尝试使用反向传播神经网络进行多类分类。我找到了this code并尝试去适应它。它基于 Machine Learning in Coursera from Andrew Ng 的选集。
我不太清楚这里scipy.optimize.minimize
函数的实现。它在代码中仅使用一次。是否迭代更新网络的权重?我如何可视化(绘制)它的性能以查看它何时收敛?
使用此功能我可以调整哪些参数以获得更好的性能?我发现here常用参数列表:
- 隐藏层中的神经元数量:这是我代码中的
hidden_layer_size=25
- 学习率:我仍然可以使用内置最小化功能来调整学习率吗?
- 动量:在我的例子中是
reg_lambda=0
吗?正则化参数以避免过度拟合,对吗? - 纪元:
maxiter=500
这是我的训练数据(目标类别在最后一列):
65535, 3670, 65535, 3885, -0.73, 1
65535, 3962, 65535, 3556, -0.72, 1
65535, 3573, 65535, 3529, -0.61, 1
3758, 3123, 4117, 3173, -0.21, 0
3906, 3119, 4288, 3135, -0.28, 0
3750, 3073, 4080, 3212, -0.26, 0
65535, 3458, 65535, 3330, -0.85, 2
65535, 3315, 65535, 3306, -0.87, 2
65535, 3950, 65535, 3613, -0.84, 2
65535, 32576, 65535, 19613, -0.35, 3
65535, 16657, 65535, 16618, -0.37, 3
65535, 16657, 65535, 16618, -0.32, 3
依赖关系如此明显,我想分类应该很容易......
但结果很糟糕。我得到的准确度为 0.6 到 0.8。这绝对不适合我的应用程序。我知道我通常需要更多数据,但是当我至少可以拟合训练数据(不考虑潜在的过度拟合)时我会很高兴
这是代码:
import numpy as np
from scipy import optimize
from sklearn import cross_validation
from sklearn.metrics import accuracy_score
import math
class NN_1HL(object):
def __init__(self, reg_lambda=0, epsilon_init=0.12, hidden_layer_size=25, opti_method='TNC', maxiter=500):
self.reg_lambda = reg_lambda
self.epsilon_init = epsilon_init
self.hidden_layer_size = hidden_layer_size
self.activation_func = self.sigmoid
self.activation_func_prime = self.sigmoid_prime
self.method = opti_method
self.maxiter = maxiter
def sigmoid(self, z):
return 1 / (1 + np.exp(-z))
def sigmoid_prime(self, z):
sig = self.sigmoid(z)
return sig * (1 - sig)
def sumsqr(self, a):
return np.sum(a ** 2)
def rand_init(self, l_in, l_out):
self.epsilon_init = (math.sqrt(6))/(math.sqrt(l_in + l_out))
return np.random.rand(l_out, l_in + 1) * 2 * self.epsilon_init - self.epsilon_init
def pack_thetas(self, t1, t2):
return np.concatenate((t1.reshape(-1), t2.reshape(-1)))
def unpack_thetas(self, thetas, input_layer_size, hidden_layer_size, num_labels):
t1_start = 0
t1_end = hidden_layer_size * (input_layer_size + 1)
t1 = thetas[t1_start:t1_end].reshape((hidden_layer_size, input_layer_size + 1))
t2 = thetas[t1_end:].reshape((num_labels, hidden_layer_size + 1))
return t1, t2
def _forward(self, X, t1, t2):
m = X.shape[0]
ones = None
if len(X.shape) == 1:
ones = np.array(1).reshape(1,)
else:
ones = np.ones(m).reshape(m,1)
# Input layer
a1 = np.hstack((ones, X))
# Hidden Layer
z2 = np.dot(t1, a1.T)
a2 = self.activation_func(z2)
a2 = np.hstack((ones, a2.T))
# Output layer
z3 = np.dot(t2, a2.T)
a3 = self.activation_func(z3)
return a1, z2, a2, z3, a3
def function(self, thetas, input_layer_size, hidden_layer_size, num_labels, X, y, reg_lambda):
t1, t2 = self.unpack_thetas(thetas, input_layer_size, hidden_layer_size, num_labels)
m = X.shape[0]
Y = np.eye(num_labels)[y]
_, _, _, _, h = self._forward(X, t1, t2)
costPositive = -Y * np.log(h).T
costNegative = (1 - Y) * np.log(1 - h).T
cost = costPositive - costNegative
