In theoretical computer science,<unk>  or<unk><unk>  problem is a mathematical field related to the analysis of machine<unk>  algorithms. It is traditionally referred to as the grammatical inference problem.
Machine<unk>  algorithms take a training set, form hypotheses or models, and make predictions about the future. Because the training set is finite and the future is uncertain,<unk>  theory usually does not yield absolute guarantees of performance of the algorithms. Instead, probabilistic bounds on the performance of machine<unk>  algorithms are quite common.
In addition to performance bounds,<unk> sts study the time complexity and feasibility of<unk> . In<unk> , a computation is considered feasible if it can be done in polynomial time. There are two kinds of time complexity results:
Negative results are proven only by assumption. The assumptions that are common in negative results are:<unk>  complexity - P ≠ NP
Cryptographic - One-way functions exist.
There are several different approaches to<unk> , which are often mathematically incompatible. This incompatibility arises from using different inference principles: principles which tell you how to generalize from limited data. The incompatibility also arises from differing definitions of probability (see frequency probability, Bayesian probability). The different approaches include:
Probably approximately correct<unk>  (PAC<unk> , proposed by Leslie Valiant;
VC theory, proposed by Vladimir Vapnik;
Bayesian inference, arising from work first done by Thomas Bayes.
Algorithmic<unk>  theory, from the work of E. M. Gold.<unk>  has led to practical algorithms. For example, PAC theory inspired boosting, VC theory led to support vector machines, and Bayesian inference led to belief networks (by Judea Pearl).
See also:
information theory
Computational learning theory
Hebbian theory
Analytical psychology
Reward system
Chaos theory
Attachment theory
Affect control theory
Cognitive science