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  2. Regularization (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Regularization_(mathematics)

    When learning a linear function , characterized by an unknown vector such that () =, one can add the -norm of the vector to the loss expression in order to prefer solutions with smaller norms. Tikhonov regularization is one of the most common forms.

  3. Normalization (machine learning) - Wikipedia

    en.wikipedia.org/wiki/Normalization_(machine...

    where each network module can be a linear transform, a nonlinear activation function, a convolution, etc. () is the input vector, () is the output vector from the first module, etc. BatchNorm is a module that can be inserted at any point in the feedforward network.

  4. Statistical learning theory - Wikipedia

    en.wikipedia.org/wiki/Statistical_learning_theory

    Statistical learning theory is a framework for machine learning drawing from the fields of statistics and functional analysis. [1] [2] [3] Statistical learning theory deals with the statistical inference problem of finding a predictive function based on data.

  5. Norm (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Norm_(mathematics)

    In probability and functional analysis, the zero norm induces a complete metric topology for the space of measurable functions and for the F-space of sequences with F–norm () / (+). [16] Here we mean by F-norm some real-valued function ‖ ‖ on an F-space with distance , such that ‖ ‖ = (,).

  6. Lp space - Wikipedia

    en.wikipedia.org/wiki/Lp_space

    In mathematics, the L p spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces.They are sometimes called Lebesgue spaces, named after Henri Lebesgue (Dunford & Schwartz 1958, III.3), although according to the Bourbaki group (Bourbaki 1987) they were first introduced by Frigyes Riesz ().

  7. Sobolev space - Wikipedia

    en.wikipedia.org/wiki/Sobolev_space

    In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of L p-norms of the function together with its derivatives up to a given order. The derivatives are understood in a suitable weak sense to make the space complete , i.e. a Banach space .

  8. Compressed sensing - Wikipedia

    en.wikipedia.org/wiki/Compressed_sensing

    The function counting the number of non-zero components of a vector was called the "norm" by David Donoho. [ note 1 ] Candès et al. proved that for many problems it is probable that the L 1 {\displaystyle L^{1}} norm is equivalent to the L 0 {\displaystyle L^{0}} norm , in a technical sense: This equivalence result allows one to solve the L 1 ...

  9. Dual norm - Wikipedia

    en.wikipedia.org/wiki/Dual_norm

    The Frobenius norm defined by ‖ ‖ = = = | | = ⁡ = = {,} is self-dual, i.e., its dual norm is ‖ ‖ ′ = ‖ ‖.. The spectral norm, a special case of the induced norm when =, is defined by the maximum singular values of a matrix, that is, ‖ ‖ = (), has the nuclear norm as its dual norm, which is defined by ‖ ‖ ′ = (), for any matrix where () denote the singular values ...