Build expected-domain features from a soft alignment matrix

Given encoding-domain predictors and a recall->encoding alignment posterior, compute expected recall-domain predictors: $$X_{rec} = \Gamma X_{enc}.$$

Usage

expected_features(
  train,
  gamma,
  drop_null = TRUE,
  renormalize = FALSE,
  eps = 1e-12
)

Arguments

train

feature_sets object for encoding-domain predictors.

gamma

Numeric matrix of shape (T_rec x T_enc) or (T_rec x (T_enc+1)) if null column present.

drop_null

Logical; if TRUE and gamma has T_enc+1 columns, drop the first column.

renormalize

Logical; if TRUE, renormalize rows to sum to 1 after dropping null.

eps

Small constant to avoid division by zero in renormalization.

Value

A feature_sets object for recall-domain predictors with the same set layout.

Details

This is the core "soft label" trick for bringing recall into regression when recall TRs do not have a known one-to-one correspondence with encoding TRs.

Gamma shapes. `gamma` should be a numeric matrix where rows index recall TRs and columns index encoding TRs:

• without a NULL state: (T_rec x T_enc)

• with a NULL state in the first column: (T_rec x (T_enc+1))

When a NULL column is present and `drop_null = TRUE`, the NULL column is dropped. If `renormalize = FALSE` (default), the remaining row mass is stored as row_weights (so uncertain TRs with high NULL probability can be down-weighted by downstream models). If `renormalize = TRUE`, rows are renormalized to sum to 1 and `row_weights` is set to 1.

See also

feature_sets, feature_sets_design

Examples

X <- matrix(rnorm(10 * 5), 10, 5)
fs_enc <- feature_sets(X, blocks(a = 2, b = 3))
gamma <- matrix(runif(6 * 10), 6, 10)
gamma <- gamma / rowSums(gamma)
fs_rec <- expected_features(fs_enc, gamma, drop_null = FALSE, renormalize = TRUE)