如何在学习中定义成本函数，千层面

Question

我正在nolearn中做一个神经网络，这是一个基于Theano的库，使用千层面。

我不明白如何定义我自己的成本函数。

输出层只有3个神经元[0, 1, 2]，我希望它在给出1或2时基本确定，但否则-如果它不确定1,2 -简单地返回0。

所以，我想出了一个成本函数(需要调优)，其中1和2的成本是0的两倍，但我不明白如何告诉网络。

# optimization method:
from lasagne.updates import sgd
update=sgd,
update_learning_rate=0.0001

这是更新的代码，但是我如何告诉SGD使用我的成本函数而不是它自己的?

编辑:

完整的净代码是:

def nn_loss(data, x_period, columns, num_epochs, batchsize, l_rate=0.02):
    net1 = NeuralNet(
        layers=[('input', layers.InputLayer),
                ('hidden1', layers.DenseLayer),
                ('output', layers.DenseLayer),
                ],
        # layer parameters:
        batch_iterator_train=BatchIterator(batchsize),
        batch_iterator_test=BatchIterator(batchsize),
        input_shape=(None, int(x_period*columns)),
        hidden1_nonlinearity=lasagne.nonlinearities.rectify,
        hidden1_num_units=100,  # number of units in 'hidden' layer
        output_nonlinearity=lasagne.nonlinearities.sigmoid,
        output_num_units=3,
        # optimization method:
        update=nesterov_momentum,
        update_learning_rate=5*10**(-3),
        update_momentum=0.9,
        on_epoch_finished=[
            EarlyStopping(patience=20),
        ],
        max_epochs=num_epochs,
        verbose=1,
        # Here are the important parameters for multi labels
        regression=True,
        # objective_loss_function=multilabel_objective,
        # custom_score=("validation score", lambda x, y: np.mean(np.abs(x - y)))
        )
    # Train the network
    start_time = time.time()
    net1.fit(data['X_train'], data['y_train'])
}

编辑使用regression=True

时出错

Got 99960 testing datasets.
# Neural Network with 18403 learnable parameters
## Layer information
  #  name       size
---  -------  ------
  0  input       180
  1  hidden1     100
  2  output        3
Traceback (most recent call last):
  File "/Users/morgado/anaconda/lib/python3.4/site-packages/theano/compile/function_module.py", line 607, in __call__
    outputs = self.fn()
ValueError: GpuElemwise. Input dimension mis-match. Input 1 (indices start at 0) has shape[1] == 1, but the output's size on that axis is 3.
During handling of the above exception, another exception occurred:
Traceback (most recent call last):
  File "train_nolearn_simple.py", line 272, in <module>
    main(**kwargs)
  File "train_nolearn_simple.py", line 239, in main
    nn_loss_fit = nn_loss(data, x_period, columns, num_epochs, batchsize)
  File "train_nolearn_simple.py", line 217, in nn_loss
    net1.fit(data['X_train'], data['y_train'])
  File "/Users/morgado/anaconda/lib/python3.4/site-packages/nolearn/lasagne/base.py", line 416, in fit
    self.train_loop(X, y)
  File "/Users/morgado/anaconda/lib/python3.4/site-packages/nolearn/lasagne/base.py", line 462, in train_loop
    self.train_iter_, Xb, yb)
  File "/Users/morgado/anaconda/lib/python3.4/site-packages/nolearn/lasagne/base.py", line 516, in apply_batch_func
    return func(Xb) if yb is None else func(Xb, yb)
  File "/Users/morgado/anaconda/lib/python3.4/site-packages/theano/compile/function_module.py", line 618, in __call__
    storage_map=self.fn.storage_map)
  File "/Users/morgado/anaconda/lib/python3.4/site-packages/theano/gof/link.py", line 297, in raise_with_op
    reraise(exc_type, exc_value, exc_trace)
  File "/Users/morgado/anaconda/lib/python3.4/site-packages/six.py", line 658, in reraise
    raise value.with_traceback(tb)
  File "/Users/morgado/anaconda/lib/python3.4/site-packages/theano/compile/function_module.py", line 607, in __call__
    outputs = self.fn()
ValueError: GpuElemwise. Input dimension mis-match. Input 1 (indices start at 0) has shape[1] == 1, but the output's size on that axis is 3.
Apply node that caused the error: GpuElemwise{Sub}[(0, 1)](GpuElemwise{Composite{scalar_sigmoid((i0 + i1))}}[(0, 0)].0, GpuFromHost.0)
Toposort index: 22
Inputs types: [CudaNdarrayType(float32, matrix), CudaNdarrayType(float32, matrix)]
Inputs shapes: [(200, 3), (200, 1)]
Inputs strides: [(3, 1), (1, 0)]
Inputs values: ['not shown', 'not shown']
Outputs clients: [[GpuCAReduce{pre=sqr,red=add}{1,1}(GpuElemwise{Sub}[(0, 1)].0), GpuElemwise{Mul}[(0, 0)](GpuElemwise{Sub}[(0, 1)].0, GpuElemwise{Composite{scalar_sigmoid((i0 + i1))}}[(0, 0)].0, GpuElemwise{sub,no_inplace}.0), GpuElemwise{mul,no_inplace}(CudaNdarrayConstant{[[ 2.]]}, GpuElemwise{Composite{(inv(i0) / i1)},no_inplace}.0, GpuElemwise{Sub}[(0, 1)].0, GpuElemwise{Composite{scalar_sigmoid((i0 + i1))}}[(0, 0)].0, GpuElemwise{sub,no_inplace}.0)]]
HINT: Re-running with most Theano optimization disabled could give you a back-trace of when this node was created. This can be done with by setting the Theano flag 'optimizer=fast_compile'. If that does not work, Theano optimizations can be disabled with 'optimizer=None'.
HINT: Use the Theano flag 'exception_verbosity=high' for a debugprint and storage map footprint of this apply node.

