Polynomial Regression using Turicreate

In this article, we will discuss the implementation of Polynomial Regression using Turicreate. Polynomial Regression: Polynomial regression is a form of regression analysis that models the relationship between a dependent say y and an independent variable say x as a nth degree polynomial. It is expressed as : 

y= b0+b1x1+ b2x12+ b2x13+…… bnx1n

[where b0, b1, b2, …… bn are regression coefficients]

So let’s learn this concept through practicals.

Step 1: Import the important libraries and generate a very small data set using SArray and SFrame in turicreate that we are going to use to perform Polynomial Regression.

Python3

# importing required python libraries
import turicreate
import matplotlib.pyplot as plt
import random

# Generating datapoints
X = [data for data in range(1, 21)]
Y = [random.randrange(100, 1000, 1) for data in range(20)]

# Creating Sarrays from the generated data points
Xs = turicreate.SArray(X, dtype=float)
Ys = turicreate.SArray(Y, dtype=float)

print(f"""Xs : {Xs}
\n-------------------------------------------------------------------------------------------\n
Ys : {Ys}""")

Output:

Step 2: Plotting the generated data

Python3

# plotting the generated data
plt.scatter(Xs, Ys)
plt.show()

Step 3: Create an SFrame containing the input, its polynomial_degrees, and the output in order to fit our regression model.

Python3

# Creating an Sframe where all the inputs and the polynomial degree and output
def createSframe(inputs, pol_degree):
    datapoints = turicreate.SFrame({'x1': inputs})
    for degree in range(2, pol_degree+1):
        datapoints[f'x{degree}'] = datapoints[f'x{degree-1}']*datapoints['x1']
    return datapoints


# Creating a SFrame with polynomial degree 20
data_points = createSframe(Xs, 20)
data_points['y'] = Ys

# showing the first 10 entries in the SFrame
data_points.head()

Step 4: Fitting Polynomial Regression to the generated Data set.

Python3

# Polynomial Regression
features = [f'x{i}' for i in range(1, 21)]
poly_model = turicreate.linear_regression.create(
    data_points, features=features, target='y')

Step 5: Predicting the result using the fitted model and storing the result in the SFrame.

Python3

# predicting the some data
# Generating test datapoints
test_X = [random.randrange(1, 60, 1) for data in range(20)]
test_Xs = turicreate.SArray(X, dtype=float)
test_data = createSframe(test_Xs, 5)
data_points['predicted_y'] = poly_model.predict(test_data)

data_points.head()

Step 6: Measuring the accuracy of our predicted result

Python

# Measuring the accuracy
# Generating test datapoints
test_X = [random.randrange(1, 60, 1) for data in range(20)]
test_Xs = turicreate.SArray(X, dtype=float)
test_data = createSframe(test_Xs, 20)
poly_model.evaluate(data_points)

Step 7: Visualizing the Polynomial Regression results using scatter plot and line plot of the input data and the predicted result.

Python3

plt.scatter(data_points['x1'], data_points['y'])
plt.plot(data_points['x1'], data_points['predicted_y'])
plt.show()