Logical (Logistic) regression

Memories

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Training set

There are n characteristics, only one, then if there is the following relationship:

The

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Logistic function (sigmoid function):

Let's do it:

Cost function:

which

Calculation

Process steps:

which

Now it is shown that the gradient representation of the logistic function and the linear regression function is the same:

Gradient of linear regression:

Gradient of the logistic:

And because:

So:

where z is the h in the formula, so the gradient function is the same as the linear regression:

Experiment:

% Logistic regression% initial data  x=[-3;      -2;     -1;     0;      1;      2;     3];  y=[0.01;    0.1;   0.3;    0.45;   0.8;    0.8;    0.99];  Plot (x, y, ' ro ');  Hold on  % fit m = Length (y); theta = [0 0];  a=0.005;  loss = 1;  Iters = 1;  EPS = 0.0001;  While loss >eps && iters <100    loss = 0;    For i = 1:length (y)        h = 1./(1+exp (-(Theta (1) +theta (2) *x (i)));        Theta (1) =theta (1) +a* (Y (i)-h);          Theta (2) =theta (2) +a* (Y (i)-h) *x (i,1);          Err = theta (1) +theta (2) *x (i,1)-Y (i);          loss = loss+err*err/m;     End     iters = iters+1;enditers  theta% drawing contrast for x = -3:0.01:3     h = 1./(1+exp (-(Theta (1) +theta (2) *x)));     Plot (x,h);  Endhold off

Logical (Logistic) regression