使用TensorFlow的递归神经网络（LSTM）进行序列预测

本篇文章介绍使用TensorFlow的递归神经网络（LSTM）进行序列预测。作者在网上找到的使用LSTM模型的案例都是解决自然语言处理的问题，而没有一个是来预测连续值的。

所以呢，这里是基于历史观察数据进行实数序列的预测。传统的神经网络模型并不能解决这种问题，进而开发出递归神经网络模型，递归神经网络模型可以存储历史数据来预测未来的事情。

在这个例子里将预测几个函数：

• 正弦函数：sin

• 同时存在正弦函数和余弦函数：sin和cos

• x＊sin(x)

首先，建立LSTM模型，lstm_model，这个模型有一系列的不同时间步的lstm单元（cell），紧跟其后的是稠密层。

def lstm_model(time_steps, rnn_layers, dense_layers=None):
     def lstm_cells(layers):
         if isinstance(layers[0], dict):
             return [tf.nn.rnn_cell.DropoutWrapper(tf.nn.rnn_cell.BasicLSTMCell(layer['steps']), layer['keep_prob'])
                     if layer.get('keep_prob') else tf.nn.rnn_cell.BasicLSTMCell(layer['steps'])
                     for layer in layers]
         return [tf.nn.rnn_cell.BasicLSTMCell(steps) for steps in layers]
     def dnn_layers(input_layers, layers):
         if layers and isinstance(layers, dict):
             return skflow.ops.dnn(input_layers,
                                   layers['layers'],
                                   activation=layers.get('activation'),
                                   dropout=layers.get('dropout'))
         elif layers:
             return skflow.ops.dnn(input_layers, layers)
         else:
             return input_layers
     def _lstm_model(X, y):
         stacked_lstm = tf.nn.rnn_cell.MultiRNNCell(lstm_cells(rnn_layers))
         x_ = skflow.ops.split_squeeze(1, time_steps, X)
         output, layers = tf.nn.rnn(stacked_lstm, x_, dtype=dtypes.float32)
         output = dnn_layers(output[-1], dense_layers)
         return skflow.models.linear_regression(output, y)
     return _lstm_model

所建立的模型期望输入数据的维度与（batch size，第一个lstm cell的时间步长time_step，特征数量num_features）相关。 
接下来我们按模型所能接受的数据方式来准备数据。

def rnn_data(data, time_steps, labels=False):
    """
    creates new data frame based on previous observation
      * example:
        l = [1, 2, 3, 4, 5]
        time_steps = 2
        -> labels == False [[1, 2], [2, 3], [3, 4]]
        -> labels == True [2, 3, 4, 5]
    """
    rnn_df = []
    for i in range(len(data) - time_steps):
        if labels:
            try:
                rnn_df.append(data.iloc[i + time_steps].as_matrix())
            except AttributeError:
                rnn_df.append(data.iloc[i + time_steps])
        else:
            data_ = data.iloc[i: i + time_steps].as_matrix()
            rnn_df.append(data_ if len(data_.shape) > 1 else [[i] for i in data_])
    return np.array(rnn_df)
def split_data(data, val_size=0.1, test_size=0.1):
    """
    splits data to training, validation and testing parts
    """
    ntest = int(round(len(data) * (1 - test_size)))
    nval = int(round(len(data.iloc[:ntest]) * (1 - val_size)))
    df_train, df_val, df_test = data.iloc[:nval], data.iloc[nval:ntest], data.iloc[ntest:]
    return df_train, df_val, df_test
def prepare_data(data, time_steps, labels=False, val_size=0.1, test_size=0.1):
    """
    Given the number of `time_steps` and some data.
    prepares training, validation and test data for an lstm cell.
    """
    df_train, df_val, df_test = split_data(data, val_size, test_size)
    return (rnn_data(df_train, time_steps, labels=labels),
            rnn_data(df_val, time_steps, labels=labels),
            rnn_data(df_test, time_steps, labels=labels))
def generate_data(fct, x, time_steps, seperate=False):
    """generate data with based on a function fct"""
    data = fct(x)
    if not isinstance(data, pd.DataFrame):
        data = pd.DataFrame(data)
    train_x, val_x, test_x = prepare_data(data['a'] if seperate else data, time_steps)
    train_y, val_y, test_y = prepare_data(data['b'] if seperate else data, time_steps, labels=True)
    return dict(train=train_x, val=val_x, test=test_x), dict(train=train_y, val=val_y, test=test

