Add copy_dim to QuantileForecast, change dim method for multivariate data

[codingWhale13]

Issue #, if available:

Description of changes:
This PR adds copy_dim to the QuantileForecast class, similar to how it is done in SampleForecast

By submitting this pull request, I confirm that you can use, modify, copy, and redistribute this contribution, under the terms of your choice.

[jaheba]

What is the purpose of copy_dim?

[codingWhale13]

What is the purpose of copy_dim?

The purpose is stated in the base class Forecast: "Returns a new Forecast object with only the selected sub-dimension."

[jaheba]

That's some weird naming.

Should we add a test for this?

[codingWhale13]

While trying to write a test, I found that in the multivariate case, the 3d NumPy arrays for samples/forecast_array (for SampleForecast/QuantileForecast respectively) seem inconsistent:

SampleForecast: (num_samples, prediction_length, target_dim)
QuantileForecast: (num_samples, target_dim, prediction_length).

Before this commit, it was both (num_samples, target_dim, prediction_length) and then it was changed in SampleForecast.

It seems to me like the change for QuantileForecasts slipped through and multivariate QuantileForecasts weren't much used since then.

Please correct me if I'm wrong and if changing the meaning of QuantileForecast.forecast_array in this way breaks anything.

[codingWhale13]

With N = batch axis, T = time axis, C = channel axis (in the context of multivariate forecasts: target_dim), here are some examples of what's used in a few random places of the code:

• InstanceSplitter and CanonicalInstanceSplitter: (N, T) - this coincides with the univariate case of Forecasts, everything good here.
• MXNet Seq2SeqEnc2Dec: (N, T, C)
• MXNet MeanScaler: both (N, T, C) and (N, C, T) are possible.

Even though comparing these different contexts only makes limited sense, it looks like T usually precedes C, to which things have been updated in the SampleForecast a while ago, as mentioned in an above comment.

Long story short, in my view this confirms that changing the dimensions of the multivariate QuantileForecast makes sense.

[lostella]

We changed to the (N, T, C) layout because that's closer to the distribution abstraction: for multivariate distributions, it's over the trailing dimension (C) that data is sampled jointly and density is evaluated. This is the case for example in PyTorch distributions, but also in the MXNet based ones we have in GluonTS.

Indeed, the change you point out just missed the QuantileForecast case. I think it makes sense to change that as you proposed: it will be a breaking change, but hopefully a minor one.