About: Ridge regression

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Ridge regression is a method of estimating the coefficients of multiple-regression models in scenarios where the independent variables are highly correlated. It has been used in many fields including econometrics, chemistry, and engineering. Also known as Tikhonov regularization, named for Andrey Tikhonov, it is a method of regularization of ill-posed problems. it is particularly useful to mitigate the problem of multicollinearity in linear regression, which commonly occurs in models with large numbers of parameters. In general, the method provides improved efficiency in parameter estimation problems in exchange for a tolerable amount of bias (see bias–variance tradeoff).

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rdf:type	Thing
rdfs:label	リッジ回帰 (ja) Ridge regression (en)
rdfs:comment	リッジ回帰（リッジかいき、Ridge regression）は、独立変数が強く相関している場合に、重回帰モデルの係数を推定する方法。計量経済学、化学、工学などの分野で使用されている。この理論は、1970年に Hoerl とケナードが Technometrics の論文「RIDGE regressions: biased estimation of nonorthogonal problems」と「RIDGE regressions: applications in nonorthogonal problems」で初めて紹介した。これは、リッジ分析の分野における 10 年間の研究の結果だった。リッジ回帰は、線形回帰モデルに多重共線性がある（強く相関する独立変数がある）場合に最小二乗推定量が不正確になることを解決するために開発された。リッジ回帰推定量は、最小二乗推定量よりも精度が高い。 (ja) Ridge regression is a method of estimating the coefficients of multiple-regression models in scenarios where the independent variables are highly correlated. It has been used in many fields including econometrics, chemistry, and engineering. Also known as Tikhonov regularization, named for Andrey Tikhonov, it is a method of regularization of ill-posed problems. it is particularly useful to mitigate the problem of multicollinearity in linear regression, which commonly occurs in models with large numbers of parameters. In general, the method provides improved efficiency in parameter estimation problems in exchange for a tolerable amount of bias (see bias–variance tradeoff). (en)
dcterms:subject	Regression analysis Linear algebra Inverse problems Estimation methods
Wikipage page ID	954328 (xsd:integer)
Wikipage revision ID	1120671107 (xsd:integer)
Link from a Wikipage to another Wikipage	Bayesian probability Elastic net regularization Non-linear least squares Technometrics Bayes' theorem Regression analysis Bias of an estimator Bias–variance tradeoff Residual (numerical analysis) Design matrix Integral equation Inverse problem Standard deviation Levenberg–Marquardt algorithm Maximum a posteriori Gauss–Markov theorem Vertical bar Low-pass filters Grace Wahba Moment matrix Multivariate normal distribution Condition number Constraint (mathematics) Cross-validation (statistics) Homoscedasticity Underdetermined system Regression model Andrey Nikolayevich Tikhonov Machine learning Singular matrices Statistics Compact operator Identity matrix Kriging Overdetermined system Mahalanobis distance Main diagonal Errors and residuals in statistics Lasso (statistics) Least squares Line fitting Logistic regression Linear algebra Expected value Normal distribution Matrix regularization Prior probability Rank (linear algebra) Regularization (mathematics) Residual sum of squares Hermitian adjoint Hilbert space Inverse problems Covariance matrix Estimation methods Cholesky factorization Lagrange multiplier Support vector machine Coefficient Efficient estimator High-pass filter Whitening transformation Wiener filter Difference operator Discrete fourier transform Ill-posed problem Mikhail Lavrentyev Ordinary least squares Multicollinearity Statistical classification Non-binding constraint Well-posed problem Restricted maximum likelihood Singular-value decomposition Statistical independence Effective number of degrees of freedom Eigenvalues Regressand Generalized singular-value decomposition dbr:Arthur_E._Hoerl dbr:Discrepancy_principle dbr:L-curve_method dbr:Unbiased_predictive_risk_estimator
Link from a Wikipage to an external page	https://books.google.com/books%3Fid=Jv_ZBwAAQBAJ&pg=PA86 https://books.google.com/books%3Fid=v0KCDwAAQBAJ https://books.google.com/books%3Fid=wmA_R3ZFrXYC https://books.google.com/books%3Fid=yPOUDwAAQBAJ&pg=PA69 http://apps.nrbook.com/empanel/index.html%23pg=1006
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