def plot2graphs(x: np.ndarray, y: np.ndarray) -> None:
linear_model = MyLR(np.array([[89.0], [-8]]), max_iter=500)
flag = 3
if flag & 1:
linear_model.fit_(x, y)
y_hat = linear_model.predict_(x)
plot_regression(x, y, y_hat)
if flag & 2:
plot_cost(x, y)
def test_MyLinearRegressing():
x = np.array([[12.4956442], [21.5007972], [
31.5527382], [48.9145838], [57.5088733]])
y = np.array([[37.4013816], [36.1473236], [
45.7655287], [46.6793434], [59.5585554]])
lr1 = MyLR([2, 0.7])
# Example 0.0:
print(lr1.predict_(x), end="\n\n")
# Output:
# array([[10.74695094],
# [17.05055804],
# [24.08691674],
# [36.24020866],
# [42.25621131]])
# Example 0.1:
print(lr1.cost_elem_(lr1.predict_(x), y), end="\n\n")
# Output:
# array([[77.72116511],
# [49.33699664],
# [72.38621816],
# [37.29223426],
# [78.28360514]])
# Example 0.2:
print(lr1.cost_(lr1.predict_(x), y), end="\n\n")
# Output:
# 315.0202193084312
# Example 1.0:
# lr2 = MyLR([0, 0])
lr2 = MyLR([1, 1], 5e-8, 1500000)
lr2.fit_(x, y)
print(lr2.thetas, end="\n\n")
# Output:
# array([[1.40709365],
# [1.1150909]])
# Example 1.1:
print(lr2.predict_(x), end="\n\n")
# Output:
# array([[15.3408728],
# [25.38243697],
# [36.59126492],
# [55.95130097],
# [65.53471499]])
# Example 1.2:
print(lr2.cost_elem_(lr2.predict_(x), y), end="\n\n")
# Output:
# array([[35.6749755],
# [4.14286023],
# [1.26440585],
# [29.30443042],
# [22.27765992]])
# Example 1.3:
print(lr2.cost_(lr2.predict_(x), y), end="\n\n")
def plot_cost(x: np.ndarray, y: np.ndarray) -> None:
plt.xlabel("$θ_1$")
plt.ylabel("cost function $J(θ_0, θ_1)$")
plt.grid()
linear_model = MyLR(np.array([[0], [0]]), max_iter=500)
thetas_0 = range(85, 95, 2)
for t0 in thetas_0:
linear_model.thetas[0][0] = t0
npoints = 100
y_cost = [0] * npoints
thetas1 = np.linspace(-15, -3.8, npoints)
for i, t1 in enumerate(thetas1):
linear_model.thetas[1][0] = t1
y_hat = linear_model.predict_(x)
y_cost[i] = linear_model.cost_(y, y_hat)
plt.plot(thetas1, y_cost, label="$J(θ_0=%d, θ_1)$" % t0)
plt.legend()
plt.show()
import numpy as np
import pandas as pd
from sklearn.metrics import mean_squared_error
from my_linear_regression import MyLinearRegression as MyLR
data = pd.read_csv("../../resources/are_blue_pills_magics.csv")
Xpill = np.array(data["Micrograms"]).reshape(-1,1)
Yscore = np.array(data["Score"]).reshape(-1,1)
linear_model1 = MyLR(np.array([[89.0], [-8]]))
# linear_model2 = MyLR(np.array([[89.0], [-6]]))
Y_model1 = linear_model1.predict_(Xpill)
# Y_model2 = linear_model2.predict_(Xpill)
print(linear_model1.cost_(Xpill, Yscore)) # 57.60304285714282 >>>
print(mean_squared_error(Yscore, Y_model1)) # 57.603042857142825 >>>
# print(linear_model2.cost_(Xpill, Yscore)) # 232.16344285714285
# print(mean_squared_error(Yscore, Y_model2))
x= Xpill
y = Yscore
plt.scatter(x, y)
linear_model1.fit_(x, y)
plt.xlabel('Quantity of blue pill (in micrograms)')
plt.ylabel('Space driving score')
plt.title('simple plot')
plt.plot(x, linear_model1.predict_(x), color='green')
for v1_x in range(len(x_matrix)):
for v1_y in range(len(x_matrix[0])):
for v2_y in range(len(theta[0])):
new_m[v1_x][v2_y] += x_matrix[v1_x][v1_y] * theta[v1_y][v2_y]
y_hat = np.array([elem for lst in new_m for elem in lst])
for i, elem in enumerate(y_hat):
plt.vlines(x=x[i], ymin=y[i], ymax=elem, colors='green', ls='--', lw=2)
cost = 2 * sum(
[pow((e1 - e2), 2) / (2 * len(y)) for e1, e2 in zip(y, y_hat)])
plt.plot(x, y_hat, color="#00ff00")
plt.xlabel("X")
plt.ylabel("Y")
title = "Cost : " + str(cost)[:9]
plt.title(title)
plt.show()
data = pd.read_csv("../resources/are_blue_pills_magics.csv")
