C1_W2_Lab05_Sklearn_GD_Soln.ipynb

Kernel: Python 3

Optional Lab: Linear Regression using Scikit-Learn

There is an open-source, commercially usable machine learning toolkit called scikit-learn. This toolkit contains implementations of many of the algorithms that you will work with in this course.

Goals

In this lab you will:

• Utilize scikit-learn to implement linear regression using Gradient Descent

Tools

You will utilize functions from scikit-learn as well as matplotlib and NumPy.

import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import SGDRegressor
from sklearn.preprocessing import StandardScaler
from lab_utils_multi import  load_house_data
from lab_utils_common import dlc
np.set_printoptions(precision=2)
plt.style.use('./deeplearning.mplstyle')

Gradient Descent

Scikit-learn has a gradient descent regression model sklearn.linear_model.SGDRegressor. Like your previous implementation of gradient descent, this model performs best with normalized inputs. sklearn.preprocessing.StandardScaler will perform z-score normalization as in a previous lab. Here it is referred to as 'standard score'.

Load the data set

X_train, y_train = load_house_data()
X_features = ['size(sqft)','bedrooms','floors','age']

Scale/normalize the training data

scaler = StandardScaler()
X_norm = scaler.fit_transform(X_train)
print(f"Peak to Peak range by column in Raw        X:{np.ptp(X_train,axis=0)}")   
print(f"Peak to Peak range by column in Normalized X:{np.ptp(X_norm,axis=0)}")

Peak to Peak range by column in Raw        X:[2.41e+03 4.00e+00 1.00e+00 9.50e+01]
Peak to Peak range by column in Normalized X:[5.85 6.14 2.06 3.69]

Create and fit the regression model

sgdr = SGDRegressor(max_iter=1000)
sgdr.fit(X_norm, y_train)
print(sgdr)
print(f"number of iterations completed: {sgdr.n_iter_}, number of weight updates: {sgdr.t_}")

SGDRegressor()
number of iterations completed: 111, number of weight updates: 10990.0

View parameters

Note, the parameters are associated with the normalized input data. The fit parameters are very close to those found in the previous lab with this data.

b_norm = sgdr.intercept_
w_norm = sgdr.coef_
print(f"model parameters:                   w: {w_norm}, b:{b_norm}")
print( "model parameters from previous lab: w: [110.56 -21.27 -32.71 -37.97], b: 363.16")

model parameters:                   w: [109.95 -20.97 -32.35 -38.07], b:[363.15]
model parameters from previous lab: w: [110.56 -21.27 -32.71 -37.97], b: 363.16

Make predictions

Predict the targets of the training data. Use both the predict routine and compute using $w$ and $b$.

# make a prediction using sgdr.predict()
y_pred_sgd = sgdr.predict(X_norm)
# make a prediction using w,b. 
y_pred = np.dot(X_norm, w_norm) + b_norm  
print(f"prediction using np.dot() and sgdr.predict match: {(y_pred == y_pred_sgd).all()}")

print(f"Prediction on training set:\n{y_pred[:4]}" )
print(f"Target values \n{y_train[:4]}")

prediction using np.dot() and sgdr.predict match: True
Prediction on training set:
[295.17 485.84 389.62 492.  ]
Target values 
[300.  509.8 394.  540. ]

Plot Results

Let's plot the predictions versus the target values.

# plot predictions and targets vs original features    
fig,ax=plt.subplots(1,4,figsize=(12,3),sharey=True)
for i in range(len(ax)):
    ax[i].scatter(X_train[:,i],y_train, label = 'target')
    ax[i].set_xlabel(X_features[i])
    ax[i].scatter(X_train[:,i],y_pred,color=dlc["dlorange"], label = 'predict')
ax[0].set_ylabel("Price"); ax[0].legend();
fig.suptitle("target versus prediction using z-score normalized model")
plt.show()

Congratulations!

In this lab you:

• utilized an open-source machine learning toolkit, scikit-learn

• implemented linear regression using gradient descent and feature normalization from that toolkit