- Microsoft Cognitive Toolkit (CNTK) 教程
- 首页
- 简介
- 入门
- CPU 和 GPU
- CNTK - 序列分类
- CNTK - 逻辑回归模型
- CNTK - 神经网络 (NN) 概念
- CNTK - 创建第一个神经网络
- CNTK - 训练神经网络
- CNTK - 内存数据集和大型数据集
- CNTK - 性能评估
- 神经网络分类
- 神经网络二元分类
- CNTK - 神经网络回归
- CNTK - 分类模型
- CNTK - 回归模型
- CNTK - 内存外数据集
- CNTK - 监控模型
- CNTK - 卷积神经网络
- CNTK - 循环神经网络
- Microsoft Cognitive Toolkit 资源
- Microsoft Cognitive Toolkit - 快速指南
- Microsoft Cognitive Toolkit - 资源
- Microsoft Cognitive Toolkit - 讨论
CNTK - 逻辑回归模型
本章介绍如何在 CNTK 中构建逻辑回归模型。
逻辑回归模型基础
逻辑回归是最简单的机器学习技术之一，尤其适用于二元分类。换句话说，在预测变量的值只能是两个分类值之一的情况下创建预测模型。逻辑回归最简单的例子之一是根据一个人的年龄、声音、头发等预测该人是男性还是女性。
示例
让我们借助另一个示例从数学上理解逻辑回归的概念：
假设我们想根据申请人的**负债、收入**和**信用评级**来预测贷款申请的信用价值；0 表示拒绝，1 表示批准。我们用 X1 表示负债，用 X2 表示收入，用 X3 表示信用评级。
在逻辑回归中，我们为每个特征确定一个权重值，用**w**表示，以及一个偏差值，用**b**表示。
现在假设：
X1 = 3.0 X2 = -2.0 X3 = 1.0
并且假设我们确定权重和偏差如下：
W1 = 0.65, W2 = 1.75, W3 = 2.05 and b = 0.33
现在，为了预测类别，我们需要应用以下公式：
Z = (X1*W1)+(X2*W2)+(X3+W3)+b i.e. Z = (3.0)*(0.65) + (-2.0)*(1.75) + (1.0)*(2.05) + 0.33 = 0.83
接下来，我们需要计算**P = 1.0/(1.0 + exp(-Z))**。这里，exp() 函数是欧拉数。
P = 1.0/(1.0 + exp(-0.83) = 0.6963
P 值可以解释为类别为 1 的概率。如果 P < 0.5，则预测类别 = 0，否则预测 (P >= 0.5) 类别 = 1。
为了确定权重和偏差的值，我们必须获得一组训练数据，其中包含已知的输入预测变量值和已知的正确类别标签值。之后，我们可以使用一种算法（通常是梯度下降）来查找权重和偏差的值。
LR 模型实现示例
对于此 LR 模型，我们将使用以下数据集：
1.0, 2.0, 0 3.0, 4.0, 0 5.0, 2.0, 0 6.0, 3.0, 0 8.0, 1.0, 0 9.0, 2.0, 0 1.0, 4.0, 1 2.0, 5.0, 1 4.0, 6.0, 1 6.0, 5.0, 1 7.0, 3.0, 1 8.0, 5.0, 1
要在 CNTK 中开始此 LR 模型的实现，我们需要首先导入以下包：
import numpy as np import cntk as C
程序的结构如下，使用 main() 函数：
def main():
print("Using CNTK version = " + str(C.__version__) + "\n")
现在，我们需要将训练数据加载到内存中，如下所示：
data_file = ".\\dataLRmodel.txt"
print("Loading data from " + data_file + "\n")
features_mat = np.loadtxt(data_file, dtype=np.float32, delimiter=",", skiprows=0, usecols=[0,1])
labels_mat = np.loadtxt(data_file, dtype=np.float32, delimiter=",", skiprows=0, usecols=[2], ndmin=2)
现在，我们将创建一个训练程序，该程序创建一个与训练数据兼容的逻辑回归模型：
features_dim = 2 labels_dim = 1 X = C.ops.input_variable(features_dim, np.float32) y = C.input_variable(labels_dim, np.float32) W = C.parameter(shape=(features_dim, 1)) # trainable cntk.Parameter b = C.parameter(shape=(labels_dim)) z = C.times(X, W) + b p = 1.0 / (1.0 + C.exp(-z)) model = p
现在，我们需要创建学习器和训练器，如下所示：
ce_error = C.binary_cross_entropy(model, y) # CE a bit more principled for LR fixed_lr = 0.010 learner = C.sgd(model.parameters, fixed_lr) trainer = C.Trainer(model, (ce_error), [learner]) max_iterations = 4000
LR 模型训练
一旦我们创建了 LR 模型，接下来就是开始训练过程：
np.random.seed(4)
N = len(features_mat)
for i in range(0, max_iterations):
row = np.random.choice(N,1) # pick a random row from training items
