Mathematics of neural networks in machine learning: Difference between revisions

Revision as of 18:01, 1 April 2020

Revision as of 12:47, 30 September 2020

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These weights are computed in turn: first compute <math>w_i</math> using only <math>(x_i, y_i, w_{i-1})</math> for <math>i = 1, \dots, p</math>. The output of the algorithm is then <math>w_p</math>, giving a new function <math>x \mapsto f_N(w_p, x)</math>. The computation is the same in each step, hence only the case <math>i = 1</math> is described.

<math>W_1w_1</math> is calculated from <math>(x_1, y_1, w_0)</math> is calculated by considering a variable weight <math>w</math> and applying [[gradient descent]] to the function <math>w\mapsto E(f_N(w, x_1), y_1)</math> to find a local minimum, starting at <math>w = w_0</math>.

This makes <math>w_1</math> the minimizing weight found by gradient descent.