Extract coefficients from fitted ellipsoid learner

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

Usage

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

Arguments

object

A LearnerSubspaceEllipsoid 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 ellipsoid shape and orientation

• b: List column of translation vectors

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

Details

The ellipsoid is defined by \(\|Ax + b\|_2 \leq 1\) 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 ellipsoid in original coordinates

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

The semi-axes lengths and orientations are determined by the eigendecomposition of \(A^{-1}\): if \(A^{-1} = V\Lambda V^T\), then the semi-axes have lengths \(\sqrt{\lambda_i}\) in directions given by columns of \(V\).

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

LearnerSubspaceEllipsoid for the learner class. coef.LearnerSubspaceBox for the axis-aligned variant. coef.LearnerSubspacePolygon for the oriented hyperrectangle variant.

Examples

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

# Extract coefficients
coefs <- coef(learner)
print(coefs$A[[1]])  # Shape matrix
print(coefs$b[[1]])  # Translation vector

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

# Compute semi-axes
A_inv <- solve(A)
eigen_decomp <- eigen(A_inv)
semi_axes <- sqrt(eigen_decomp$values)
directions <- eigen_decomp$vectors
} # }