本讲主要说下逻辑回归的相关问题和具体的实现方法
1. 什么是逻辑回归
逻辑回归是线性回归的一种，那么什么是回归，什么是线性回归
回归指的是公式已知，对公式中的未知参数进行估计，注意公式必须是已知的，否则是没有办法进行回归的
线性回归指的是回归中的公式是一次的，例如z=ax+by
逻辑回归其实就是在线性回归的基础上套了一个sigmoid函数，具体的样子如下
2. 正则化项
3. 最小二乘法和最大似然法
4. java实现梯度下降法
实验：
样本：
-0.017612 14.053064 0 -1.395634 4.662541 1 -0.752157 6.538620 0 -1.322371 7.152853 0 0.423363 11.054677 0 0.406704 7.067335 1 0.667394 12.741452 0 -2.460150 6.866805 1 0.569411 9.548755 0 -0.026632 10.427743 0 0.850433 6.920334 1 1.347183 13.175500 0 1.176813 3.167020 1 -1.781871 9.097953 0 -0.566606 5.749003 1 0.931635 1.589505 1 -0.024205 6.151823 1 -0.036453 2.690988 1 -0.196949 0.444165 1 1.014459 5.754399 1 1.985298 3.230619 1 -1.693453 -0.557540 1 -0.576525 11.778922 0 -0.346811 -1.678730 1 -2.124484 2.672471 1 1.217916 9.597015 0 -0.733928 9.098687 0 -3.642001 -1.618087 1 0.315985 3.523953 1 1.416614 9.619232 0 -0.386323 3.989286 1 0.556921 8.294984 1 1.224863 11.587360 0 -1.347803 -2.406051 1 1.196604 4.951851 1 0.275221 9.543647 0 0.470575 9.332488 0 -1.889567 9.542662 0 -1.527893 12.150579 0 -1.185247 11.309318 0 -0.445678 3.297303 1 1.042222 6.105155 1 -0.618787 10.320986 0 1.152083 0.548467 1 0.828534 2.676045 1 -1.237728 10.549033 0 -0.683565 -2.166125 1 0.229456 5.921938 1 -0.959885 11.555336 0 0.492911 10.993324 0 0.184992 8.721488 0 -0.355715 10.325976 0 -0.397822 8.058397 0 0.824839 13.730343 0 1.507278 5.027866 1 0.099671 6.835839 1 -0.344008 10.717485 0 1.785928 7.718645 1 -0.918801 11.560217 0 -0.364009 4.747300 1 -0.841722 4.119083 1 0.490426 1.960539 1 -0.007194 9.075792 0 0.356107 12.447863 0 0.342578 12.281162 0 -0.810823 -1.466018 1 2.530777 6.476801 1 1.296683 11.607559 0 0.475487 12.040035 0 -0.783277 11.009725 0 0.074798 11.023650 0 -1.337472 0.468339 1 -0.102781 13.763651 0 -0.147324 2.874846 1 0.518389 9.887035 0 1.015399 7.571882 0 -1.658086 -0.027255 1 1.319944 2.171228 1 2.056216 5.019981 1 -0.851633 4.375691 1 -1.510047 6.061992 0 -1.076637 -3.181888 1 1.821096 10.283990 0 3.010150 8.401766 1 -1.099458 1.688274 1 -0.834872 -1.733869 1 -0.846637 3.849075 1 1.400102 12.628781 0 1.752842 5.468166 1 0.078557 0.059736 1 0.089392 -0.715300 1 1.825662 12.693808 0 0.197445 9.744638 0 0.126117 0.922311 1 -0.679797 1.220530 1 0.677983 2.556666 1 0.761349 10.693862 0 -2.168791 0.143632 1 1.388610 9.341997 0 0.317029 14.739025 0
主要代码
public class LogRegression {
public static void main(String[] args) {
LogRegression lr = new LogRegression();
Instances instances = new Instances();
lr.train(instances, 0.01f, 200, (short)1);
}
public void train(Instances instances, float step, int maxIt, short algorithm) {
float[][] datas = instances.datas;
float[] labels = instances.labels;
int size = datas.length;
int dim = datas[0].length;
float[] w = new float[dim];
for(int i = 0; i < dim; i++) {
w[i] = 1;
}
switch(algorithm){
//批量梯度下降
case 1:
for(int i = 0; i < maxIt; i++) {
//求输出
float[] out = new float[size];
for(int s = 0; s < size; s++) {
float lire = innerProduct(w, datas[s]);
out[s] = sigmoid(lire);
}
for(int d = 0; d < dim; d++) {
float sum = 0;
for(int s = 0; s < size; s++) {
sum += (labels[s] - out[s]) * datas[s][d];
}
w[d] = w[d] + step * sum;
}
System.out.println(Arrays.toString(w));
}
break;
//随机梯度下降
case 2:
for(int i = 0; i < maxIt; i++) {
for(int s = 0; s < size; s++) {
float lire = innerProduct(w, datas[s]);
float out = sigmoid(lire);
float error = labels[s] - out;
for(int d = 0; d < dim; d++) {
w[d] += step * error * datas[s][d];
}
}
System.out.println(Arrays.toString(w));
}
break;
}
}
private float innerProduct(float[] w, float[] x) {
float sum = 0;
for(int i = 0; i < w.length; i++) {
sum += w[i] * x[i];
}
return sum;
}
private float sigmoid(float src) {
return (float) (1.0 / (1 + Math.exp(-src)));
}
}
效果