The Informational Complexity of Learning: Perspectives on by Partha Niyogi

By Partha Niyogi

Among different issues, The Informational Complexity of Learning:Perspectives on Neural Networks and Generative Grammar brings jointly vital yet very various studying difficulties in the related analytical framework. the 1st issues the matter of studying practical mappings utilizing neural networks, by way of studying traditional language grammars within the rules and parameters culture of Chomsky.
those studying difficulties are doubtless very various. Neural networks are real-valued, infinite-dimensional, non-stop mappings. nevertheless, grammars are boolean-valued, finite-dimensional, discrete (symbolic) mappings. moreover the examine groups that paintings within the components nearly by no means overlap.
The book's target is to bridge this hole. It makes use of the formal concepts constructed in statistical studying conception and theoretical machine technological know-how during the last decade to investigate either forms of studying difficulties. via asking an analogous query - how a lot details does it take to benefit? - of either difficulties, it highlights their similarities and alterations. particular effects comprise version choice in neural networks, energetic studying, language studying and evolutionary types of language switch.
The Informational Complexity of studying: views on NeuralNetworks and Generative Grammar is a truly interdisciplinary paintings. somebody drawn to the interplay of laptop technology and cognitive technological know-how should still benefit from the ebook. Researchers in synthetic intelligence, neural networks, linguistics, theoretical laptop technological know-how, and statistics will locate it relatively relevant.

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Extra resources for The Informational Complexity of Learning: Perspectives on Neural Networks and Generative Grammar

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There is a vast body of literature on approximation theory and the theory of empirical risk minimization. In recent times, some of the results in these areas have been applied by the computer science and neural network community to study formal learning models. Here we would like to make certain observations about our result, suggest extensions and future work, and to make connections with other work done in related areas. 1 Observations on the Main Result • The theorem has a PAC (Valiant, 1984) like setting.

This additional error (caused by finiteness of data) is formalized later as the estimation error. The amount of data needed to ensure a small estimation error is referred to as the sample complexity of the problem. The hypothesis complexity, the sample complexity and the generalization error are related. If the class H is very large or in other words has high complexity, then for the same estimation error, the sample complexity increases. If the hypothesis complexity is small, the sample complexity is also small but now for the same estimation error, the approximation error is high.

Ules. Phrase structure grammars build sentences out of phrases; and phrases out of other phrases or syntactic categories. Over the last decade, a parametric theory of grammars (Chomsky, 1981) has begun to evolve. According to this, a grammar G(Pl. ,Pn) is parameterized by a finite (in this case, n) number of typically boolean-valued parameters PI through Pn. If these parameters are set to one set of values, one would obtain the grammar of a specific language, say, German. Setting them to another set of values would define the grammar of another language, say English.

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