CosanRidgeRegression.h

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//
// Created by Xinyu Zhang on 3/27/21.
//
 
#ifndef COSAN_COSANRIDGEREGRESSION_H
#define COSAN_COSANRIDGEREGRESSION_H
#include <cosan/model/CosanLinearRegression.h>
 
namespace Cosan{
 
    /**
     * y = a+bx
     * minimize \sum_{i=1}^n (y_i-a-b^Tx_i)^2+\|b\|_2^2 -> find the optimal a and b
     * @tparam NumericType
     * @details https://en.wikipedia.org/wiki/Ridge_regression
     */
    template<Numeric NumericType>
    class CosanRidgeRegression: public CosanLinearRegression<NumericType>{
        public:
//        Initialization
//            CosanRidgeRegression()=delete;
//            CosanRidgeRegression(NumericType Lambda):CosanLinearRegression<NumericType>(false){
//                MLambda=Lambda;
//            }
            CosanRidgeRegression(bool bias=false): CosanLinearRegression<NumericType>(bias){}
            CosanRidgeRegression(NumericType Lambda,bool bias=false): CosanLinearRegression<NumericType>(bias){
                MLambda=Lambda;
            }
 
//            CosanLinearRegression(CosanMatrix<NumericType>& X,const CosanMatrix<NumericType>& Y,bool Bias): CosanLinearModel<NumericType>(Bias){
//                    fit(X,Y);
//            }
            CosanRidgeRegression(CosanRawData<NumericType>& RD,bool bias = false): CosanLinearModel<NumericType>(bias){
                    fit(RD.GetInput(),RD.GetTarget());
            }
            CosanRidgeRegression(CosanData<NumericType>& CD,bool bias = false): CosanLinearModel<NumericType>(bias){
                    fit(CD.GetInput(),CD.GetTarget());
            }
 
            template<class T,
                    std::enable_if_t<std::is_same_v<std::decay_t<T>,CosanMatrix<NumericType>>,bool> = true >
            CosanRidgeRegression(T&& X,const CosanMatrix<NumericType>& Y,
                                 NumericType Lambda,bool Bias): CosanLinearRegression<NumericType>(Bias){
                MLambda=Lambda;
                fit(X,Y);
            }
 
            void SetParams(NumericType Lambda) {MLambda = Lambda; };
            NumericType GetParams() {return MLambda;}
//            bool Load(const string & path);
//            bool Save(const string & path);
            EModelType GetModelType() override {return MdRidgeRegression;};
            const std::string  GetName()  const override{ return "Linear Ridge Regression";}
 
            template<class T,
                    std::enable_if_t<std::is_same_v<std::decay_t<T>,CosanMatrix<NumericType>>,bool > = true >
            void fit(T && X,const CosanMatrix<NumericType>& Y)  {
                CosanMatrix<NumericType> Identity = MLambda*CosanMatrix<NumericType>::Identity(X.cols(),X.cols());
                if (this->MBias==true){
                    X.conservativeResize(X.rows(), X.cols()+1);
                    X.col(X.cols()-1) = CosanMatrix<NumericType>::Ones(X.rows(),1);
                    Identity.conservativeResize(Identity.rows()+1, Identity.cols()+1);
                    Identity.col(Identity.cols()-1) = CosanMatrix<NumericType>::Zero(Identity.rows(),1);
                    Identity.row(Identity.rows()-1) = CosanMatrix<NumericType>::Zero(1,Identity.cols());
                }
//                const auto& svd = X.jacobiSvd(Eigen::ComputeFullU | Eigen::ComputeFullV);
//                const auto& s = svd.singularValues();
//                const auto r = s.rows();
//                const auto& D = s.cwiseQuotient((s.array().square() + MLambda).matrix()).asDiagonal();
//                MBeta = svd.matrixV().leftCols(r) * D * svd.matrixU().transpose().topRows(r) * Y;
                this->MBeta = (X.transpose()*X+Identity).ldlt().solve(X.transpose()*Y);
//                MBeta = (X.transpose()*X+CosanMatrix(MLambda*Eigen::MatrixXd::Identity(X.cols(),X.cols()))).bdcSvd(Eigen::ComputeThinU | Eigen::ComputeThinV).solve(X.transpose()*Y);
//                MBeta = (X.transpose()*X+CosanMatrix(MLambda*Eigen::MatrixXd::Identity(X.cols(),X.cols()))).colPivHouseholderQr().solve(X.transpose()*Y);
                if (this->MBias==true){
                    removeColumn(X,X.cols()-1);
                }
            }
 
        private:
            NumericType MLambda;
    };
}
 
#endif //COSAN_COSANRIDGEREGRESSION_H