Handling NaNs in embeddings for parameter selection vs. final cross mapping

[SpatLyu]

When tuning parameters (E, k, tau) for simplex projection forecasting, s-mapping forecasting or intersectional cardinality operation, we face a trade-off between two NaN-handling strategies:

1. Unified masking: Restrict all candidate (E, k, tau) combinations to the intersection of valid time indices (i.e., positions where all embeddings are fully observed).
   → Ensures fair comparison during parameter selection.
   → But the final model (using the "best" (E, k, tau)) may underutilize data, as its own valid set is typically larger.

2. Per-parameter masking: Evaluate each (E, k, tau) on its own maximal valid set.
   → Reflects each parameter’s true predictive capacity.
   → But comparisons become biased—higher skill might stem from more (or easier) samples, not better dynamics.

Thoughts?

[SpatLyu]

When tuning parameters (E, k, tau) for simplex projection forecasting, s-mapping forecasting or intersectional cardinality operation, we face a trade-off between two NaN-handling strategies:

1. Unified masking: Restrict all candidate (E, k, tau) combinations to the intersection of valid time indices (i.e., positions where all embeddings are fully observed).
   → Ensures fair comparison during parameter selection.
   → But the final model (using the "best" (E, k, tau)) may underutilize data, as its own valid set is typically larger.
2. Per-parameter masking: Evaluate each (E, k, tau) on its own maximal valid set.
   → Reflects each parameter’s true predictive capacity.
   → But comparisons become biased—higher skill might stem from more (or easier) samples, not better dynamics.

Thoughts?

Using unified masking in parameter selection now( tEDM version 1.2)