The goal is to predict a timeseries Y of 87601 timesteps (10 years) and 9 targets. The input features X (exogenous input) are 11 timeseries of 87600 timesteps. The output has one more timestep, as this is the initial value. The output Yt at timestep t depends on the input Xt and on the previous output Yt-1.
Hence, the model should look like this: Model layout
I could only find this thread on this: LSTM: How to feed the output back to the input? #4068. I tried to implemented this with Keras as follows:
def build_model():
# Input layers
input_x = layers.Input(shape=(features,), name='input_x')
input_y = layers.Input(shape=(targets,), name='input_y-1')
# Merge two inputs
merge = layers.concatenate([input_x,input_y], name='merge')
# Normalise input
norm = layers.Lambda(normalise, name='scale')(merge)
# Hidden layers
x = layers.Dense(128, input_shape=(features,))(norm)
# Output layer
output = layers.Dense(targets, activation='relu', name='output')(x)
model = Model(inputs=[input_x,input_y], outputs=output)
model.compile(loss='mean_squared_error', optimizer=Adam())
return model
def make_prediction(model, X, y):
y_pred = [y[0,None,:]]
for i in range(len(X)):
y_pred.append(model.predict([X[i,None,:],y_pred[i]]))
y_pred = np.asarray(y_pred)
y_pred = y_pred.reshape(y_pred.shape[0],y_pred.shape[2])
return y_pred
# Fit
model = build_model()
model.fit([X_train, y_train[:-1]], [y_train[1:]]], epochs=200,
batch_size=24, shuffle=False)
# Predict
y_hat = make_prediction(model, X_train, y_train)
This works, but is it not what I want to achieve, as there is no connection between input and output. Hence, the model doesn't learn how to correct for an error in the fed-back output, which results in poor accuracy when predicting as the error on the output is accumulated at every timestep.
Is there a way in Keras to implement the output-input feed-back during training stage? Also, as the initial value of Y is always known, I want to feed this to the network as well.
