我正在尝试实现一个简单的线性回归的梯度下降算法。我使用的是Armadillo C++线性代数库，并且我对Armadillo还不太熟悉。我正在尝试做的是：
void linRegression(mat &features, mat &targets, double alpha,double error){ mat theta = ones(features.n_cols+1); mat temp = zeros(features.n_cols+1); mat features_new = join_horiz(ones(features.n_rows),features); mat predictions; double con = alpha*(1.0/features.n_rows); int j = 0; while(j<1000){ mat step_error = (features_new*theta - targets); for(unsigned int i=0;i<theta.n_rows;i++){ temp(i) = con*sum(step_error%features_new.col(i)); } theta = theta-temp; mat pred = predict(theta,features_new); cout<<theta<<endl; j++; }}但是theta的值不断增加，最终趋向于无穷大。我不确定我做错了什么。
回答：
我认为while循环中的计算不正确。至少你可以不用for循环，让它更优雅。这里是一个单特征问题的简短代码：
#include <iostream>#include <armadillo>using namespace std;using namespace arma;int main(int argc, char** argv){ mat features(10, 1); features << 6.110100 << endr << 5.527700 << endr << 8.518600 << endr << 7.003200 << endr << 5.859800 << endr << 8.382900 << endr << 7.476400 << endr << 8.578100 << endr << 6.486200 << endr << 5.054600 << endr; mat targets(10, 1); targets << 17.59200 << endr << 9.130200 << endr << 13.66200 << endr << 11.85400 << endr << 6.823300 << endr << 11.88600 << endr << 4.348300 << endr << 12.00000 << endr << 6.598700 << endr << 3.816600 << endr; mat theta = ones(features.n_cols + 1); mat features_new = join_horiz(ones(features.n_rows), features); double alpha = 0.01; double con = alpha*(1.0 / features.n_rows); int j = 0; while (j < 20000){ mat step_error = (features_new*theta - targets); theta = theta - con * (features_new.t() * step_error); j++; } theta.print("theta:"); system("pause"); return 0;}程序返回的结果是：
theta: 0.5083 1.3425通过正常方程法获得的结果是：
theta: 0.5071 1.3427编辑
你的代码确实是正确的！问题可能出在特征归一化上。我扩展了我的例子到两个特征的回归，并添加了归一化。没有归一化的话，对我来说也不起作用。
#include <iostream>#include <armadillo>using namespace std;using namespace arma;int main(int argc, char** argv){ mat features(10, 2); features << 2104 << 3 << endr << 1600 << 3 << endr << 2400 << 3 << endr << 1416 << 2 << endr << 3000 << 4 << endr << 1985 << 4 << endr << 1534 << 3 << endr << 1427 << 3 << endr << 1380 << 3 << endr << 1494 << 3 << endr; mat m = mean(features, 0); mat s = stddev(features, 0, 0); int i, j; //归一化 for (i = 0; i < features.n_rows; i++) { for (j = 0; j < features.n_cols; j++) { features(i, j) = (features(i, j) - m(j))/s(j); } } mat targets(10, 1); targets << 399900 << endr << 329900 << endr << 369000 << endr << 232000 << endr << 539900 << endr << 299900 << endr << 314900 << endr << 198999 << endr << 212000 << endr << 242500 << endr; mat theta = ones(features.n_cols + 1); mat features_new = join_horiz(ones(features.n_rows), features); double alpha = 0.01; double con = alpha*(1.0 / features.n_rows); while (j < 20000){ mat step_error = (features_new*theta - targets); theta = theta - con * (features_new.t() * step_error); j++; } cout << theta << endl; system("pause"); return 0;}结果是：
theta:
3.1390e+005 9.9704e+004 -5.6835e+003