Computational learning theory
Template:See also Template:Short descriptionTemplate:More citations needed Template:Machine learning
In computer science, computational learning theory (or just learning theory) is a subfield of artificial intelligence devoted to studying the design and analysis of machine learning algorithms.<ref name="ACL">Template:Cite web</ref>
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.Template:Citation needed In computational learning theory, a computation is considered feasible if it can be done in polynomial time.Template:Citation needed There are two kinds of time complexity results:
- Positive resultsTemplate:Spaced ndashShowing that a certain class of functions is learnable in polynomial time.
- Negative resultsTemplate:Spaced ndashShowing that certain classes cannot be learned in polynomial time.<ref>Template:Cite book</ref>
Negative results often rely on commonly believed, but yet unproven assumptions,Template:Citation needed such as:
- Computational complexity – P ≠ NP (the P versus NP problem);
- Cryptographic – One-way functions exist.
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 (see frequency probability, Bayesian probability) and different assumptions on the generation of samples.Template:Citation needed The different approaches include:
- Exact learning, proposed by Dana Angluin;<ref>Template:Cite thesis</ref><ref>Template:Cite journal</ref>
- Probably approximately correct learning (PAC learning), proposed by Leslie Valiant;<ref>Template:Cite journal</ref>
- VC theory, proposed by Vladimir Vapnik and Alexey Chervonenkis;<ref>Template:Cite journal</ref>
- Inductive inference as developed by Ray Solomonoff;<ref>Template:Cite journal</ref><ref>Template:Cite journal</ref>
- Algorithmic learning theory, from the work of E. Mark Gold;<ref>Template:Cite journal</ref>
- Online machine learning, from the work of Nick LittlestoneTemplate:Citation needed.
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.
See also
- Error tolerance (PAC learning)
- Grammar induction
- Information theory
- Occam learning
- Stability (learning theory)
References
Further reading
A description of some of these publications is given at important publications in machine learning.
Surveys
- Angluin, D. 1992. Computational learning theory: Survey and selected bibliography. In Proceedings of the Twenty-Fourth Annual ACM Symposium on Theory of Computing (May 1992), 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. On universal learning algorithms. 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.htmlTemplate:Dl
Error tolerance
- Michael Kearns and Ming Li. Learning in the presence of malicious errors. SIAM Journal on Computing, 22(4):807–837, August 1993. http://citeseer.ist.psu.edu/kearns93learning.html
- Kearns, M. (1993). 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, (1988) 42-55.
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