import matplotlib.pyplot as plt
from linearRegression.linearRegression import LinearRegression
from metrics import *
np.random.seed(42)
N = 30
P = 5
X = pd.DataFrame(np.random.randn(N, P))
y = pd.Series(np.random.randn(N))
# This is for Non_vectorized
for fit_intercept in [True, False]:
for type in ['inverse', 'constant']:
for batch in [1, X.shape[0] // 2, X.shape[0]]:
LR = LinearRegression(fit_intercept=fit_intercept)
LR.fit_non_vectorised(
X, y, batch, lr_type=type
) # here you can use fit_non_vectorised / fit_autograd methods
y_hat = LR.predict(X)
print("Fit_intercept : {} , type : {} , batch_size : {}".format(
str(fit_intercept), type, batch))
print('RMSE: ', round(rmse(y_hat, y), 3), end=" ")
print('MAE: ', round(mae(y_hat, y), 3))
print()
# This is for vectorized
for fit_intercept in [True, False]:
for type in ['inverse', 'constant']:
for batch in [1, X.shape[0] // 2, X.shape[0]]:
LR = LinearRegression(fit_intercept=fit_intercept)
import numpy as np import pandas as pd import matplotlib.pyplot as plt from linearRegression.linearRegression import LinearRegression N = 30 P = 5 X = pd.DataFrame(np.random.randn(N, P)) y = pd.Series(np.random.randn(N)) fit_intercept = True y = X[2] X[4] = X[2] LR = LinearRegression(fit_intercept=fit_intercept) LR.fit_vectorised(X, y, n_iter=1000) LR.plot_contour(X, y)
iris = Data()
iris.load_iris()
X = iris.data
y = iris.target
# get a random train/test split
num_data = len(y)
train_num = math.floor(0.8 * num_data)
test_num = num_data - train_num
# shuffle data
c = list(zip(X, y))
random.shuffle(c)
X, y = zip(*c)
train_X = np.asarray(X[:train_num])
train_y = np.asarray(y[:train_num])
test_X = np.asarray(X[train_num:])
test_y = np.asarray(y[train_num:])
##### Linear Regression #####
lr = LinearRegression()
lr.fit(train_X, train_y)
predictions = []
for x_ in test_X:
predictions.append(lr.predict(x_)[0])
predictions = np.asarray(predictions)
accuracy = measures.accuracy(predictions, test_y)
print('Accuracy:', accuracy)
##### End Linear Regression #####
x = np.array([i * np.pi / 180 for i in range(60, 300, 4)])
np.random.seed(10) #Setting seed for reproducibility
y = 4 * x + 7 + np.random.normal(0, 3, len(x))
x = x.reshape(60, 1) #Converting 1D to 2D for matrix operations consistency
y = pd.Series(y)
max_degree = 10
degrees = []
thetas = []
for degree in range(1, max_degree + 1):
degrees.append(degree)
pf = PolynomialFeatures(degree)
x_poly = pf.transform(x)
X = pd.DataFrame(x_poly)
LR = LinearRegression(fit_intercept=False)
LR.fit_vectorised(X, y, 30, n_iter=7, lr=0.0001)
curr_theta = LR.coef_
tot_theta = np.linalg.norm(curr_theta)
thetas.append(tot_theta)
plt.yscale('log')
plt.plot(degrees, thetas)
plt.title('Magnitude of theta vs Degree of Polynomial Features')
plt.xlabel('Degree')
plt.ylabel('Magnitude of Theta (log scale)')
plt.savefig('plots/q5')
from metrics import mae, rmse
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from linearRegression.linearRegression import LinearRegression
from preprocessing.polynomial_features import PolynomialFeatures
N = 10
P = 2
X = pd.DataFrame(np.random.randn(N, P))
y = pd.Series(np.random.randn(N))
X[3] = 4 * X[1]
print(X)
# For Gradiant Method
model2 = LinearRegression()
model2.fit_non_vectorised(X, y, 10)
y_hat = model2.predict(X)
print('RMSE: ', rmse(y_hat, y))
print('MAE: ', mae(y_hat, y))
print()
# For Normal Method
model = LinearRegression()
model.fit_normal(X, y)
y_hat = model.predict(X)
print(model.coef_)
print('RMSE: ', rmse(y_hat, y))
print('MAE: ', mae(y_hat, y))
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from linearRegression.linearRegression import LinearRegression
from metrics import *
np.random.seed(42)
N = 30
P = 5
X = pd.DataFrame(np.random.randn(N, P))
y = pd.Series(np.random.randn(N))
for fit_intercept in [True, False]:
LR = LinearRegression(fit_intercept=fit_intercept)
LR.fit(X, y)
y_hat = LR.predict(X)
LR.plot()
print('RMSE: ', rmse(y_hat, y))
print('MAE: ', mae(y_hat, y))
np.random.seed(42)
N = 30
P = 5
X1 = pd.DataFrame(np.random.randn(N, P))
X = pd.concat([X1, 2 * X1[3], 5 * X1[4]], axis=1)
y = pd.Series(np.random.randn(N))
niter = 100
print('with multicollinearity')
print()
for j in ['constant', 'inverse']:
print('learning rate', j, ':')
print()
print('Vectorised:')
for fit_intercept in [True, False]:
LR = LinearRegression(fit_intercept=fit_intercept)
LR.fit_vectorised(
X, y, 30, n_iter=niter, lr_type=j
) # here you can use fit_non_vectorised / fit_autograd methods
y_hat = LR.predict(X)
print('RMSE: ', rmse(y_hat, y))
print('MAE: ', mae(y_hat, y))
print()
print()
print()
print('without multicollinearity')
print()
for j in ['constant', 'inverse']:
print('learning rate', j, ':')
print()
print('Vectorised:')
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from linearRegression.linearRegression import LinearRegression
from linearRegression.gradient_descent import GD
from metrics import *
np.random.seed(42)
N = 30
P = 5
X = pd.DataFrame(np.random.randn(N, P))
y = pd.Series(np.random.randn(N))
gd_variant = "vectorised" # non-vectorised, autograd
for fit_intercept in [True, False]:
LR = LinearRegression(fit_intercept=fit_intercept)
LR.fit(X, y, gd_variant) # here you can supply the gd variants
y_hat = LR.predict(X)
LR.plot_residuals()
print('RMSE: ', rmse(y_hat, y))
print('MAE: ', mae(y_hat, y))