java - Java 中的梯度下降线性回归

Question

这有点远景，但我想知道是否有人可以看看这个。我在这里正确地进行线性回归的批量梯度下降吗？它给出了单个自变量和截距的预期答案，但不是多个自变量。

/**
 * (using Colt Matrix library)
 * @param alpha Learning Rate
 * @param thetas Current Thetas
 * @param independent 
 * @param dependent
 * @return new Thetas
 */
public DoubleMatrix1D descent(double         alpha,
                              DoubleMatrix1D thetas,
                              DoubleMatrix2D independent,
                              DoubleMatrix1D dependent ) {
    Algebra algebra     = new Algebra();

    // ALPHA*(1/M) in one.
    double  modifier    = alpha / (double)independent.rows();

    //I think this can just skip the transpose of theta.
    //This is the result of every Xi run through the theta (hypothesis fn)
    //So each Xj feature is multiplied by its Theata, to get the results of the hypothesis
    DoubleMatrix1D hypothesies = algebra.mult( independent, thetas );

    //hypothesis - Y  
    //Now we have for each Xi, the difference between predictect by the hypothesis and the actual Yi
    hypothesies.assign(dependent, Functions.minus);

    //Transpose Examples(MxN) to NxM so we can matrix multiply by hypothesis Nx1
    DoubleMatrix2D transposed = algebra.transpose(independent);

    DoubleMatrix1D deltas     = algebra.mult(transposed, hypothesies );


    // Scale the deltas by 1/m and learning rate alhpa.  (alpha/m)
    deltas.assign(Functions.mult(modifier));

    //Theta = Theta - Deltas
    thetas.assign( deltas, Functions.minus );

    return( thetas );
}

Answer 1

您的实现没有任何问题，根据您的评论，共线性 中的问题是您在生成 x2 时引起的。这在回归估计中是有问题的。

要测试您的算法，您可以生成两个独立的随机数列。选择 w0、w1 和 w2 的值，即 intercept、x1 的系数和 x2 分别。计算相关值 y。

然后看看你的随机/批量梯度下降算法是否可以恢复w0、w1和w2值