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

译者信息：侠天，专注于大数据、机器学习和数学相关的内容，并有个人公众号：bigdata_ny分享相关技术文章。

英文原文： Sequence prediction using recurrent neural networks(LSTM) with TensorFlow