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Extract coefficients from fitted oriented hyperrectangle learner

coef.LearnerSubspacePolygon.Rd

Extracts fitted subspace parameters from a trained LearnerSubspacePolygon object. Returns the transformation matrix \(A\) and translation vector \(b\) that define the fitted oriented hyperrectangle.

Usage

# S3 method for class 'LearnerSubspacePolygon'
coef(object, ...)

Arguments

object

A LearnerSubspacePolygon object with fitted subspace parameters

...

Additional arguments (currently unused)

Value

A data.table with columns:

  • hyperparameters: List column containing hyperparameter names

  • A: List column of positive definite matrices defining hyperrectangle shape and orientation

  • b: List column of translation vectors

  • cat_hp: Categorical level (only if task has categorical hyperparameters)

Details

The oriented hyperrectangle is defined by \(\|Ax + b\|_\infty \leq 1\) where:

  • \(A \in \mathbb{R}^{p \times p}\) is a positive definite matrix

  • \(b \in \mathbb{R}^p\) is the translation vector

  • \(x\) are points inside the hyperrectangle in original coordinates

  • The L-infinity norm maintains rectangular shape with sharp corners

The center of the hyperrectangle is: \(c = -A^{-1}b\)

Unlike LearnerSubspaceBox where \(A\) is diagonal (axis-aligned), here \(A\) is a general positive definite matrix allowing arbitrary rotation while maintaining the rectangular structure.

The eigendecomposition of \(A\) reveals the orientation: if \(A = V\Lambda V^T\), then \(V\) gives the principal directions and \(\Lambda\) the scaling along those directions.

When the task includes categorical hyperparameters, separate coefficient sets are returned for each categorical level, identified by the cat_hp column.

Error Handling

Throws an error if the learner has not been trained. Call train() before extracting coefficients.

See also

LearnerSubspacePolygon for the learner class. coef.LearnerSubspaceBox for the axis-aligned variant. coef.LearnerSubspaceEllipsoid for the ellipsoid variant. augment.LearnerSubspacePolygon for adding density parameters.

Examples

if (FALSE) { # \dontrun{
# Train learner
task <- TaskSubspace$new(data, target_measure = "auc",
                         hps = c("learning_rate", "max_depth"))
learner <- LearnerSubspacePolygon$new(task)
learner$train(q_val = 0.9, lambda = 0.1)

# Extract coefficients
coefs <- coef(learner)
print(coefs$A[[1]])  # Shape matrix (not diagonal)
print(coefs$b[[1]])  # Translation vector

# Compute hyperrectangle center
A <- coefs$A[[1]]
b <- coefs$b[[1]]
center <- -solve(A) %*% b

# Analyze orientation
eigen_decomp <- eigen(A)
principal_directions <- eigen_decomp$vectors
scalings <- eigen_decomp$values
} # }