J = np.sum(cost) / m
if reg_lambda != 0:
t1f = t1[:, 1:]
t2f = t2[:, 1:]
reg = (self.reg_lambda / (2 * m)) * (self.sumsqr(t1f) + self.sumsqr(t2f))
J = J + reg
return J
def function_prime(self, thetas, input_layer_size, hidden_layer_size, num_labels, X, y, reg_lambda):
t1, t2 = self.unpack_thetas(thetas, input_layer_size, hidden_layer_size, num_labels)
m = X.shape[0]
t1f = t1[:, 1:]
t2f = t2[:, 1:]
Y = np.eye(num_labels)[y]
Delta1, Delta2 = 0, 0
for i, row in enumerate(X):
a1, z2, a2, z3, a3 = self._forward(row, t1, t2)
# Backprop
d3 = a3 - Y[i, :].T
d2 = np.dot(t2f.T, d3) * self.activation_func_prime(z2)
Delta2 += np.dot(d3[np.newaxis].T, a2[np.newaxis])
Delta1 += np.dot(d2[np.newaxis].T, a1[np.newaxis])
Theta1_grad = (1 / m) * Delta1
Theta2_grad = (1 / m) * Delta2
if reg_lambda != 0:
Theta1_grad[:, 1:] = Theta1_grad[:, 1:] + (reg_lambda / m) * t1f
Theta2_grad[:, 1:] = Theta2_grad[:, 1:] + (reg_lambda / m) * t2f
return self.pack_thetas(Theta1_grad, Theta2_grad)
def fit(self, X, y):
num_features = X.shape[0]
input_layer_size = X.shape[1]
num_labels = len(set(y))
theta1_0 = self.rand_init(input_layer_size, self.hidden_layer_size)
theta2_0 = self.rand_init(self.hidden_layer_size, num_labels)
thetas0 = self.pack_thetas(theta1_0, theta2_0)
options = {'maxiter': self.maxiter}
_res = optimize.minimize(self.function, thetas0, jac=self.function_prime, method=self.method,
args=(input_layer_size, self.hidden_layer_size, num_labels, X, y, 0), options=options)
self.t1, self.t2 = self.unpack_thetas(_res.x, input_layer_size, self.hidden_layer_size, num_labels)
np.savetxt("weights_t1.txt", self.t1, newline="\n")
np.savetxt("weights_t2.txt", self.t2, newline="\n")
def predict(self, X):
return self.predict_proba(X).argmax(0)
def predict_proba(self, X):
_, _, _, _, h = self._forward(X, self.t1, self.t2)
return h
##################
# IR data #
##################
values = np.loadtxt('infrared_data.txt', delimiter=', ', usecols=[0,1,2,3,4])
targets = np.loadtxt('infrared_data.txt', delimiter=', ', dtype=(int), usecols=[5])
X_train, X_test, y_train, y_test = cross_validation.train_test_split(values, targets, test_size=0.4)
nn = NN_1HL()
nn.fit(values, targets)
print("Accuracy of classification: "+str(accuracy_score(y_test, nn.predict(X_test))))
最佳答案
在给定的代码 scipy.optimize.minimize
中,给定函数的导数(雅可比矩阵),迭代地最小化函数。根据文档, use 可以为每次迭代后调用的函数指定回调参数 - 这将让您测量性能,尽管我不确定它是否会让您停止优化流程。
您列出的所有参数都是超参数,很难直接优化它们:
隐藏层中的神经元数量是离散值参数,因此无法通过梯度技术进行优化。此外,它会影响 NeuralNet 架构,因此在训练网络时无法对其进行优化。不过,您可以做的是使用一些更高级别的例程来搜索可能的选项,例如带有交叉验证的详尽网格搜索(例如查看 GridSearchCV )或用于超参数搜索的其他工具( hyperopt 、 spearmint 、 MOE 等) )。
学习率对于大多数可用的优化方法来说似乎都无法定制。但实际上,梯度下降中的学习率只是一种牛顿法,Hessian 方法通过 1/eta I
进行“近似”——对角矩阵,在主对角线上具有倒置的学习率。因此,您可以使用这种启发式尝试基于粗麻布的方法。
动量与正则化完全无关。这是一种优化技术,并且由于您使用 scipy 进行优化,因此不适合您。
关于python - scipy.optimize.minimize 在神经网络中的使用,我们在Stack Overflow上找到一个类似的问题: https://stackoverflow.com/questions/27815580/