Keras LSTM如何在多元设置中对多个时间序列进行预测？

我正在尝试使用Keras对多个变量进行同时预测。在这里使用此示例，我想预测所有功能的值，包括pm 2.5，DEWP，TEMP等，而不仅仅是污染（pm 2.5）。本质上，在给定所有变量的情况下，这是建立一个模型来将所有变量作为时间序列进行预测，而不仅仅是预测一个变量。

我使用重塑后的3D数据修改了原始示例代码，但出现了错误。这是代码：

from sklearn.preprocessing import LabelEncoder, MinMaxScaler

from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import LSTM, Dense


from math import sqrt
from numpy import concatenate
from matplotlib import pyplot
from pandas import read_csv
from pandas import DataFrame
from pandas import concat


from pandas import read_csv, DataFrame, concat
from datetime import datetime
# load data
def parse(x):
    return datetime.strptime(x, '%Y %m %d %H')
dataset = read_csv('raw.csv',  parse_dates = [['year', 'month', 'day', 'hour']], index_col=0, date_parser=parse)
dataset.drop('No', axis=1, inplace=True)
# manually specify column names
dataset.columns = ['pollution', 'dew', 'temp', 'press', 'wnd_dir', 'wnd_spd', 'snow', 'rain']
dataset.index.name = 'date'
# mark all NA values with 0
dataset['pollution'].fillna(0, inplace=True)
# drop the first 24 hours
dataset = dataset[24:]
# summarize first 5 rows
print(dataset.head(5))
# save to file
dataset.to_csv('pollution.csv')


# convert series to supervised learning
def series_to_supervised(data, n_in=1, n_out=1, dropnan=True):
    n_vars = 1 if type(data) is list else data.shape[1]
    df = DataFrame(data)
    cols, names = list(), list()
    # input sequence (t-n, ... t-1)
    for i in range(n_in, 0, -1):
        cols.append(df.shift(i))
        names += [('var%d(t-%d)' % (j+1, i)) for j in range(n_vars)]
    # forecast sequence (t, t+1, ... t+n)
    for i in range(0, n_out):
        cols.append(df.shift(-i))
        if i == 0:
            names += [('var%d(t)' % (j+1)) for j in range(n_vars)]
        else:
            names += [('var%d(t+%d)' % (j+1, i)) for j in range(n_vars)]
    # put it all together
    agg = concat(cols, axis=1)
    agg.columns = names
    # drop rows with NaN values
    if dropnan:
        agg.dropna(inplace=True)
    return agg


# load dataset
dataset = read_csv('pollution.csv', header=0, index_col=0)
values = dataset.values
# integer encode direction
encoder = LabelEncoder()
values[:,4] = encoder.fit_transform(values[:,4])
# ensure all data is float
values = values.astype('float32')
# normalize features
scaler = MinMaxScaler(feature_range=(0, 1))
scaled = scaler.fit_transform(values)
# frame as supervised learning
reframed = series_to_supervised(scaled, 1, 1)


# split into train and test sets
values = reframed.values
n_train_hours = 365 * 24
train = values[:n_train_hours, :]
test = values[n_train_hours:, :]
# split into input and outputs
train_X, train_y = train[:, :-8], train[:, -8:]
test_X, test_y = test[:, :-8], test[:, -8:]
# reshape input to be 3D [samples, timesteps, features]
train_X_3d = train_X.reshape((train_X.shape[0], 1, train_X.shape[1]))
test_X_3d = test_X.reshape((test_X.shape[0], 1, test_X.shape[1]))
train_y_3d = train_y.reshape((train_y.shape[0], 1, train_y.shape[1]))
test_y_3d = test_y.reshape((test_y.shape[0], 1, test_y.shape[1]))
print(train_X.shape, train_y.shape, test_X.shape, test_y.shape)
print(train_X_3d.shape, train_y_3d.shape, test_X_3d.shape, test_y_3d.shape)

# design network
model = Sequential()
model.add(LSTM(50, input_shape=(train_X_3d.shape[1], train_X_3d.shape[2])))
#model.add(Dense(1))
model.compile(loss='mae', optimizer='adam')
# fit network
history = model.fit(train_X_3d, train_y_3d, 
                    epochs=50, batch_size=72, 
                    validation_data=(test_X_3d, test_y_3d), verbose=2, shuffle=False)
# plot history
pyplot.plot(history.history['loss'], label='train')
pyplot.plot(history.history['val_loss'], label='test')
pyplot.legend()
pyplot.show()

