computer and System Sciences, 52:255--267, 1996.

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S. Goldman and H. Mathias. Teaching a smarter learner. In Proceedings of the Workshop on Computational Learning Theory (COLT'93), pages 67--76. ACM Press, 1993.

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S. Goldman and H. Mathias. Teaching a smarter learner. In Proceedings of the Workshop on Computational Learning Theory (COLT'93), pages 67--76. A. C. M. Press, 1993. 36

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S. A. Goldman and H. D. Mathias. Teaching a smarter learner. Journal of Computer and System Sciences, 52(2), 1996: 255-267.

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Control, 37:302--320. Goldman, S. and Mathias, D. (1993). Teaching a smarter learner. In Proceedings of the Sixth Annual ACM Conference on Computational Learning Theory, pages 67--76.

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