LeastSquares.hpp

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//
// Created by dodo on 11/10/17.
//

#ifndef MACHINE_LEARNING_LEASTSQUARES_HPP
#define MACHINE_LEARNING_LEASTSQUARES_HPP

#include <utility>
#include <vector>
#include "../include/matrix/Matrix.hpp"

using namespace std;

class LeastSquares {
 public:
  enum RegressionType {
    REGULAR, WEIGHTED
  };
 private:
  MatrixD X, y, coefs, residuals;
  RegressionType regressionType;
 public :
  LeastSquares(MatrixD data, MatrixD labels, RegressionType regType = REGULAR) : regressionType(regType) {
    X = std::move(data);
    X.addColumn(MatrixD::ones(X.nRows(), 1), 0);
    y = std::move(labels);
  }

  RegressionType getRegressionType() const {
    return regressionType;
  }

  void setRegressionType(RegressionType regressionType) {
    this->regressionType = regressionType;
  }

  void fit() {
    // The formula for least squares is the following
    // B^ = (X'X)^{-1} X'y
    // Weighted least squares is like this
    // B^ = (X'WX)^{-1} X'Wy
    // where W is a Square matrix with the weights in the diagonal
    // if W = I, weighted least squares behaves just like ordinary least squares

    MatrixD W;
    if (regressionType == WEIGHTED) {
      MatrixD vars = X.transpose().var();
      W = vars.asDiagonal();
    } else
      W = MatrixD::identity(X.nRows());

    MatrixD Xt = X.transpose();
    MatrixD first_part = Xt * W * X;
    first_part = first_part.inverse();
    MatrixD second_part = Xt * W * y;
    coefs = first_part * second_part;

    residuals = y - (X * coefs);
    residuals = residuals.transpose() * residuals;
  }

  MatrixD predict(MatrixD m) {
    m.addColumn(MatrixD::ones(1, X.nCols()), 0);
    return m.transpose() * coefs;
  }

  const MatrixD &getCoefs() const {
    return coefs;
  }

  const MatrixD &getResiduals() const {
    return residuals;
  }
};

#endif //MACHINE_LEARNING_LEASTSQUARES_HPP