# make a prediction
yhat = model.predict(test_X_3d)
yhat

输出为：

                     pollution  dew  temp   press wnd_dir  wnd_spd  snow  rain
date                                                                          
2010-01-02 00:00:00      129.0  -16  -4.0  1020.0      SE     1.79     0     0
2010-01-02 01:00:00      148.0  -15  -4.0  1020.0      SE     2.68     0     0
2010-01-02 02:00:00      159.0  -11  -5.0  1021.0      SE     3.57     0     0
2010-01-02 03:00:00      181.0   -7  -5.0  1022.0      SE     5.36     1     0
2010-01-02 04:00:00      138.0   -7  -5.0  1022.0      SE     6.25     2     0
(8760, 8) (8760, 8) (35039, 8) (35039, 8)
(8760, 1, 8) (8760, 1, 8) (35039, 1, 8) (35039, 1, 8)
Train on 8760 samples, validate on 35039 samples
Epoch 1/50
---------------------------------------------------------------------------
InvalidArgumentError                      Traceback (most recent call last)
~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/framework/ops.py in _create_c_op(graph, node_def, inputs, control_inputs)
   1609   try:
-> 1610     c_op = c_api.TF_FinishOperation(op_desc)
   1611   except errors.InvalidArgumentError as e:

InvalidArgumentError: Dimensions must be equal, but are 50 and 8 for 'loss/lstm_loss/sub' (op: 'Sub') with input shapes: [?,50], [?,1,8].

During handling of the above exception, another exception occurred:

ValueError                                Traceback (most recent call last)
<ipython-input-1-00c079ab5854> in <module>
     97 history = model.fit(train_X_3d, train_y_3d, 
     98                     epochs=50, batch_size=72,
---> 99                     validation_data=(test_X_3d, test_y_3d), verbose=2, shuffle=False)
    100 # plot history
    101 pyplot.plot(history.history['loss'], label='train')

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/keras/engine/training.py in fit(self, x, y, batch_size, epochs, verbose, callbacks, validation_split, validation_data, shuffle, class_weight, sample_weight, initial_epoch, steps_per_epoch, validation_steps, validation_freq, max_queue_size, workers, use_multiprocessing, **kwargs)
    726         max_queue_size=max_queue_size,
    727         workers=workers,
--> 728         use_multiprocessing=use_multiprocessing)
    729 
    730   def evaluate(self,

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/keras/engine/training_v2.py in fit(self, model, x, y, batch_size, epochs, verbose, callbacks, validation_split, validation_data, shuffle, class_weight, sample_weight, initial_epoch, steps_per_epoch, validation_steps, validation_freq, **kwargs)
    322                 mode=ModeKeys.TRAIN,
    323                 training_context=training_context,
--> 324                 total_epochs=epochs)
    325             cbks.make_logs(model, epoch_logs, training_result, ModeKeys.TRAIN)
    326 

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/keras/engine/training_v2.py in run_one_epoch(model, iterator, execution_function, dataset_size, batch_size, strategy, steps_per_epoch, num_samples, mode, training_context, total_epochs)
    121         step=step, mode=mode, size=current_batch_size) as batch_logs:
    122       try:
--> 123         batch_outs = execution_function(iterator)
    124       except (StopIteration, errors.OutOfRangeError):
    125         # TODO(kaftan): File bug about tf function and errors.OutOfRangeError?

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/keras/engine/training_v2_utils.py in execution_function(input_fn)
     84     # `numpy` translates Tensors to values in Eager mode.
     85     return nest.map_structure(_non_none_constant_value,
---> 86                               distributed_function(input_fn))
     87 
     88   return execution_function

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/eager/def_function.py in __call__(self, *args, **kwds)
    455 
    456     tracing_count = self._get_tracing_count()
--> 457     result = self._call(*args, **kwds)
    458     if tracing_count == self._get_tracing_count():
    459       self._call_counter.called_without_tracing()

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/eager/def_function.py in _call(self, *args, **kwds)
    501       # This is the first call of __call__, so we have to initialize.
    502       initializer_map = object_identity.ObjectIdentityDictionary()
--> 503       self._initialize(args, kwds, add_initializers_to=initializer_map)
    504     finally:
    505       # At this point we know that the initialization is complete (or less

