为什么这里的套索没有为我提供零系数？

Question

我得到了实现我的版本深特征选择的想法就是从这里开始的纸，http://link.springer.com/chapter/10.1007%2F978-3-319-16706-0_20

根据本文深特征选择的基本思路是之前任何全连接隐藏添加一个一对一的映射层层，然后通过添加正则化项（无论是套索还是弹性网）来在输入层权重中生成零。

我的问题是，即使看起来我已经很好地实现了深度特征选择框架，但在测试由numpy.rand.random（1000,50）生成的随机数据时，未能给出关于初始权重的任何零。像正规化一样，套索是常见的事情吗？我是否会调整我用于这个框架的参数（甚至更大的时代）？或者我的代码有问题吗？

class DeepFeatureSelectionMLP: 
    def __init__(self, X, Y, hidden_dims=[100], epochs=1000, 
       lambda1=0.001, lambda2=1.0, alpha1=0.001, alpha2=0.0, learning_rate=0.1): 
     # Initiate the input layer 

     # Get the dimension of the input X 
     n_sample, n_feat = X.shape 
     n_classes = len(np.unique(Y)) 

     # One hot Y 
     one_hot_Y = np.zeros((len(Y), n_classes)) 
     for i,j in enumerate(Y): 
      one_hot_Y[i][j] = 1 

     self.epochs = epochs 

     Y = one_hot_Y 

     # Store up original value 
     self.X = X 
     self.Y = Y 

     # Two variables with undetermined length is created 
     self.var_X = tf.placeholder(dtype=tf.float32, shape=[None, n_feat], name='x') 
     self.var_Y = tf.placeholder(dtype=tf.float32, shape=[None, n_classes], name='y') 

     self.input_layer = One2OneInputLayer(self.var_X) 

     self.hidden_layers = [] 
     layer_input = self.input_layer.output 

     # Create hidden layers 
     for dim in hidden_dims: 
      self.hidden_layers.append(DenseLayer(layer_input, dim)) 
      layer_input = self.hidden_layers[-1].output 

     # Final classification layer, variable Y is passed 
     self.softmax_layer = SoftmaxLayer(self.hidden_layers[-1].output, n_classes, self.var_Y) 

     n_hidden = len(hidden_dims) 

     # regularization terms on coefficients of input layer 
     self.L1_input = tf.reduce_sum(tf.abs(self.input_layer.w)) 
     self.L2_input = tf.nn.l2_loss(self.input_layer.w) 

     # regularization terms on weights of hidden layers   
     L1s = [] 
     L2_sqrs = [] 
     for i in xrange(n_hidden): 
      L1s.append(tf.reduce_sum(tf.abs(self.hidden_layers[i].w))) 
      L2_sqrs.append(tf.nn.l2_loss(self.hidden_layers[i].w)) 

     L1s.append(tf.reduce_sum(tf.abs(self.softmax_layer.w))) 
     L2_sqrs.append(tf.nn.l2_loss(self.softmax_layer.w)) 

     self.L1 = tf.add_n(L1s) 
     self.L2_sqr = tf.add_n(L2_sqrs) 

     # Cost with two regularization terms 
     self.cost = self.softmax_layer.cost \ 
        + lambda1*(1.0-lambda2)*0.5*self.L2_input + lambda1*lambda2*self.L1_input \ 
        + alpha1*(1.0-alpha2)*0.5 * self.L2_sqr + alpha1*alpha2*self.L1 

     self.optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate).minimize(self.cost) 

     self.y = self.softmax_layer.y 

    def train(self, batch_size=100): 
     sess = tf.Session() 
     sess.run(tf.initialize_all_variables()) 

     for i in xrange(self.epochs): 
      x_batch, y_batch = get_batch(self.X, self.Y, batch_size) 
      sess.run(self.optimizer, feed_dict={self.var_X: x_batch, self.var_Y: y_batch}) 
      if (i + 1) % 50 == 0: 
       l = sess.run(self.cost, feed_dict={self.var_X: x_batch, self.var_Y: y_batch}) 
       print('epoch {0}: global loss = {1}'.format(i, l)) 
       self.selected_w = sess.run(self.input_layer.w) 
       print(self.selected_w) 

class One2OneInputLayer(object): 
    # One to One Mapping! 
    def __init__(self, input): 
     """ 
      The second dimension of the input, 
      for each input, each row is a sample 
      and each column is a feature, since 
      this is one to one mapping, n_in equals 
      the number of features 
     """ 
     n_in = input.get_shape()[1].value 

     self.input = input 

     # Initiate the weight for the input layer 
     w = tf.Variable(tf.zeros([n_in,]), name='w') 

     self.w = w 
     self.output = self.w * self.input 
     self.params = [w] 

class DenseLayer(object): 
    # Canonical dense layer 
    def __init__(self, input, n_out, activation='sigmoid'): 
     """ 
      The second dimension of the input, 
      for each input, each row is a sample 
      and each column is a feature, since 
      this is one to one mapping, n_in equals 
      the number of features 

      n_out defines how many nodes are there in the 
      hidden layer 
     """ 
     n_in = input.get_shape()[1].value 
     self.input = input 

     # Initiate the weight for the input layer 

     w = tf.Variable(tf.ones([n_in, n_out]), name='w') 
     b = tf.Variable(tf.ones([n_out]), name='b') 

     output = tf.add(tf.matmul(input, w), b) 
     output = activate(output, activation) 

     self.w = w 
     self.b = b 
     self.output = output 
     self.params = [w] 

class SoftmaxLayer(object): 
    def __init__(self, input, n_out, y): 
     """ 
      The second dimension of the input, 
      for each input, each row is a sample 
      and each column is a feature, since 
      this is one to one mapping, n_in equals 
      the number of features 

      n_out defines how many nodes are there in the 
      hidden layer 
     """ 
     n_in = input.get_shape()[1].value 
     self.input = input 

     # Initiate the weight and biases for this layer 
     w = tf.Variable(tf.random_normal([n_in, n_out]), name='w') 
     b = tf.Variable(tf.random_normal([n_out]), name='b') 

     pred = tf.add(tf.matmul(input, w), b) 

     cost = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(pred, y)) 

     self.y = y 
     self.w = w 
     self.b = b 
     self.cost = cost 
     self.params= [w] 

Answer 1

诸如Adam的渐变下降算法在使用l1正则化时不给出确切的零。相反，类似ftrl或proximal adagrad可以给你确切的零。