CS 307: Week 04

import numpy as np
import matplotlib.pyplot as plt
from sklearn.tree import DecisionTreeRegressor
from sklearn.neighbors import KNeighborsRegressor

n = 200
X = np.random.uniform(low=-2*np.pi, high=2*np.pi, size=(n,1))
y = np.sin(X) + np.random.normal(loc=0, scale=0.25, size=(n,1))

# setup figure
fig, (ax1, ax2) = plt.subplots(1, 2)
fig.set_size_inches(10, 5)
fig.set_dpi(100)

# add overall title
fig.suptitle('Simulated Sine Wave Data')

# x values to make predictions at for plotting purposes
x_plot = np.linspace(-2*np.pi, 2*np.pi, 1000).reshape((1000, 1))

# create subplot for "simulation study"
ax1.set_title("Simulation Study")
ax1.scatter(X, y, color="dodgerblue")
ax1.set_xlabel("x")
ax1.set_ylabel("y")
ax1.grid(True, linestyle='--', color='lightgrey')
# add true regression function, the "signal" that we want to learn
ax1.plot(x_plot, np.sin(x_plot), color='black')

# create subplot for "reality"
ax2.set_title("Reality")
ax2.scatter(X, y, color="dodgerblue")
ax2.set_xlabel("x")
ax2.set_ylabel("y")
ax2.grid(True, linestyle='--', color='lightgrey')

# show plot
plt.show()

knn100 = KNeighborsRegressor(n_neighbors=100)
knn010 = KNeighborsRegressor(n_neighbors=10)
knn001 = KNeighborsRegressor(n_neighbors=1)

knn100.fit(X, y)
knn010.fit(X, y)
knn001.fit(X, y)

KNeighborsRegressor(n_neighbors=1)

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# setup figure
fig, (ax1, ax2, ax3) = plt.subplots(1, 3)
fig.set_size_inches(15, 5)
fig.set_dpi(100)

# add overall title
fig.suptitle('Simulated Sine Wave Data')

# x values to make predictions at for plotting purposes
x_plot = np.linspace(-2*np.pi, 2*np.pi, 1000).reshape((1000, 1))

# create subplot for "simulation study"
ax1.set_title("KNN, k = 100")
ax1.scatter(X, y, color="dodgerblue")
ax1.set_xlabel("x")
ax1.set_ylabel("y")
ax1.grid(True, linestyle='--', color='lightgrey')
ax1.plot(x_plot, np.sin(x_plot), color='black')
ax1.plot(x_plot, knn100.predict(x_plot), color='red')

# create subplot for "reality"
ax2.set_title("KNN, k = 10")
ax2.scatter(X, y, color="dodgerblue")
ax2.set_xlabel("x")
ax2.set_ylabel("y")
ax2.grid(True, linestyle='--', color='lightgrey')
ax2.plot(x_plot, np.sin(x_plot), color='black')
ax2.plot(x_plot, knn010.predict(x_plot), color='red')

# create subplot for "reality"
ax3.set_title("KNN, k = 1")
ax3.scatter(X, y, color="dodgerblue")
ax3.set_xlabel("x")
ax3.set_ylabel("y")
ax3.grid(True, linestyle='--', color='lightgrey')
ax3.plot(x_plot, np.sin(x_plot), color='black')
ax3.plot(x_plot, knn001.predict(x_plot), color='red')

# show plot
plt.show()

dt01 = DecisionTreeRegressor(max_depth=1)
dt05 = DecisionTreeRegressor(max_depth=5)
dt10 = DecisionTreeRegressor(max_depth=10)

dt01.fit(X, y)
dt05.fit(X, y)
dt10.fit(X, y)

DecisionTreeRegressor(max_depth=10)

# setup figure
fig, (ax1, ax2, ax3) = plt.subplots(1, 3)
fig.set_size_inches(15, 5)
fig.set_dpi(100)

# add overall title
fig.suptitle('Simulated Sine Wave Data')

# x values to make predictions at for plotting purposes
x_plot = np.linspace(-2*np.pi, 2*np.pi, 1000).reshape((1000, 1))

# create subplot for "simulation study"
ax1.set_title("DT, max_depth = 1")
ax1.scatter(X, y, color="dodgerblue")
ax1.set_xlabel("x")
ax1.set_ylabel("y")
ax1.grid(True, linestyle='--', color='lightgrey')
ax1.plot(x_plot, np.sin(x_plot), color='black')
ax1.plot(x_plot, dt01.predict(x_plot), color='red')

# create subplot for "reality"
ax2.set_title("DT, max_depth = 05")
ax2.scatter(X, y, color="dodgerblue")
ax2.set_xlabel("x")
ax2.set_ylabel("y")
ax2.grid(True, linestyle='--', color='lightgrey')
ax2.plot(x_plot, np.sin(x_plot), color='black')
ax2.plot(x_plot, dt05.predict(x_plot), color='red')

# create subplot for "reality"
ax3.set_title("DT, max_depth = 10")
ax3.scatter(X, y, color="dodgerblue")
ax3.set_xlabel("x")
ax3.set_ylabel("y")
ax3.grid(True, linestyle='--', color='lightgrey')
ax3.plot(x_plot, np.sin(x_plot), color='black')
ax3.plot(x_plot, dt10.predict(x_plot), color='red')

# show plot
plt.show()

# train RMSE goes down as flexibility goes up
print(np.sqrt(np.mean(((dt01.predict(X)).reshape(200, 1) - y) ** 2)))
print(np.sqrt(np.mean(((dt05.predict(X)).reshape(200, 1) - y) ** 2)))
print(np.sqrt(np.mean(((dt10.predict(X)).reshape(200, 1) - y) ** 2)))

0.5922964673600705
0.2321060292671149
0.06085014708879982