trainer.train_minibatch({ X: features_mat[row], y: labels_mat[row] })
if i % 1000 == 0 and i > 0:
mcee = trainer.previous_minibatch_loss_average
print(str(i) + " Cross-entropy error on curr item = %0.4f " % mcee)
现在，借助以下代码，我们可以打印模型权重和偏差：
np.set_printoptions(precision=4, suppress=True)
print("Model weights: ")
print(W.value)
print("Model bias:")
print(b.value)
print("")
if __name__ == "__main__":
main()
训练逻辑回归模型 -完整示例
import numpy as np
import cntk as C
def main():
print("Using CNTK version = " + str(C.__version__) + "\n")
data_file = ".\\dataLRmodel.txt" # provide the name and the location of data file
print("Loading data from " + data_file + "\n")
features_mat = np.loadtxt(data_file, dtype=np.float32, delimiter=",", skiprows=0, usecols=[0,1])
labels_mat = np.loadtxt(data_file, dtype=np.float32, delimiter=",", skiprows=0, usecols=[2], ndmin=2)
features_dim = 2
labels_dim = 1
X = C.ops.input_variable(features_dim, np.float32)
y = C.input_variable(labels_dim, np.float32)
W = C.parameter(shape=(features_dim, 1)) # trainable cntk.Parameter
b = C.parameter(shape=(labels_dim))
z = C.times(X, W) + b
p = 1.0 / (1.0 + C.exp(-z))
model = p
ce_error = C.binary_cross_entropy(model, y) # CE a bit more principled for LR
fixed_lr = 0.010
learner = C.sgd(model.parameters, fixed_lr)
trainer = C.Trainer(model, (ce_error), [learner])
max_iterations = 4000
np.random.seed(4)
N = len(features_mat)
for i in range(0, max_iterations):
row = np.random.choice(N,1) # pick a random row from training items
trainer.train_minibatch({ X: features_mat[row], y: labels_mat[row] })
if i % 1000 == 0 and i > 0:
mcee = trainer.previous_minibatch_loss_average
print(str(i) + " Cross-entropy error on curr item = %0.4f " % mcee)
np.set_printoptions(precision=4, suppress=True)
print("Model weights: ")
print(W.value)
print("Model bias:")
print(b.value)
if __name__ == "__main__":
main()
输出
Using CNTK version = 2.7 1000 cross entropy error on curr item = 0.1941 2000 cross entropy error on curr item = 0.1746 3000 cross entropy error on curr item = 0.0563 Model weights: [-0.2049] [0.9666]] Model bias: [-2.2846]
使用训练好的 LR 模型进行预测
一旦 LR 模型经过训练，我们就可以像下面这样使用它进行预测：
首先，我们的评估程序导入 numpy 包并将训练数据加载到特征矩阵和类别标签矩阵中，与我们上面实现的训练程序相同：
import numpy as np def main(): data_file = ".\\dataLRmodel.txt" # provide the name and the location of data file features_mat = np.loadtxt(data_file, dtype=np.float32, delimiter=",", skiprows=0, usecols=(0,1)) labels_mat = np.loadtxt(data_file, dtype=np.float32, delimiter=",", skiprows=0, usecols=[2], ndmin=2)
接下来，是时候设置训练程序确定的权重和偏差的值了：
print("Setting weights and bias values \n")
weights = np.array([0.0925, 1.1722], dtype=np.float32)
bias = np.array([-4.5400], dtype=np.float32)
