Logistic regression learning and C + + implementation

Logistic regression is a classification method, which is used for two classification problems, and its basic idea is:

1. Look for the appropriate hypothesis function, the classification function, to predict the results of the input data;
2. The structure loss function is used to indicate the deviation between the predicted output and the actual classes in the training data;
3. Minimize the loss function to obtain optimal model parameters.

First look at the sigmoid function:

\ (g (x) =\frac{1}{1-e^{x}}\)

Its function image is:

Hypothetical functions in logistic regression (classification Functions):

\ (H_{\theta} (x) =g (\theta ^{t}x) =\frac{1}{1+e^{-\theta ^{t}x}}\)

Explain:

\ (\theta \)--The parameters we request at the back;

\ (t\)--vector transpose, the default vector is the column vector;

\ (\theta ^{t}x\)--column vector \ (theta\) first transpose, then with \ (x\) to do the point multiplication, for example:

\ (\begin{bmatrix}1\\ -1\\ 3\end{bmatrix}^{t}\begin{bmatrix}1\\ 1\\ -1\end{bmatrix} = \begin{bmatrix}1 &-1 & 3\ end{bmatrix}\begin{bmatrix}1\\ 1\\ -1\end{bmatrix}=1\times 1+ ( -1) \times1+3\times (-1) = -3\)

Logistic regression learning and C + + implementation