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)