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Example demonstrating how gradient descent may be used to solve a linear regression problem

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This example project demonstrates how the gradient descent algorithm may be used to solve a linear regression problem. A more detailed description of this example can be found here.

The example code is in Python (version 2.6 or higher will work). The only other requirement is NumPy.

This code demonstrates how a gradient descent search may be used to solve the linear regression problem of fitting a line to a set of points. In this problem, we wish to model a set of points using a line. The line model is defined by two parameters - the line's slope

m, and y-intercept

b. Gradient descent attemps to find the best values for these parameters, subject to an error function.

The code contains a main function called

run. This function defines a set of parameters used in the gradient descent algorithm including an initial guess of the line slope and y-intercept, the learning rate to use, and the number of iterations to run gradient descent for.

initial_b = 0 # initial y-intercept guess initial_m = 0 # initial slope guess num_iterations = 1000

Using these parameters a gradient descent search is executed on a sample data set of 100 ponts. Here is a visualization of the search running for 200 iterations using an initial guess of

m = 0,

b = 0, and a learning rate of

0.000005.

To run the example, simply run the

gradient_descent_example.pyfile using Python

python gradient_descent_example.py

The output will look like this

Starting gradient descent at b = 0, m = 0, error = 5565.10783448 Running... After 1000 iterations b = 0.0889365199374, m = 1.47774408519, error = 112.614810116