This article describes a new methodlogy for the detection of influential subsets in Ridge Regression. Studies the jointly influential of casess(X′_i,Y_i )and(X′,Y)for the Ridge Regression (K)= (X′X+K I)~(-1)X′Y(O≤K<+∞) of β.
Define a radial basis function (RBF) at center of each cluster and learning a two-layer neural network which consists of these RBFs, Simultaneously, for the purpose of avoiding over-fitting, we make use of ridge regression method, which adding a weight penalty term including a appropriate regularization parameter on the cost function and then lead to a more smooth function.
A nonlinear ridge regression modeling method based on Radial Basis Function was put forward, and the kernel of this modeling method is, firstly Radial Basis Function is used to realize the nonlinear mapping of input, and then a linear model using Ridge Regression is built, meanwhile, a re-estimation formula based on the Generalized Cross Validation(GCV) is adopted to calculate the ridge parameter k .
A nonlinear ridge regression modeling method based on genetic algorithm(GA-NLRR)is put forward,and the kernel of this modeling method is using Radial Basis Function to realize the nonlinear mapping of input,then build up a linear model using Ridge Regression,meanwhile,genetic algorithm is adopted to calculate the ridge parameter.
The new regression analysis methods applied in water science such as bridge regression, principal component regression, robust regression, auto-regression, envelope regression, multi-stratum recursive regression, fuzzy regression and grey regression are introduced systematically in this paper.
Hence, we developed QSAR models based on a large set of theoretical molecular descriptors using ridge regression methodology, which overcomes this limitation and also because the independent variables are highly intercorrelated.
Ridge regression is a classical statistical technique that attempts to address the bias-variance trade-off in the design of linear regression models.
A reformulation of ridge regression in dual variables permits a non-linear form of ridge regression via the well-known 'kernel trick'.
In this paper, we introduce a reduced rank kernel ridge regression (RRKRR) algorithm, capable of generating an optimally sparse kernel expansion that is functionally identical to that resulting from conventional kernel ridge regression (KRR).
The proposed method is demonstrated to out-perform an alternative sparse kernel ridge regression algorithm on the Motorcycle and Boston Housing benchmarks.
An investigation is made on the application of the constrained differential dynamic programming in the reservoir optimization dispatching. In order to find a scheme of reservoir optimization dispatching, an operating formula is presented for connected reservoirs in different periods by the least square method of regression analysis, when singularity occurs in the regression matrix, the method of ridge regression is used to overcome it.
In this paper, ridge regress method is used to handle well logs DLW, HG, HGG, DZW, and generate post-maps of rock character in the geo-physical well logs, the principle and method of ridge regress are introduced.The predict formula of rock character by studying of sample, computing results, and post-maps of rock character generated by computer are given. This method has practical meaning for interpretation of well log data by computer and automatic mapping.