Portuguese README available here. A simple gradient descent algorithm to create a polynomial model that estimates a Ford Focus price in U.K. based only in its mileage. It is programmed and tested on Octave, but most likely works on Matlab too.
The gradient descent implemented here is general enough to solve the polynomial minimization problem.
The dataset present in the data folder is part of the 100,000 UK Used Car Data set, by Kaggle user Aditya. To train the algorithm I extracted 500 random entries from the complete dataset and created a sample. I use the same sample in both the linear and quadratic algorithms training.
To simply run the gradient descent algorithm, open Octave and set the working folder to the project's folder then type main to run the linear training or mainQuadratic to run the quadratic polynomial training. The model coefficients will be stored in the theta variable and plots will show you the training dataset and resulting model. Additionally, a GIF animation with 50 steps of the training will be saved to the img folder.
You can change any parameters directly on the main or mainQuadratic scripts or use the functions directly. To run only the gradient descent algorithm on your own dataset and your own polynomial you must run the following command:
[theta, costFunction_history, theta_history] = gradientDescent(X, y, theta, alpha, num_iters);
Where num_iters is the number of iterations you want the gradient descent to run, alpha is the algorithm's learning rate, theta is a vector of order n with the polynomial coefficients initial values (n is the number of coefficients in your polynomial), y is the training data results, or labels, and X is a n x m matriz with the training data inputs (n is the number of coefficients in your polynomial and m is the number of inputs in the training dataset). This function will return the polynomial coefficients (theta), the history of your cost function values (costFunction_history) and the history of your coefficient values (theta_history).
An example of a valid X for a complete quadratic polynomial is as shown below:
X = [ones(length(training_inputs), 1), training_inputs, training_inputs.^2];
For any higher order polynomial you just have to add columns for each coefficient. A 6th order coefficient could be added by a new column with training_inputs.^6 in the matrix.