这将会创建一个数据让模型可以查找过去time_steps步来预测数据。比如，LSTM模型的第一个cell是10 time_steps cell，为了做预测我们需要输入10个历史数据点。y值跟我们想预测的第十个值相关。 
现在创建一个基于LSTM模型的回归量。

regressor = skflow.TensorFlowEstimator(model_fn=lstm_model(TIMESTEPS, RNN_LAYERS, DENSE_LAYERS),
                                       n_classes=0,
                                       verbose=1,
                                       steps=TRAINING_STEPS,
                                       optimizer='Adagrad',
                                       learning_rate=0.03,
                                       batch_size=BATCH_SIZE)

预测sin函数

X, y = generate_data(np.sin, np.linspace(0, 100, 10000), TIMESTEPS, seperate=False)
# create a lstm instance and validation monitor
validation_monitor = skflow.monitors.ValidationMonitor(X['val'], y['val'], n_classes=0,
                                                       print_steps=PRINT_STEPS,
                                                       early_stopping_rounds=1000,
                                                       logdir=LOG_DIR)
regressor.fit(X['train'], y['train'], validation_monitor, logdir=LOG_DIR)
# > last training steps
# Step #9700, epoch #119, avg. train loss: 0.00082, avg. val loss: 0.00084
# Step #9800, epoch #120, avg. train loss: 0.00083, avg. val loss: 0.00082
# Step #9900, epoch #122, avg. train loss: 0.00082, avg. val loss: 0.00082
# Step #10000, epoch #123, avg. train loss: 0.00081, avg. val loss: 0.00081

预测测试数据

mse = mean_squared_error(regressor.predict(X['test']), y['test'])
print ("Error: {}".format(mse))
# 0.000776

真实sin函数

预测sin函数

预测sin和cos混合函数

def sin_cos(x):
    return pd.DataFrame(dict(a=np.sin(x), b=np.cos(x)), index=x)
X, y = generate_data(sin_cos, np.linspace(0, 100, 10000), TIMESTEPS, seperate=False)
# create a lstm instance and validation monitor
validation_monitor = skflow.monitors.ValidationMonitor(X['val'], y['val'], n_classes=0,
                                                       print_steps=PRINT_STEPS,
                                                       early_stopping_rounds=1000,
                                                       logdir=LOG_DIR)
regressor.fit(X['train'], y['train'], validation_monitor, logdir=LOG_DIR)
# > last training steps
# Step #9500, epoch #117, avg. train loss: 0.00120, avg. val loss: 0.00118
# Step #9600, epoch #118, avg. train loss: 0.00121, avg. val loss: 0.00118
# Step #9700, epoch #119, avg. train loss: 0.00118, avg. val loss: 0.00118
# Step #9800, epoch #120, avg. train loss: 0.00118, avg. val loss: 0.00116
# Step #9900, epoch #122, avg. train loss: 0.00118, avg. val loss: 0.00115
# Step #10000, epoch #123, avg. train loss: 0.00117, avg. val loss: 0.00115

预测测试数据

mse = mean_squared_error(regressor.predict(X['test']), y['test'])
print ("Error: {}".format(mse))
# 0.001144

真实的sin_cos函数

预测的sin_cos函数

预测x*sin函数

def x_sin(x):
     return x * np.sin(x)
 X, y = generate_data(x_sin, np.linspace(0, 100, 10000), TIMESTEPS, seperate=False)
 # create a lstm instance and validation monitor
 validation_monitor = skflow.monitors.ValidationMonitor(X['val'], y['val'], n_classes=0,
                                                        print_steps=PRINT_STEPS,
                                                        early_stopping_rounds=1000,
                                                        logdir=LOG_DIR)
 regressor.fit(X['train'], y['train'], validation_monitor, logdir=LOG_DIR)
 # > last training steps
 # Step #32500, epoch #401, avg. train loss: 0.48248, avg. val loss: 15.98678
 # Step #33800, epoch #417, avg. train loss: 0.47391, avg. val loss: 15.92590
 # Step #35100, epoch #433, avg. train loss: 0.45570, avg. val loss: 15.77346
 # Step #36400, epoch #449, avg. train loss: 0.45853, avg. val loss: 15.61680
 # Step #37700, epoch #465, avg. train loss: 0.44212, avg. val loss: 15.48604
 # Step #39000, epoch #481, avg. train loss: 0.43224, avg. val loss: 15.43947

预测测试数据

mse = mean_squared_error(regressor.predict(X['test']), y['test'])
print ("Error: {}".format(mse))
# 61.024454351

真实的x*sin函数

预测的x*sin函数