Xpill = np.array(data["Micrograms"]).reshape(-1, 1)
Yscore = np.array(data["Score"]).reshape(-1, 1)
linear_model1 = MyLR(np.array([[89.0], [-8]]))
linear_model2 = MyLR(np.array([[89.0], [-6]]))
Y_model1 = linear_model1.predict_(Xpill)
Y_model2 = linear_model2.predict_(Xpill)
linear_model1.plot(Xpill, Yscore)
# plot(Xpill, Yscore, np.array([89.0, -8.0]))
# print(linear_model2.mse_(Xpill, Yscore))
from my_linear_regression import MyLinearRegression
from polynomial_model import add_polynomial_features
if __name__ == "__main__":
x = np.arange(1, 11).reshape(-1, 1)
y = np.array([[1.39270298], [3.88237651], [4.37726357], [4.63389049],
[7.79814439], [6.41717461], [8.63429886], [8.19939795],
[10.37567392], [10.68238222]])
plt.scatter(x, y)
plt.show()
i = 2
arr = np.zeros(9)
l = list(range(2, 11))
while i <= 10:
x_ = add_polynomial_features(x, i)
my_lr = MyLinearRegression(np.ones(i + 1).reshape(-1, 1))
my_lr.fit_(x_, y)
arr[i - 2] = (my_lr.cost_(my_lr.predict_(x_), y))
continuous_x = np.arange(1, 10.01, 0.01).reshape(-1, 1)
x_ = add_polynomial_features(continuous_x, i)
y_hat = my_lr.predict_(x_)
plt.scatter(x, y)
plt.plot(continuous_x, y_hat, color='orange')
plt.show()
i += 1
plt.bar(l, arr, color='orange')
plt.show()
print(arr)
#for plotting of polynomial curves - cotinuous data set over range of original data
#then add polynomial features and normalise
continuous_x = np.arange(1, 7.01, 0.01).reshape(-1, 1)
x_ = add_polynomial_features(continuous_x, 10)
for i in range(10):
x_[:, i] = minmax(x_[:, i])
thetas = np.ones(11).reshape(-1, 1)
cost_values = []
thetas_list = []
mlr = MLR(thetas, alpha=0.009, n_cycle=5000)
for degree in range(2, 11):
mlr.thetas = thetas[:degree + 1]
thetas_list.append(mlr.fit_(new_train[:, :degree], y_train))
cost_values.append(
mlr.mse_(y_train,
mlr.predict_(new_train[:, :degree])[1]))
i = 2
for elem in thetas_list:
mlr.thetas = elem
y_hat = mlr.predict_(x_[:, :i])[1]
plt.plot(continuous_x, y_hat, '--')
plt.title(str(degree))
plt.title(('degree = ' + str(i) + ' cost: ' + str(cost_values[i - 2])))
plt.plot(x_train, y_train, 'go')
plt.plot(x_test, y_test, 'ro')
plt.show()
i += 1
Xpill = np.array(data["Micrograms"]).reshape(-1,1)
Yscore = np.array(data["Score"]).reshape(-1,1)
thetas = np.array([1, 1])
#plt.plot(Xpill, Yscore, 'o')
mlr = MyLR(thetas, alpha=0.05, n_cycle=5000)
#th = mlr.fit_(Xpill, Yscore)
#print(th)
#plt.plot(Xpill, (th[1] * Xpill + th[0]), '-r')
#plt.show()
for j in range(80, 100, 5):
res = []
for i in range(-11, -7, 1):
mlr.thetas = np.array([j, i])
dummy, y_hat = mlr.predict_(Xpill)
res.append(mlr.mse_(Yscore, y_hat))
np.array(res)
plt.plot(np.arange(-11, -7), res)
plt.show()
for j in range(80, 100, 5):
res = []
for i in range(-11, -7, 1):
mlr.thetas = np.array([j, i])
dummy, y_hat = mlr.predict_(Xpill)
res.append(mean_squared_error(Yscore, y_hat))
np.array(res)
plt.plot(np.arange(-11, -7), res, '-r')
plt.show()
array2 = n[sep:, :]
return (array1[:, :-1], array2[:, :-1], array1[:, -1], array2[:, -1])
if __name__ == "__main__":
data = pd.read_csv("../resources/are_blue_pills_magics.csv")
x = np.array(data[['Micrograms']])
y = np.array(data[['Score']])
lst = data_spliter(x, y, 0.5)
x_train = lst[0]
y_train = lst[2]
y_train = y_train[:, np.newaxis]
x_test = lst[1]
y_test = lst[3]
y_test = y_test[:, np.newaxis]
i = 2
my_lr = MyLinearRegression([[1], [1]])
my_lr.fit_(x_train, y_train)
y_hat = my_lr.predict_(x_test)
print(my_lr.cost_(y_hat, y_test))
while i <= 10:
x_ = add_polynomial_features(x_train, i)
my_lr = MyLinearRegression(np.ones(i + 1).reshape(-1, 1))
