Stochastic Gradient Descent - Example

Example

Let's suppose we want to fit a straight line to a training set of two-dimensional points using least squares. The objective function to be minimized is:

The last line in the above pseudocode for this specific problem will become:

\begin{bmatrix} w_1 \\ w_2 \end{bmatrix} := \begin{bmatrix} w_1 \\ w_2 \end{bmatrix} - \alpha \begin{bmatrix} 2(w_1 + w_2 x_i - y_i) \\ 2x_i(w_1 + w_2 x_i - y_i) \end{bmatrix}.

Read more about this topic:  Stochastic Gradient Descent

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