Add laplace distribution to torch distributions

[melopeo]

Description of changes:
Add Laplace distribution to torch/distributions

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[kashif]

@melopeo is the loss with Laplace generally huge? compared with say the Student-t head?

[melopeo]

Hello @kashif ,

thanks for reaching out.

I just did a small experiment based on your question. By using the "constant" synthetic dataset I get the following:

• student-t: Epoch 99: : 50it [00:01, 45.90it/s, loss=-5.83, v_num=205, train_loss=-5.68]
• Laplace: Epoch 99: : 50it [00:00, 50.11it/s, loss=-4.71, v_num=204, train_loss=-4.58]

From this experiment it seems that the losses are on the same scale.

Here is the code I used for it.

from pprint import pprint
  
  from gluonts.dataset.repository import get_dataset
  from gluonts.evaluation import make_evaluation_predictions, Evaluator
  from gluonts.torch import DeepAREstimator as DeepAREstimatorTorch
  from gluonts.torch.distributions import (
      StudentTOutput,
      LaplaceOutput,
  )
    
  distr_output = StudentTOutput()
  # distr_output = LaplaceOutput()
  
  if __name__ == "__main__":
      dataset = get_dataset("constant", regenerate=False)
  
      estimator = DeepAREstimatorTorch(
          prediction_length=dataset.metadata.prediction_length,
          freq=dataset.metadata.freq,
          distr_output=distr_output,
      )
  
      predictor = estimator.train(dataset.train)
  
      forecast_it, ts_it = make_evaluation_predictions(
          dataset.test, predictor=predictor, num_samples=100
      )
  
      agg_metrics, item_metrics = Evaluator()(
          ts_it, forecast_it, num_series=len(dataset.test)
      )
      pprint(agg_metrics)

[kashif]

ok cool! thanks!