How to prepare the inputs in Keras implementation of Wavenet for time-series prediction

Question

In Keras implementation of Wavenet, the input shape is (None, 1). I have a time series (val(t)) in which the target is to predict the next data point given a window of past values (the window size depends on maximum dilation). The input-shape in wavenet is confusing. I have few questions about it:

1. How Keras figure out the input dimension (None) when a full sequence is given? According to dilations, we want the input to have a length of 2^8.
2. If a input series of shape (1M, 1) is given as training X, do we need to generate vectors of 2^8 time-steps as input? It seems, we can just use the input series as input of wave-net (Not sure why raw time series input does not give error).
3. In general, how we can debug such Keras networks. I tried to apply the function on numerical data like Conv1D(16, 1, padding='same', activation='relu')(inputs), however, it gives error.

#

n_filters = 32
filter_width = 2
dilation_rates = [2**i for i in range(7)] * 2 

from keras.models import Model
from keras.layers import Input, Conv1D, Dense, Activation, Dropout, Lambda, Multiply, Add, Concatenate
from keras.optimizers import Adam

history_seq = Input(shape=(None, 1))
x = history_seq

skips = []
for dilation_rate in dilation_rates:

    # preprocessing - equivalent to time-distributed dense
    x = Conv1D(16, 1, padding='same', activation='relu')(x) 

    # filter
    x_f = Conv1D(filters=n_filters,
                 kernel_size=filter_width, 
                 padding='causal',
                 dilation_rate=dilation_rate)(x)

    # gate
    x_g = Conv1D(filters=n_filters,
                 kernel_size=filter_width, 
                 padding='causal',
                 dilation_rate=dilation_rate)(x)

    # combine filter and gating branches
    z = Multiply()([Activation('tanh')(x_f),
                    Activation('sigmoid')(x_g)])

    # postprocessing - equivalent to time-distributed dense
    z = Conv1D(16, 1, padding='same', activation='relu')(z)

    # residual connection
    x = Add()([x, z])    

    # collect skip connections
    skips.append(z)

# add all skip connection outputs 
out = Activation('relu')(Add()(skips))

# final time-distributed dense layers 
out = Conv1D(128, 1, padding='same')(out)
out = Activation('relu')(out)
out = Dropout(.2)(out)
out = Conv1D(1, 1, padding='same')(out)

# extract training target at end
def slice(x, seq_length):
    return x[:,-seq_length:,:]

pred_seq_train = Lambda(slice, arguments={'seq_length':1})(out)

model = Model(history_seq, pred_seq_train)
model.compile(Adam(), loss='mean_absolute_error')

Answer 1

you are using extreme values for dilatation rate, they don't make sense. try to reduce them using, for example, a sequence made of [1, 2, 4, 8, 16, 32]. the dilatation rates aren't a constraint on the dimension of the input passed

your network work simply passing this input

n_filters = 32
filter_width = 2
dilation_rates = [1, 2, 4, 8, 16, 32]

....

model = Model(history_seq, pred_seq_train)
model.compile(Adam(), loss='mean_absolute_error')

n_sample = 5
time_step = 100

X = np.random.uniform(0,1, (n_sample,time_step,1))

model.predict(X)

specify a None dimension in Keras means to leave the model free to receive every dimension. this not means you can pass samples of various dimension, they always must have the same format... you can build the model every time with a different dimension size

for time_step in np.random.randint(100,200, 4):

  print('temporal dim:', time_step)
  n_sample = 5

  model = Model(history_seq, pred_seq_train)
  model.compile(Adam(), loss='mean_absolute_error')

  X = np.random.uniform(0,1, (n_sample,time_step,1))

  print(model.predict(X).shape)

I suggest also you a premade library in Keras which provide WAVENET implementation: https://github.com/philipperemy/keras-tcn you can use it as a baseline and investigate also the code to create a WAVENET