Answer 1

当你实例化你的神经网络时，你可以传递一个你之前定义的自定义损失函数:

import theano.tensor as T
import numpy as np
from nolearn.lasagne import NeuralNet
# I'm skipping other inputs for the sake of concision
def multilabel_objective(predictions, targets):
    epsilon = np.float32(1.0e-6)
    one = np.float32(1.0)
    pred = T.clip(predictions, epsilon, one - epsilon)
    return -T.sum(targets * T.log(pred) + (one - targets) * T.log(one - pred), axis=1)
net = NeuralNet(
    # your other parameters here (layers, update, max_epochs...)
    # here are the one you're interested in:
    objective_loss_function=multilabel_objective,
    custom_score=("validation score", lambda x, y: np.mean(np.abs(x - y)))
    )

正如您所看到的，也可以定义自定义分数(使用关键字custom_score)

Answer 2

请看下面的例子(取自这里)，它指定了自己的损失函数:

import lasagne
import theano.tensor as T
import theano
from lasagne.nonlinearities import softmax
from lasagne.layers import InputLayer, DenseLayer, get_output
from lasagne.updates import sgd, apply_momentum
l_in = InputLayer((100, 20))
l1 = DenseLayer(l_in, num_units=3, nonlinearity=softmax)
x = T.matrix('x')  # shp: num_batch x num_features
y = T.ivector('y') # shp: num_batch
l_out = get_output(l1, x)
params = lasagne.layers.get_all_params(l1)
loss = T.mean(T.nnet.categorical_crossentropy(l_out, y))
updates_sgd = sgd(loss, params, learning_rate=0.0001)
updates = apply_momentum(updates_sgd, params, momentum=0.9)
train_function = theano.function([x, y], updates=updates)

凑巧的是，这段代码在输出层也有三个单元

Answer 3

我在一个分类任务中使用了一个自定义损失函数，我想我也会和你分享。我基本上是想根据标签对训练数据进行不同的强调。

import lasagne
import theano.tensor as T
import theano
def weighted_crossentropy(predictions, targets):
  weights_per_label = theano.shared(lasagne.utils.floatX([0.2, 0.4, 0.4]))
  weights = weights_per_label[targets]  #returns a targets-shaped weight matrix
  loss = lasagne.objectives.aggregate(T.nnet.categorical_crossentropy(predictions, targets), weights=weights)
  return loss
net = NeuralNet(
    # layers and parameters
    objective_loss_function=weighted_crossentropy,
    # ...
    )

这就是我发现如何实现它的地方