N = len(features_mat)
features_dim = 2
接下来，我们的评估程序将通过遍历每个训练项来计算逻辑回归概率，如下所示：
print("item pred_prob pred_label act_label result")
for i in range(0, N): # each item
x = features_mat[i]
z = 0.0
for j in range(0, features_dim):
z += x[j] * weights[j]
z += bias[0]
pred_prob = 1.0 / (1.0 + np.exp(-z))
pred_label = 0 if pred_prob < 0.5 else 1
act_label = labels_mat[i]
pred_str = ‘correct’ if np.absolute(pred_label - act_label) < 1.0e-5 \
else ‘WRONG’
print("%2d %0.4f %0.0f %0.0f %s" % \ (i, pred_prob, pred_label, act_label, pred_str))
现在让我们演示如何进行预测：
x = np.array([9.5, 4.5], dtype=np.float32)
print("\nPredicting class for age, education = ")
print(x)
z = 0.0
for j in range(0, features_dim):
z += x[j] * weights[j]
z += bias[0]
p = 1.0 / (1.0 + np.exp(-z))
print("Predicted p = " + str(p))
if p < 0.5: print("Predicted class = 0")
else: print("Predicted class = 1")
完整的预测评估程序
import numpy as np
def main():
data_file = ".\\dataLRmodel.txt" # provide the name and the location of data file
features_mat = np.loadtxt(data_file, dtype=np.float32, delimiter=",",
skiprows=0, usecols=(0,1))
labels_mat = np.loadtxt(data_file, dtype=np.float32, delimiter=",",
skiprows=0, usecols=[2], ndmin=2)
print("Setting weights and bias values \n")
weights = np.array([0.0925, 1.1722], dtype=np.float32)
bias = np.array([-4.5400], dtype=np.float32)
N = len(features_mat)
features_dim = 2
print("item pred_prob pred_label act_label result")
for i in range(0, N): # each item
x = features_mat[i]
z = 0.0
for j in range(0, features_dim):
z += x[j] * weights[j]
z += bias[0]
pred_prob = 1.0 / (1.0 + np.exp(-z))
pred_label = 0 if pred_prob < 0.5 else 1
act_label = labels_mat[i]
pred_str = ‘correct’ if np.absolute(pred_label - act_label) < 1.0e-5 \
else ‘WRONG’
print("%2d %0.4f %0.0f %0.0f %s" % \ (i, pred_prob, pred_label, act_label, pred_str))
x = np.array([9.5, 4.5], dtype=np.float32)
print("\nPredicting class for age, education = ")
print(x)
z = 0.0
for j in range(0, features_dim):
z += x[j] * weights[j]
z += bias[0]
p = 1.0 / (1.0 + np.exp(-z))
print("Predicted p = " + str(p))
if p < 0.5: print("Predicted class = 0")
else: print("Predicted class = 1")
if __name__ == "__main__":
main()
输出
设置权重和偏差值。
Item pred_prob pred_label act_label result 0 0.3640 0 0 correct 1 0.7254 1 0 WRONG 2 0.2019 0 0 correct 3 0.3562 0 0 correct 4 0.0493 0 0 correct 5 0.1005 0 0 correct 6 0.7892 1 1 correct 7 0.8564 1 1 correct 8 0.9654 1 1 correct 9 0.7587 1 1 correct 10 0.3040 0 1 WRONG 11 0.7129 1 1 correct Predicting class for age, education = [9.5 4.5] Predicting p = 0.526487952 Predicting class = 1
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