def start_linear_regression(training_records, output):
"""
In this method, we compare the weights calculated using our gradient descent approach with the sklearn's output.
`Our method`
>>> regressor = LinearRegression(iterations=NUM_OF_ITERATIONS, learning_rate=LEARNING_RATE)
>>> weights_table, mse_costs, predicted_outputs = regressor.calculate_weights(training_records, output)
As you see above there are 3 tables returned from our approach.
1. weights_table - This is where we store the history of the weights from iteration 0 to the last iteration.
To access the set of weights in the last iteration simply use `weights_table[-1]`
2. mse_costs - Table which stores the mean square error for each iteration.
3. predicted_outputs - This is the predicted output using our machine(i.e weights)
The following code fragment shows how to invoke sklearn's Linear regression.
`sklearn's method`
>>> clf = linear_model.LinearRegression(fit_intercept=False)
>>> clf.fit(training_records, output)
Lastly, we just print the weights and it is left to the user to visually compare them.
:parameter training_records - N X P matrix of training samples.
:parameter output - N X 1 vector of output.
:return:
"""
regressor = LinearRegression(iterations=NUM_OF_ITERATIONS,
learning_rate=LEARNING_RATE)
print np.shape(training_records)
print np.shape(output)
weights_table, mse_costs, predicted_outputs = regressor.calculate_weights(
training_records, output)
clf = linear_model.LinearRegression(fit_intercept=False)
clf.fit(training_records, output)
print "Starting gradient descent with {0} iterations and a learning rate of {1}".format(
NUM_OF_ITERATIONS, LEARNING_RATE)
print "Running..."
final_weights = [
weights_table[-1][i] for i in range(0, NUM_OF_FEATURES + 1)
]
print "After %s iterations of Gradient Descent (our implementation), the final weights are : %s" % (
NUM_OF_ITERATIONS, final_weights)
print "Using Sklearn's Linear Regression, the weights are : %s" % clf.coef_
return weights_table, mse_costs
