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Universal approximation theorem. Artificial neural networks are combinations of multiple simple mathematical functions that implement more complicated functions from (typically) real-valued vectors to real-valued vectors. The spaces of multivariate functions that can be implemented by a network are determined by the structure of the network ...
Deep learning is the subset of machine learning methods based on neural networks with representation learning. The adjective "deep" refers to the use of multiple layers in the network. Methods used can be either supervised, semi-supervised or unsupervised. [2]
Stochastic gradient descent is a popular algorithm for training a wide range of models in machine learning, including (linear) support vector machines, logistic regression (see, e.g., Vowpal Wabbit) and graphical models. [21] When combined with the back propagation algorithm, it is the de facto standard algorithm for training artificial neural ...
In real analysis and approximation theory, the Kolmogorov–Arnold representation theorem (or superposition theorem) states that every multivariate continuous function can be represented as a superposition of the two-argument addition of continuous functions of one variable. It solved a more constrained form of Hilbert's thirteenth problem, so ...
Machine learningand data mining. Q-learning is a model-free reinforcement learning algorithm to learn the value of an action in a particular state. It does not require a model of the environment (hence "model-free"), and it can handle problems with stochastic transitions and rewards without requiring adaptations. [1]
Bias and variance as function of model complexity. In statistics and machine learning, the bias–variance tradeoff describes the relationship between a model's complexity, the accuracy of its predictions, and how well it can make predictions on previously unseen data that were not used to train the model. In general, as we increase the number ...
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] In this framework, the learner receives samples and must select a generalization function (called the hypothesis) from a certain class of possible functions.
The "no free lunch" (NFL) theorem is an easily stated and easily understood consequence of theorems Wolpert and Macready actually prove. It is weaker than the proven theorems, and thus does not encapsulate them. Various investigators have extended the work of Wolpert and Macready substantively. In terms of how the NFL theorem is used in the ...