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In mathematical analysis, the spaces of test functions and distributions are topological vector spaces (TVSs) that are used in the definition and application of distributions. Test functions are usually infinitely differentiable complex -valued (or sometimes real -valued) functions on a non-empty open subset that have compact support.
Singapore math (or Singapore maths in British English [1]) is a teaching method based on the national mathematics curriculum used for first through sixth grade in Singaporean schools. [2] [3] The term was coined in the United States [4] to describe an approach originally developed in Singapore to teach students to learn and master fewer ...
Minimum and maximum value of a function. Consider the following notation: (+) This denotes the minimum value of the objective function x 2 + 1, when choosing x from the set of real numbers. The minimum value in this case is 1, occurring at x = 0.
State-value function. The state-value function () is defined as, expected discounted return starting with state , i.e. =, and successively following policy . Hence, roughly speaking, the value function estimates "how good" it is to be in a given state.
In particular, three data sets are commonly used in different stages of the creation of the model: training, validation, and test sets. The model is initially fit on a training data set, [3] which is a set of examples used to fit the parameters (e.g. weights of connections between neurons in artificial neural networks) of the model. [4]
White noise analysis. In probability theory, a branch of mathematics, white noise analysis, otherwise known as Hida calculus, is a framework for infinite-dimensional and stochastic calculus, based on the Gaussian white noise probability space, to be compared with Malliavin calculus based on the Wiener process. [1]
Parameter space. The parameter space is the space of possible parameter values that define a particular mathematical model. It is also sometimes called weight space, and is often a subset of finite-dimensional Euclidean space. In statistics, parameter spaces are particularly useful for describing parametric families of probability distributions.
Vapnik–Chervonenkis dimension. In Vapnik–Chervonenkis theory, the Vapnik–Chervonenkis (VC) dimension is a measure of the size (capacity, complexity, expressive power, richness, or flexibility) of a class of sets. The notion can be extended to classes of binary functions. It is defined as the cardinality of the largest set of points that ...