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\ -\u0026gt; labels == False [[1, 2], [2, 3], [3, 4]]\ -\u0026gt; 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) \u0026gt; 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)\# \u0026gt; 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)\# \u0026gt; 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)\ # \u0026gt; 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