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computer science Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, ...
, computational learning theory (or just learning theory) is a subfield of
artificial intelligence Artificial intelligence (AI) is the capability of computer, computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making. It is a field of re ...
devoted to studying the design and analysis of
machine learning Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of Computational statistics, statistical algorithms that can learn from data and generalise to unseen data, and thus perform Task ( ...
algorithms.


Overview

Theoretical results in machine learning mainly deal with a type of inductive learning called supervised learning. In supervised learning, an algorithm is given samples that are labeled in some useful way. For example, the samples might be descriptions of mushrooms, and the labels could be whether or not the mushrooms are edible. The algorithm takes these previously labeled samples and uses them to induce a classifier. This classifier is a function that assigns labels to samples, including samples that have not been seen previously by the algorithm. The goal of the supervised learning algorithm is to optimize some measure of performance such as minimizing the number of mistakes made 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: * Computational complexity – P ≠ NP (the P versus NP problem); * CryptographicOne-way functions exist. There are several different approaches to computational learning theory based on making different assumptions about the
inference Inferences are steps in logical reasoning, moving from premises to logical consequences; etymologically, the word '' infer'' means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinct ...
principles used to generalise from limited data. This includes different definitions of probability (see
frequency probability Frequentist probability or frequentism is an interpretation of probability; it defines an event's probability (the ''long-run probability'') as the limit of a sequence, limit of its Empirical probability, relative frequency in infinitely many E ...
, Bayesian probability) and different assumptions on the generation of samples. The different approaches include: * Exact learning, proposed by Dana Angluin; * Probably approximately correct learning (PAC learning), proposed by Leslie Valiant; * VC theory, proposed by Vladimir Vapnik and Alexey Chervonenkis; *
Inductive inference Inductive reasoning refers to a variety of methods of reasoning in which the conclusion of an argument is supported not with deductive certainty, but with some degree of probability. Unlike ''deductive'' reasoning (such as mathematical inducti ...
as developed by Ray Solomonoff; *
Algorithmic learning theory Algorithmic learning theory is a mathematical framework for analyzing machine learning problems and algorithms. Synonyms include formal learning theory and algorithmic inductive inference. Algorithmic learning theory is different from statistica ...
, from the work of E. Mark Gold; * Online machine learning, from the work of Nick Littlestone. 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.html


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. *


External links


Basics of Bayesian inference
{{Differentiable computing Computational fields of study de:Maschinelles Lernen