ml-class / mlclass / logistic_regression.py

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204``` ```import warnings from scipy.optimize import fmin_l_bfgs_b import numpy as np import scipy.sparse def append_ones(X): m, n = X.shape if scipy.sparse.issparse(X): return scipy.sparse.hstack((np.ones((m, 1)), X)).tocsr() else: return np.column_stack((np.ones(m), X)) def sigmoid(x): return 1.0 / (1.0 + np.exp(-x)) class LogisticRegressionGD: '''Gradient descent''' def __init__(self, lambda_=1, **fmin_args): self.lambda_ = lambda_ self.fmin_args = fmin_args def cost_grad(self, theta, X, y): m = X.shape[0] sx = sigmoid(X.dot(theta)) j = -np.log(np.where(y, sx, 1 - sx)).sum() j += self.lambda_ * theta.dot(theta) / 2.0 j /= m grad = X.T.dot(sx - y) / m grad += self.lambda_ * theta / m return j, grad def fit(self, X, y): theta = np.zeros(X.shape[1]) self.theta, j, ret = fmin_l_bfgs_b(self.cost_grad, theta, args=(X, y), **self.fmin_args) if ret['warnflag'] != 0: warnings.warn('L-BFGS failed to converge') def predict(self, X): return sigmoid(X.dot(self.theta)) class LogisticRegressionNR: '''Newton-Raphson method''' def __init__(self, eps=1e-7): self.eps = eps def fit(self, X, y): self.theta = np.zeros(X.shape[1]) j_prev = 0 while True: # compute the cost, gradient, and the Hessian sx = sigmoid(X.dot(self.theta)) j = y.dot(np.log(sx)) + (1 - y).dot(np.log(1 - sx)) grad = X.T.dot(y - sx) hess = -X.T.dot((sx * (1 - sx))[:,None] * X) if np.abs(j - j_prev) < self.eps: break self.theta -= np.linalg.inv(hess).dot(grad) j_prev = j def predict(self, X): return sigmoid(X.dot(self.theta)) class SoftmaxRegressionGD: def __init__(self, lambda_=1, **fmin_args): self.lambda_ = lambda_ self.fmin_args = fmin_args def cost_grad(self, Theta_flat): m, n = self.X.shape k = self.Y.shape[1] Theta = Theta_flat.reshape((k, n)) P = np.exp(self.X.dot(Theta.T)) P /= np.sum(P, axis=1)[:,None] j = -np.sum(np.log(P) * self.Y) j += self.lambda_ * Theta_flat.dot(Theta_flat) / 2.0 j /= m grad = self.X.T.dot(P - self.Y).T grad += self.lambda_ * Theta grad /= m return j, grad.ravel() def fit(self, X, Y): self.X, self.Y = X, Y theta = np.zeros(Y.shape[1] * X.shape[1]) theta, j, ret = fmin_l_bfgs_b(self.cost_grad, theta, **self.fmin_args) if ret['warnflag'] != 0: warnings.warn('L-BFGS failed to converge') self.Theta = theta.reshape((Y.shape[1], X.shape[1])) def predict(self, X): P = np.exp(X.dot(self.Theta.T)) P /= np.sum(P, axis=1)[:,None] return np.argmax(P, axis=1) if __name__ == '__main__': def softmax(): from data import load_svm X, y = load_svm('../data/iris.scale') Y = np.eye(3)[(y - 1 + 0.5).astype(np.int)] m = SoftmaxRegressionGD(lambda_=0) m.fit(X, Y) print np.mean(m.predict(X) == (y - 1 + 0.5).astype(np.int)) softmax() def ex2(): from data import load_txt X, y = load_txt('../data/ex2data1.txt') X = np.column_stack((np.ones(X.shape[0]), X)) lr = LogisticRegressionGD(lambda_=0) lr.fit(X, y) print('Classifying [45, 85]:', lr.predict(np.array([1, 45, 85]))) print('Training accuracy:', np.mean((lr.predict(X) > 0.5) == y)) # plot data import matplotlib.pyplot as plt xs = [min(X[:, 1]), max(X[:, 1])] ys = [-(lr.theta[1] * x + lr.theta[0]) / lr.theta[2] for x in xs] plt.plot(xs, ys, '-') pos = y == 1 neg = y == 0 plt.plot(X[pos][:, 1], X[pos][:, 2], 'g+') plt.plot(X[neg][:, 1], X[neg][:, 2], 'ro') plt.show() def ex2_reg(): from data import load_txt def map_feature(x, y): cols = [] for sum in range(7): for i in range(sum + 1): cols.append(x ** (sum - i) * y ** i) return np.column_stack(cols) X, y = load_txt('../data/ex2data2.txt') X_mapped = map_feature(X[:, 0], X[:, 1]) lr = LogisticRegressionGD(lambda_=1) lr.fit(X_mapped, y) print('Training accuracy:', np.mean((lr.predict(X_mapped) > 0.5) == y)) # plot data import matplotlib.pyplot as plt u = np.linspace(-1, 1.5, 50) v = np.linspace(-1, 1.5, 50) z = np.zeros((u.size, v.size)) for i in range(u.size): for j in range(v.size): z[j, i] = map_feature(u[i], v[j]).dot(lr.theta) plt.contour(u, v, z, 0) pos = y == 1 neg = y == 0 plt.plot(X[pos][:, 0], X[pos][:, 1], 'g+') plt.plot(X[neg][:, 0], X[neg][:, 1], 'ro') plt.show() def ps1_1(): import matplotlib.pyplot as plt y = np.loadtxt('../data/q1y.dat') X = np.loadtxt('../data/q1x.dat') X = np.column_stack((np.ones_like(y), X)) lr = LogisticRegressionNR() lr.fit(X, y) print lr.theta pos = y == 0 neg = y == 1 plt.plot(X[pos,1], X[pos,2], 'rx') plt.plot(X[neg,1], X[neg,2], 'go') w = lr.theta x = np.array([X[:,1].min(), X[:,1].max()]) y = (-w[1] * x - w[0]) / w[2] plt.plot(x, y) plt.show() ```
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