Computational learning theory


In computer science, computational learning theory is a subfield of artificial intelligence devoted to studying the design and analysis of machine learning algorithms.

Overview

Theoretical results in machine learning often focus on a type of inductive learning known as supervised learning. In supervised learning, an algorithm is provided with labeled samples. For instance, the samples might be descriptions of mushrooms, with labels indicating whether they are edible or not. The algorithm uses these labeled samples to create a classifier. This classifier assigns labels to new samples, including those it has not previously encountered. The goal of the supervised learning algorithm is to optimize performance metrics, such as minimizing errors on new samples.
In addition to performance bounds, computational learning theory studies the time complexity and feasibility of learning. In
computational learning theory, a computation is considered feasible if it can be done in polynomial time. There are two kinds of time
complexity results:
  • Positive resultsShowing that a certain class of functions is learnable in polynomial time.
  • Negative resultsShowing that certain classes cannot be learned in polynomial time.
Negative results often rely on commonly believed, but yet unproven assumptions, such as:
There are several different approaches to computational learning theory based on making different assumptions about the inference principles used to generalise from limited data. This includes different definitions of probability and different assumptions on the generation of samples. The different approaches include:
While its primary goal is to understand learning abstractly, computational learning theory has led to the development of practical algorithms. For example, PAC theory inspired boosting, VC theory led to support vector machines, and Bayesian inference led to belief networks.

Surveys

  • Angluin, D. 1992. Computational learning theory: Survey and selected bibliography. In Proceedings of the Twenty-Fourth Annual ACM Symposium on Theory of Computing, pages 351–369. http://portal.acm.org/citation.cfm?id=129712.129746
  • D. Haussler. Probably approximately correct learning. In AAAI-90 Proceedings of the Eight National Conference on Artificial Intelligence, Boston, MA, pages 1101–1108. American Association for Artificial Intelligence, 1990. http://citeseer.ist.psu.edu/haussler90probably.html

    Feature selection

  • A. Dhagat and L. Hellerstein, "PAC learning with irrelevant attributes", in 'Proceedings of the IEEE Symp. on Foundation of Computer Science', 1994. http://citeseer.ist.psu.edu/dhagat94pac.html

    Optimal O notation learning

  • Oded Goldreich, Dana Ron. . http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.47.2224

    Negative results

  • M. Kearns and Leslie Valiant. 1989. Cryptographic limitations on learning Boolean formulae and finite automata. In Proceedings of the 21st Annual ACM Symposium on Theory of Computing, pages 433–444, New York. ACM. http://citeseer.ist.psu.edu/kearns89cryptographic.html

    Error tolerance

  • Michael Kearns and Ming Li. Learning in the presence of malicious errors. SIAM Journal on Computing, 22:807–837, August 1993. http://citeseer.ist.psu.edu/kearns93learning.html
  • Kearns, M.. Efficient noise-tolerant learning from statistical queries. In Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing, pages 392–401. http://citeseer.ist.psu.edu/kearns93efficient.html

    Equivalence

  • D.Haussler, M.Kearns, N.Littlestone and M. Warmuth, Equivalence of models for polynomial learnability, Proc. 1st ACM Workshop on Computational Learning Theory, 42-55.
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