Issue 127: add offset to ts models

[SamuelBrand1]

This PR closes #127.

@damonbayer identified that the problem with NA forecast output was occurring in numerator forecasts when the data hit zero due to log transform.

I've added an offset following identical pattern (1 / max observed to symmetrise in log domain) to elsewhere in this repo.

[dylanhmorris]

I would've thought offset of 1 for raw counts; we're using 1 / max_visits as the offset for proportions

[damonbayer]

@dylanhmorris Agree that it's not consistent with what we do in the scoring, but an offset of 1 could be relatively big since the case counts can be so low.

[dylanhmorris]

@dylanhmorris Agree that it's not consistent with what we do in the scoring, but an offset of 1 could be relatively big since the case counts can be so low.

Just subtract 1 when you convert the forecast back to natural scale? (i.e. we explicitly forecast the quantity log(1+x) and then compute x)

[damonbayer]

@dylanhmorris Yes. Let's actually "undo" the offset here after fitting the model, before saving the results. (The output of generate is already on the natural scale). If we do that, I don't particularly care what the offset is.

Somewhere in here:

pyrenew-hew/pipelines/timeseries_forecasts.R

Lines 85 to 89 in dbcfb6b

	forecast_samples <- fit |>
	generate(h = forecast_horizon, times = n_samples) |>
	as_tibble() |>
	mutate("{output_col}" := .sim, .draw = as.integer(.rep)) |> # nolint
	select(date, .draw, !!output_sym)

[dylanhmorris]

@SamuelBrand1 can you implement?

[SamuelBrand1]

I would've thought offset of 1 for raw counts; we're using 1 / max_visits as the offset for proportions

The same underlying idea applies I think: in log domain the maximum value is log(max_visits) and the minimum is -log(max_visits) if we have a zero in the natural domain. I assumed this was the idea, its symmetrises the log-domain data in the presence of zeros which seems a good idea irrespective of whether its counts or proportions?

[SamuelBrand1]

@dylanhmorris Agree that it's not consistent with what we do in the scoring, but an offset of 1 could be relatively big since the case counts can be so low.

Just subtract 1 when you convert the forecast back to natural scale? (i.e. we explicitly forecast the quantity log(1+x) and then compute x)

fable does the backtransform automatically in the case of log(x + offset) transforms https://fable.tidyverts.org/articles/transformations.html . Although, for more complex transforms you have to wrap the transform with its backtransform in fabletools::new_transformation.

[SamuelBrand1]

@SamuelBrand1 can you implement?

As above, I think the back-transform is done automatically... Do you want this for the pyrenew output?

[damonbayer]

@SamuelBrand1 fable is very impressive! Thanks!