my_lr.fit_(x_, y_train)
x_2 = add_polynomial_features(x_test, i)
y_hat = my_lr.predict_(x_2)
print(my_lr.cost_(y_hat, y_test))
i += 1
lr6 = MLR([1, 1, 1, 1, 1, 1, 1, 1]) lr7 = MLR([1, 1, 1, 1, 1, 1, 1, 1, 1]) lr8 = MLR([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) lr9 = MLR([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) lr1.fit_(x1, Y) lr2.fit_(x2, Y) lr3.fit_(x3, Y) lr4.fit_(x4, Y) #lr5.fit_(x5, Y) #lr6.fit_(x6, Y) #lr7.fit_(x7, Y) #lr8.fit_(x8, Y) #lr9.fit_(x9, Y) y_1 = lr1.predict_(x1) y_2 = lr2.predict_(x2) y_3 = lr3.predict_(x3) y_4 = lr4.predict_(x4) #y_5 = lr5.predict_(x5) #y_6 = lr6.predict_(x6) #y_7 = lr7.predict_(x7) #y_8 = lr8.predict_(x8) #y_9 = lr9.predict_(x9) print(lr3.cost_(x3, Y)) plt.plot(X, Y, 'o') plt.plot(X, y_1, 'g') plt.plot(X, y_2, 'r') plt.plot(X, y_3, 'b')
y_test = np.array([39, 52, 70, 58, 50, 32, 62]).reshape(-1, 1) plt.plot(x_test, y_test, 'o') new = add_polynomial_features(x, 10) thetas = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] cost_values = [] #for plotting of polynomial curves - cotinuous data set over range of original data continuous_x = np.arange(1, 7.01, 0.01).reshape(-1, 1) x_ = add_polynomial_features(continuous_x, 10) degree = 2 mlr = MLR(np.array(thetas[:degree + 1]), alpha=0.002, n_cycle=1500) mlr.fit_(new[:, :degree], y) cost_values.append(mlr.mse_(y, mlr.predict_(new[:, :degree])[1])) y_hat = mlr.predict_(x_[:, :degree])[1] plt.plot(continuous_x, y_hat, '--') plt.title(str(degree)) plt.show() degree = 3 mlr = MLR(np.array(thetas[:degree + 1]), alpha=0.00005, n_cycle=4000) mlr.fit_(new[:, :degree], y) cost_values.append(mlr.mse_(y, mlr.predict_(new[:, :degree])[1])) y_hat = mlr.predict_(x_[:, :degree])[1] plt.plot(x, y, 'o') plt.plot(continuous_x, y_hat, '--') plt.title(str(degree)) plt.show()
import numpy as np
from my_linear_regression import MyLinearRegression as MyLR
x = np.array([12.4956442, 21.5007972, 31.5527382, 48.9145838, 57.5088733])
y = np.array([37.4013816, 36.1473236, 45.7655287, 46.6793434, 59.5585554])
lr1 = MyLR([2, 0.7])
# Example 0.0:
print("Example 0.0")
print(lr1.predict_(x))
# Output:
# array([[10.74695094],
# [17.05055804],
# [24.08691674],
# [36.24020866],
# [42.25621131]])
# Example 0.1:
print("\nExample 0.1")
print(lr1.cost_elem_(lr1.predict_(x), y))
# Output:
# array([[77.72116511],
# [49.33699664],
# [72.38621816],
# [37.29223426],
# [78.28360514]])
# Example 0.2:
print("\nExample 0.2")
print(lr1.cost_(lr1.predict_(x), y))
def print_costfn(t0, y):
for i in np.linspace(t0 - 10, t0 + 50, 3000):
linear_model3 = MyLR(np.array([[-10], [i]]))
Y_model3 = linear_model3.predict_(Xpill)
plt.plot(linear_model3.thetas[1], linear_model3.cost_(y, Y_model3),
'gs')
plt.title(data.columns[i])
plt.plot(x_test[:, i:i + 1], y_test, 'ro', markersize=3)
plt.show()
#initialise thetas as array with feature number + 1 zeros
thetas = np.zeros(new_features.shape[1] + 1)
#should be able to use same alpha and cycle number for all, as same data
#carry out linear regression on training data
cost_list = []
mlr = MLR(thetas, alpha=0.1, n_cycle=400)
mlr.fit_(x_train, y_train)
y_hat = mlr.predict_(x_test)[1]
cost_list.append(mlr.mse_(y_test, y_hat))
plot(x_test, y_test, y_hat, features)
#carry out 9 ridge regressions on training data, with lambda from 0.1 to 0.9
mrg = MRG(thetas, alpha=0.1, n_cycle=400)
for i in range(1, 10):
mrg.lambda_ = i / 10
mrg.thetas = thetas
plt.title('lambda = ' + str(i / 10))
mrg.fit_(x_train, y_train)
y_hat = mrg.predict_(x_test)[1]
cost_list.append(mlr.mse_(y_test, y_hat))
#plot(x_test, y_test, y_hat, features)