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In computational learning theory, probably approximately correct (PAC) learning is a framework for mathematical analysis of machine learning. It was proposed in 1984 by Leslie Valiant . [ 1 ]
Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of statistical algorithms that can learn from data and generalize to unseen data, and thus perform tasks without explicit instructions. [1]
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.
A learning algorithm over is a computable map from to . In other words, it is an algorithm that takes as input a finite sequence of training samples and outputs a function from X {\displaystyle X} to Y {\displaystyle Y} .
Examples of instance-based learning algorithms are the k-nearest neighbors algorithm, kernel machines and RBF networks. [ 2 ] : ch. 8 These store (a subset of) their training set; when predicting a value/class for a new instance, they compute distances or similarities between this instance and the training instances to make a decision.
Empirically, for machine learning heuristics, choices of a function that do not satisfy Mercer's condition may still perform reasonably if at least approximates the intuitive idea of similarity. [6] Regardless of whether k {\displaystyle k} is a Mercer kernel, k {\displaystyle k} may still be referred to as a "kernel".
Ensemble learning, including both regression and classification tasks, can be explained using a geometric framework. [15] Within this framework, the output of each individual classifier or regressor for the entire dataset can be viewed as a point in a multi-dimensional space.
In machine learning, lazy learning is a learning method in which generalization of the training data is, in theory, delayed until a query is made to the system, as opposed to eager learning, where the system tries to generalize the training data before receiving queries.