def __compute_cost(theta, feat, label):
"""计算代价函数.
Args:
theta: 参数, 维度(特征数).
feat: 特征, 维度(样本数, 特征数).
label: 标签, 维度(样本数).
Returns:
代价函数数值.
"""
hypothesis = sigmoid(np.dot(feat, theta))
cost = np.sum(-np.multiply(label, np.log(hypothesis)) -
np.multiply(1 - label, np.log(1 - hypothesis))) / len(feat)
return cost
def __compute_grad(theta, feat, label):
"""计算梯度.
Args:
theta: 参数, 维度(特征数).
feat: 特征, 维度(样本数, 特征数).
label: 标签, 维度(样本数).
Returns:
梯度数值.
"""
hypothesis = sigmoid(np.dot(feat, theta))
grad = np.sum(np.multiply(
np.tile(hypothesis - label, (feat.shape[1], 1)).T, feat),
axis=0) / len(feat)
return grad
def __compute_cost(theta, feat, label, lambda_factor):
"""计算代价函数.
Args:
theta: 参数, 维度(特征数).
feat: 特征, 维度(样本数, 特征数).
label: 标签, 维度(样本数).
lambda_factor: 正则化因子.
Returns:
代价函数数值.
"""
num = len(feat)
hypothesis = sigmoid(np.dot(feat, theta))
cost = np.sum(-np.multiply(label, np.log(hypothesis)) -
np.multiply(1 - label, np.log(1 - hypothesis))) / num
penalty = lambda_factor / (2 * num) * np.sum(theta[1:])
return cost + penalty
def __compute_grad(theta, feat, label, lambda_factor):
"""计算梯度.
Args:
theta: 参数, 维度(特征数).
feat: 特征, 维度(样本数, 特征数).
label: 标签, 维度(样本数).
lambda_factor: 正则化因子.
Returns:
梯度数值.
"""
num = len(feat)
hypothesis = sigmoid(np.dot(feat, theta))
grad = np.sum(np.multiply(np.tile(hypothesis - label, (feat.shape[1], 1)).T,
feat), axis=0) / num
penalty = np.zeros(len(theta))
penalty[1:] = lambda_factor / num * theta[1:]
return grad + penalty
def __cmd():
"""命令行函数."""
feat, label = load_txt(Path(__file__).parent / 'data1.txt')
num = len(feat) # 样本数
# 样本作图.
ax = __plot_data(feat, label)
# 梯度下降.
init_theta = np.zeros(3)
feat = np.concatenate([np.ones((num, 1)), feat], axis=-1) # 增加全为1的第0列.
optimal = minimize(__compute_cost,
init_theta,
args=(feat, label),
method='TNC',
jac=__compute_grad)
best_theta = optimal['x']
logging.info(f'梯度下降得到的最优参数: [{best_theta[0]:.5f} '
f'{best_theta[1]:.5f} {best_theta[2]:.5f}].')
# 绘出决策边界, sigmoid(theta * feature) = 0.5的直线, 即theta * feature = 0的直线.
boundary_x = np.array([min(feat[:, 1]) - 2, max(feat[:, 2]) + 2])
boundary_y = -1 / best_theta[2] * (boundary_x * best_theta[1] +
best_theta[0])
ax.plot(boundary_x, boundary_y, label='Decision Boundary')
handles, labels = ax.get_legend_handles_labels()
handles = [handles[0], handles[2], handles[1]]
labels = [labels[0], labels[2], labels[1]]
ax.legend(handles, labels)
plt.show()
# 预测.
prob = sigmoid(np.dot(np.array([[1, 45, 85]]), best_theta))[0]
logging.info(f'科目1分数为45, 科目2分数为85时, 入学概率为: {prob:.3f}.')
# 训练集准确率.
prediction = predict(best_theta, feat)
acc = np.sum(prediction == label) / num
logging.info(f'训练集准确率为: {acc * 100:.0f}%.')