翻訳と辞書 Words near each other ・ Regular tuning ・ Regular Urban Survivors ・ Regular way contracts ・ RegularChains ・ Regulares ・ Regularis Concordia ・ Regularis Concordia (Winchester) ・ Regularity rally ・ Regularity theorem ・ Regularity theorem for Lebesgue measure ・ Regularization ・ Regularization (linguistics) ・ Regularization (mathematics) ・ Regularization (physics) ・ Regularization by spectral filtering ・ Regularization perspectives on support vector machines ・ Regularized canonical correlation analysis ・ Regularized Inglish ・ Regularized meshless method ・ Regulate ・ Regulate (song) ・ Regulate the Chemicals ・ Regulate... G Funk Era, Pt. II ・ Regulate...G Funk Era ・ Regulated Area (No 2) ・ Regulated function ・ Regulated Industries and Utilities Committee (Georgia Senate) ・ Regulated Industries Committee (Georgia House) ・ Regulated integral ・ Regulated market Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Regularization perspectives on support vector machines ： ウィキペディア英語版 Regularization perspectives on support vector machines Regularization perspectives on support vector machines provide a way of interpreting support vector machines (SVMs) in the context of other machine learning algorithms. SVM algorithms categorize multidimensional data, with the goal of fitting the training set data well, but also avoiding overfitting, so that the solution generalizes to new data points. Regularization algorithms also aim to fit training set data and avoid overfitting. They do this by choosing a fitting function that has low error on the training set, but also is not too complicated, where complicated functions are functions with high norms in some function space. Specifically, Tikhonov regularization algorithms choose a function that minimize the sum of training set error plus the function's norm. The training set error can be calculated with different loss functions. For example, regularized least squares is a special case of Tikhonov regularization using the squared error loss as the loss function.〔(【引用サイトリンク】first=Lorenzo ) 〕 Regularization perspectives on support vector machines interpret SVM as a special case Tikhonov regularization, specifically Tikhonov regularization with the hinge loss for a loss function. This provides a theoretical framework with which to analyze SVM algorithms and compare them to other algorithms with the same goals: to generalize without overfitting. SVM was first proposed in 1995 by Corinna Cortes and Vladimir Vapnik, and framed geometrically as a method for finding hyperplanes that can separate multidimensional data into two categories. This traditional geometric interpretation of SVMs provides useful intuition about how SVMs work, but is difficult to relate to other machine learning techniques for avoiding overfitting like regularization, early stopping, sparsity and Bayesian inference. However, once it was discovered that SVM is also a special case of Tikhonov regularization, regularization perspectives on SVM provided the theory necessary to fit SVM within a broader class of algorithms.〔〔 〕 This has enabled detailed comparisons between SVM and other forms of Tikhonov regularization, and theoretical grounding for why it is beneficial to use SVM's loss function, the hinge loss. ==Theoretical background== In the statistical learning theory framework, an algorithm is a strategy for choosing a function $f:\backslash mathbf\; X\; \backslash to\; \backslash mathbf\; Y$ given a training set $S\; =\; \backslash$ of inputs, $x\_i$, and their labels, $y\_i$ (the labels are usually $\backslash pm1$). Regularization strategies avoid overfitting by choosing a function that fits the data, but is not too complex. Specifically: $f\; =\; \backslash text\backslash min\_\backslash sum\_^n\; V(y\_i,f(x\_i))+\backslash lambda||f||^2\_\backslash mathcal\backslash right\backslash \}$, where $\backslash mathcal$ is a hypothesis space〔A hypothesis space is the set of functions used to model the data in a machine learning problem. Each function corresponds to a hypothesis about the structure of the data. Typically the functions in a hypothesis space form a Hilbert space of functions with norm formed from the loss function.〕 of functions, $V:\backslash mathbf\; Y\; \backslash times\; \backslash mathbf\; Y\; \backslash to\; \backslash mathbb\; R$ is the loss function, $||\backslash cdot||\_\backslash mathcal\; H$ is a norm on the hypothesis space of functions, and $\backslash lambda\backslash in\backslash mathbb\; R$ is the regularization parameter.〔For insight on choosing the parameter, see, e.g., 〕 When $\backslash mathcal$ is a reproducing kernel Hilbert space, there exists a kernel function $K:\; \backslash mathbf\; X\; \backslash times\; \backslash mathbf\; X\; \backslash to\; \backslash mathbb\; R$ that can be written as an $n\backslash times\; n$ symmetric positive definite matrix $\backslash mathbf\; K$. By the representer theorem,〔See 〕 $f(x\_i)\; =\; \backslash sum\_^n\; c\_j\; \backslash mathbf\; K\_$, and $||f||^2\_\; =\; \backslash langle\; f,f\backslash rangle\_\backslash mathcal\; H\; =\; \backslash sum\_^n\backslash sum\_^n\; c\_ic\_jK(x\_i,x\_j)\; =\; c^T\backslash mathbf\; K\; c$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Regularization perspectives on support vector machines」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.