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/eager/def_function.py in _initialize(self, args, kwds, add_initializers_to)
    406     self._concrete_stateful_fn = (
    407         self._stateful_fn._get_concrete_function_internal_garbage_collected(  # pylint: disable=protected-access
--> 408             *args, **kwds))
    409 
    410     def invalid_creator_scope(*unused_args, **unused_kwds):

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/eager/function.py in _get_concrete_function_internal_garbage_collected(self, *args, **kwargs)
   1846     if self.input_signature:
   1847       args, kwargs = None, None
-> 1848     graph_function, _, _ = self._maybe_define_function(args, kwargs)
   1849     return graph_function
   1850 

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/eager/function.py in _maybe_define_function(self, args, kwargs)
   2148         graph_function = self._function_cache.primary.get(cache_key, None)
   2149         if graph_function is None:
-> 2150           graph_function = self._create_graph_function(args, kwargs)
   2151           self._function_cache.primary[cache_key] = graph_function
   2152         return graph_function, args, kwargs

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/eager/function.py in _create_graph_function(self, args, kwargs, override_flat_arg_shapes)
   2039             arg_names=arg_names,
   2040             override_flat_arg_shapes=override_flat_arg_shapes,
-> 2041             capture_by_value=self._capture_by_value),
   2042         self._function_attributes,
   2043         # Tell the ConcreteFunction to clean up its graph once it goes out of

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/framework/func_graph.py in func_graph_from_py_func(name, python_func, args, kwargs, signature, func_graph, autograph, autograph_options, add_control_dependencies, arg_names, op_return_value, collections, capture_by_value, override_flat_arg_shapes)
    913                                           converted_func)
    914 
--> 915       func_outputs = python_func(*func_args, **func_kwargs)
    916 
    917       # invariant: `func_outputs` contains only Tensors, CompositeTensors,

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/eager/def_function.py in wrapped_fn(*args, **kwds)
    356         # __wrapped__ allows AutoGraph to swap in a converted function. We give
    357         # the function a weak reference to itself to avoid a reference cycle.
--> 358         return weak_wrapped_fn().__wrapped__(*args, **kwds)
    359     weak_wrapped_fn = weakref.ref(wrapped_fn)
    360 

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/keras/engine/training_v2_utils.py in distributed_function(input_iterator)
     71     strategy = distribution_strategy_context.get_strategy()
     72     outputs = strategy.experimental_run_v2(
---> 73         per_replica_function, args=(model, x, y, sample_weights))
     74     # Out of PerReplica outputs reduce or pick values to return.
     75     all_outputs = dist_utils.unwrap_output_dict(

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/distribute/distribute_lib.py in experimental_run_v2(self, fn, args, kwargs)
    758       fn = autograph.tf_convert(fn, ag_ctx.control_status_ctx(),
    759                                 convert_by_default=False)
--> 760       return self._extended.call_for_each_replica(fn, args=args, kwargs=kwargs)
    761 
    762   def reduce(self, reduce_op, value, axis):

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/distribute/distribute_lib.py in call_for_each_replica(self, fn, args, kwargs)
   1785       kwargs = {}
   1786     with self._container_strategy().scope():
-> 1787       return self._call_for_each_replica(fn, args, kwargs)
   1788 
   1789   def _call_for_each_replica(self, fn, args, kwargs):

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/distribute/distribute_lib.py in _call_for_each_replica(self, fn, args, kwargs)
   2130         self._container_strategy(),
   2131         replica_id_in_sync_group=constant_op.constant(0, dtypes.int32)):
-> 2132       return fn(*args, **kwargs)
   2133 
   2134   def _reduce_to(self, reduce_op, value, destinations):

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/autograph/impl/api.py in wrapper(*args, **kwargs)
    290   def wrapper(*args, **kwargs):
    291     with ag_ctx.ControlStatusCtx(status=ag_ctx.Status.DISABLED):
--> 292       return func(*args, **kwargs)
    293 
    294   if inspect.isfunction(func) or inspect.ismethod(func):

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/keras/engine/training_v2_utils.py in train_on_batch(model, x, y, sample_weight, class_weight, reset_metrics)
    262       y,
    263       sample_weights=sample_weights,
--> 264       output_loss_metrics=model._output_loss_metrics)
    265 
    266   if reset_metrics:

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/keras/engine/training_eager.py in train_on_batch(model, inputs, targets, sample_weights, output_loss_metrics)
    309           sample_weights=sample_weights,
    310           training=True,
--> 311           output_loss_metrics=output_loss_metrics))
    312   if not isinstance(outs, list):
    313     outs = [outs]

