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Bidirectional Response Alignment with aligned_interbattery()

Source: vignettes/aligned_interbattery.Rmd
aligned_interbattery.Rmd

Why use aligned_interbattery()?

Use aligned_interbattery() when you have two paired block families for the same subjects and neither side is the privileged response surface. You want a shared common space, but you also want to predict from X to Y, from Y to X, or complete a partially observed bundle using both sides together.

The key contract is symmetric: each subject gets common scores plus one score system for the X side and one for the Y side. That makes this a better fit than forcing one side to play the role of “predictors” and the other to play the role of “responses.”

What does a quick fit look like? 

fit <- aligned_interbattery(
  X = train$X,
  Y = train$Y,
  ncomp = 2,
  max_iter = 10
)
kable(quick_summary, align = c("l", "r"))
path mean_test_mse
x:D1 + x:D2 -> y:E1 0.0038
y:E1 -> x:D1 0.0159
x:D1 + y:E1 -> x:D2 0.0039

The important point is not which direction wins on this toy simulation. It is that one fitted object supports all three contracts: X -> Y, Y -> X, and joint completion from partially observed bundles.

What do the inputs look like?

You can supply nested subject -> domain lists on both sides. Blocks with the same domain name and column schema share loadings across subjects, which is the main way the model learns a common geometry rather than fitting each subject independently.

c(
  n_subjects = length(train$X),
  x_domains_per_subject = length(train$X$S1),
  y_domains_per_subject = length(train$Y$S1)
)
#>            n_subjects x_domains_per_subject y_domains_per_subject 
#>                     3                     2                     1

Here each subject has two X-side domains (D1, D2) and one Y-side domain (E1). In a real study those domains might be assays, feature families, or paired modalities collected on the same rows.

How do you project from one side or both?

If you observe both sides for the same new rows, project() can return the common scores together with the side-specific score systems.

common_scores <- project(
  fit,
  partial_both,
  from = "both",
  side = "common"
)

dim(common_scores)
#> [1] 9 2

If you only want to reconstruct the blocks you actually observed, use type = "reconstruction".

reconstructed <- predict(
  fit,
  partial_both,
  from = "both",
  type = "reconstruction"
)

names(reconstructed)
#> [1] "x" "y"

That separation matters. Reconstruction is for the observed side bundle. Prediction is for completing the opposite side or an unobserved block given the common space you inferred from what you have.

Where next?