Visualize fitted ellipsoids

Creates pairwise scatter plots showing fitted ellipsoids overlaid on hyperparameter configurations. Uses marginal ellipse projections to visualize the smooth ellipsoidal boundaries in 2D pairwise plots.

Usage

# S3 method for class 'LearnerSubspaceEllipsoid'
autoplot(
  object,
  select = "all",
  force = FALSE,
  wrap = TRUE,
  size_top = 0.7,
  size_all = 0.5,
  ...
)

Arguments

object

A trained LearnerSubspaceEllipsoid object with fitted subspace

select

Character vector of hyperparameter names to plot, or "all" (default) to plot all hyperparameters

force

Logical indicating whether to skip the confirmation prompt when plotting many hyperparameters. Default: FALSE

wrap

Logical indicating whether to combine plots using patchwork::wrap_plots(). Default: TRUE

size_top

Numeric point size for top-performing configurations (orange crosses). Default: 0.7

size_all

Numeric point size for all data points (gray background). Default: 0.5

...

Additional arguments passed to patchwork::wrap_plots() (only used when wrap = TRUE)

Value

If wrap = TRUE: A single patchwork object combining all plots.

If wrap = FALSE and no categorical hyperparameters: A list of ggplot objects, one per hyperparameter pair.

If wrap = FALSE and categorical hyperparameters present: A named list where each element is a list of ggplot objects for that categorical level.

Details

Plot Structure:

Each plot shows:

• Gray points: All configurations in the dataset (low alpha)

• Orange crosses: Top-performing configurations used for fitting

• Blue ellipse: Projection of the fitted ellipsoid onto 2D plane

• Blue diamond: Center of the ellipsoid

For \(p\) selected hyperparameters, creates \(\binom{p}{2}\) pairwise plots.

Visualization Method:

The ellipsoid is defined by \(\|Ax + b\|_2 \leq 1\). For visualization:

1. Computes center: \(c = -A^{-1}b\)

2. Computes covariance: \(\Sigma = A^{-1}(A^{-1})^T\)

3. For each 2D pair \((i,j)\), extracts marginal covariance \(\Sigma_{ij}\)

4. Uses Cholesky decomposition to transform unit circle to ellipse: \(x = L \theta + c_{ij}\) where \(L\) is lower Cholesky factor of \(\Sigma_{ij}\) and \(\theta\) are points on unit circle

The resulting ellipse represents the marginal distribution of the ellipsoid projected onto the 2D hyperparameter pair, showing smooth boundaries characteristic of ellipsoidal subspaces.

Univariate Case:

When only one hyperparameter is selected, displays a histogram with vertical lines marking the ellipsoid boundaries (reduces to interval) and rug plot for top configurations.

Categorical Hyperparameters:

When the task includes a categorical hyperparameter, separate plots are created for each categorical level, showing the corresponding fitted ellipsoid.

Interactive Prompt:

When plotting more than 3 hyperparameters with wrapping enabled, the function prompts for confirmation due to potential readability issues. Use force = TRUE to bypass this prompt.

Dependencies:

Requires ggplot2 and scales. If wrap = TRUE, also requires patchwork.

See also

LearnerSubspaceEllipsoid for the learner class. coef.LearnerSubspaceEllipsoid for extracting fitted parameters. autoplot.LearnerSubspaceBox for axis-aligned visualization. autoplot.LearnerSubspacePolygon for oriented hyperrectangle visualization.

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)

# Plot all hyperparameters (wrapped)
autoplot(learner)

# Plot specific hyperparameters
autoplot(learner, select = c("learning_rate", "max_depth"))

# Get individual plots without wrapping
plots <- autoplot(learner, wrap = FALSE)
plots[[1]]  # First pairwise plot

# Customize ellipse smoothness
autoplot(learner, n_points = 500)  # More points for smoother curves

# Customize wrapping layout
autoplot(learner, ncol = 2, guides = "collect")

# With categorical hyperparameters
task <- TaskSubspace$new(data, target_measure = "auc",
                         hps = c("learning_rate", "max_depth"),
                         cat_hps = "optimizer")
learner <- LearnerSubspaceEllipsoid$new(task)
learner$train(q_val = 0.9)
autoplot(learner)  # Separate plots per optimizer
} # }