Computational learning theory

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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. [1]

Contents

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.[ citation needed ] In computational learning theory, a computation is considered feasible if it can be done in polynomial time.[ citation needed ] There are two kinds of time complexity results:

Negative results often rely on commonly believed, but yet unproven assumptions,[ citation needed ] 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 (see frequency probability, Bayesian probability) and different assumptions on the generation of samples.[ citation needed ] 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.

See also

References

  1. ↑ "ACL - Association for Computational Learning".
  2. ↑ Kearns, Michael; Vazirani, Umesh (August 15, 1994). An Introduction to Computational Learning Theory. MIT Press. ISBN   978-0262111935.
  3. ↑ Dana Angluin (1976). An Application of the Theory of Computational Complexity to the Study of Inductive Inference (Ph.D. thesis). University of California at Berkeley.
  4. ↑ D. Angluin (1978). "On the Complexity of Minimum Inference of Regular Sets". Information and Control. 39 (3): 337–350.
  5. ↑ Valiant, Leslie (1984). "A Theory of the Learnable" (PDF). Communications of the ACM. 27 (11): 1134–1142. doi:10.1145/1968.1972. S2CID   12837541. Archived from the original (PDF) on 2019-05-17. Retrieved 2022-11-24.
  6. ↑ Vapnik, V.; Chervonenkis, A. (1971). "On the uniform convergence of relative frequencies of events to their probabilities" (PDF). Theory of Probability and Its Applications. 16 (2): 264–280. doi:10.1137/1116025.
  7. ↑ Solomonoff, Ray (March 1964). "A Formal Theory of Inductive Inference Part 1". Information and Control. 7 (1): 1–22. doi: 10.1016/S0019-9958(64)90223-2 .
  8. ↑ Solomonoff, Ray (1964). "A Formal Theory of Inductive Inference Part 2". Information and Control. 7 (2): 224–254. doi:10.1016/S0019-9958(64)90131-7.
  9. ↑ Gold, E. Mark (1967). "Language identification in the limit" (PDF). Information and Control. 10 (5): 447–474. doi: 10.1016/S0019-9958(67)91165-5 .

Further reading

A description of some of these publications is given at important publications in machine learning.

Surveys

Feature selection

Optimal O notation learning

Negative results

Error tolerance

Equivalence

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