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/keras/engine/training_eager.py in _process_single_batch(model, inputs, targets, output_loss_metrics, sample_weights, training)
    250               output_loss_metrics=output_loss_metrics,
    251               sample_weights=sample_weights,
--> 252               training=training))
    253       if total_loss is None:
    254         raise ValueError('The model cannot be run '

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/keras/engine/training_eager.py in _model_loss(model, inputs, targets, output_loss_metrics, sample_weights, training)
    164 
    165         if hasattr(loss_fn, 'reduction'):
--> 166           per_sample_losses = loss_fn.call(targets[i], outs[i])
    167           weighted_losses = losses_utils.compute_weighted_loss(
    168               per_sample_losses,

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/keras/losses.py in call(self, y_true, y_pred)
    219       y_pred, y_true = tf_losses_util.squeeze_or_expand_dimensions(
    220           y_pred, y_true)
--> 221     return self.fn(y_true, y_pred, **self._fn_kwargs)
    222 
    223   def get_config(self):

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/keras/losses.py in mean_absolute_error(y_true, y_pred)
    781   y_pred = ops.convert_to_tensor(y_pred)
    782   y_true = math_ops.cast(y_true, y_pred.dtype)
--> 783   return K.mean(math_ops.abs(y_pred - y_true), axis=-1)
    784 
    785 

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/ops/math_ops.py in binary_op_wrapper(x, y)
    897     with ops.name_scope(None, op_name, [x, y]) as name:
    898       if isinstance(x, ops.Tensor) and isinstance(y, ops.Tensor):
--> 899         return func(x, y, name=name)
    900       elif not isinstance(y, sparse_tensor.SparseTensor):
    901         try:

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/ops/gen_math_ops.py in sub(x, y, name)
  11086   # Add nodes to the TensorFlow graph.
  11087   _, _, _op = _op_def_lib._apply_op_helper(
> 11088         "Sub", x=x, y=y, name=name)
  11089   _result = _op.outputs[:]
  11090   _inputs_flat = _op.inputs

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/framework/op_def_library.py in _apply_op_helper(self, op_type_name, name, **keywords)
    791         op = g.create_op(op_type_name, inputs, dtypes=None, name=scope,
    792                          input_types=input_types, attrs=attr_protos,
--> 793                          op_def=op_def)
    794       return output_structure, op_def.is_stateful, op
    795 

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/framework/func_graph.py in create_op(***failed resolving arguments***)
    546     return super(FuncGraph, self)._create_op_internal(  # pylint: disable=protected-access
    547         op_type, inputs, dtypes, input_types, name, attrs, op_def,
--> 548         compute_device)
    549 
    550   def capture(self, tensor, name=None):

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/framework/ops.py in _create_op_internal(self, op_type, inputs, dtypes, input_types, name, attrs, op_def, compute_device)
   3427           input_types=input_types,
   3428           original_op=self._default_original_op,
-> 3429           op_def=op_def)
   3430       self._create_op_helper(ret, compute_device=compute_device)
   3431     return ret

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/framework/ops.py in __init__(self, node_def, g, inputs, output_types, control_inputs, input_types, original_op, op_def)
   1771           op_def, inputs, node_def.attr)
   1772       self._c_op = _create_c_op(self._graph, node_def, grouped_inputs,
-> 1773                                 control_input_ops)
   1774     # pylint: enable=protected-access
   1775 

~/anaconda3/envs/topic_forecaster/lib/python3.7/site-packages/tensorflow_core/python/framework/ops.py in _create_c_op(graph, node_def, inputs, control_inputs)
   1611   except errors.InvalidArgumentError as e:
   1612     # Convert to ValueError for backwards compatibility.
-> 1613     raise ValueError(str(e))
   1614 
   1615   return c_op

ValueError: Dimensions must be equal, but are 50 and 8 for 'loss/lstm_loss/sub' (op: 'Sub') with input shapes: [?,50], [?,1,8].

该数据集可在此处获得。

我的问题是：

• Keras LSTM层不是为此设计的吗？也许只是一个时间序列？
• 如果LSTM很好，那么可以解决什么问题呢？
• 如果LSTM不好，如果要对功能部件之间的交互进行建模并为所有功能部件做出预测，我还应该使用其他什么方法？

谢谢！