Bad performance with NegativeBinomialOutput

[Alit10]

Hello,

I am trying to model with probabilistic forecasting library and DeepAR seems like a good model to use. I applied to forecast sales for many stores and products at a weekly frequency. My data is skewed toward low values and contains many zero sales.
From the documentation and this issue #302 I understood that NegativeBinomial is the right distribution for my case but I get really low values prediction.

For example :

When I compare the sum of predictions vs sum of target I see a big difference. With the studentOutput distribution it's a little bit better.

Do you have an Idea how I can fix this issue?

The estimator I am using : batch_size = 128
estimator_mx = DeepAREstimator(
cell_type="gru",
prediction_length=n_ahead,
context_length=12, # Cb il regarde en arriere
freq="W",
num_cells=124,
num_layers=2,
#embedding_dimension=[128, 128, 2, 2, 64, 2, 1, 64,2],
distr_output=NegativeBinomialOutput(),
use_feat_dynamic_real=True,
use_feat_static_cat=True,
cardinality=stat_cat_cardinalities,
scaling=True,
#dropout_rate=0.1,
lags_seq = list(range(1,8)),
#train_sampler = BucketInstanceSampler(scale_histogram=sc),

trainer=Trainer(
    learning_rate=0.001,
    learning_rate_decay_factor=0.6,
    epochs=100,
    batch_size=batch_size,
    #num_batches_per_epoch=len(train_ds) // batch_size,
    patience=3,
    minimum_learning_rate=5e-05,
    clip_gradient=0.3,
    weight_decay=1e-08,
)

)

predictor = estimator_mx.train(train_ds)