機械学習に必要な最急降下法の実装に必要な知識まとめ ref: https://qiita.com/junichiro/items/527b1f211ed814528ded

file0.txt

x := x - \frac{\partial}{\partial x}J(x, y) \\
y := y - \frac{\partial}{\partial y}J(x, y) \\

file1.txt

\theta_1 := \theta_1 - \frac{\partial}{\partial \theta_1}J(\theta_1, \theta_2) \\
\theta_2 := \theta_2 - \frac{\partial}{\partial \theta_2}J(\theta_1, \theta_2) \\

file2.txt

\theta_1 := \theta_1 - \alpha\frac{\partial}{\partial \theta_1}J(\theta_1, \theta_2) \\
\theta_2 := \theta_2 - \alpha\frac{\partial}{\partial \theta_2}J(\theta_1, \theta_2) \\

file3.txt

J = 目的関数
grad = 目的関数の偏微分項
% fmincg は最急降下法を解くライブラリ
[theta, cost] = fmincg([J_theta, grad], initial_theta)

file4.txt

\begin{bmatrix}
a & c & e\\
b & d & f
\end{bmatrix}
=>
\begin{bmatrix}
a \\
b \\
c \\
d \\
e \\
f
\end{bmatrix}

file5.txt

\begin{bmatrix}
a \\
b \\
c \\
d \\
e \\
f
\end{bmatrix}
=>
\begin{bmatrix}
a & c & e\\
b & d & f
\end{bmatrix}

file6.txt

A = [1 3 5; 2 4 6];
% unrolling
A = A(:)
ans =

   1
   2
   3
   4
   5
   6

% reshape
A = reshape(A, 2, 3)
>> reshape(A, 2, 3)
ans =

   1   2   3
   4   5   6