Shape-recognition sensitivity study

Run a full-factorial sensitivity sweep for the janusplot 24-category shape classifier. For each combination of ground-truth shape, sample size n, noise level sigma, and replicate, the sweep:

Generates n points from the noiseless canonical curve on [0, 1] + Gaussian noise with SD = sigma (fraction of the y-range, so signal-to-noise is comparable across shapes).
Fits mgcv::gam(y ~ s(x), method = "REML").
Runs janusplot_shape_metrics() to classify the fitted smooth.
Records correctness at both the fine (24-category) and archetype (7-family) levels.

The function is the package-native implementation of simulation/scripts/scenario_4_shape_recognition.R. A small precomputed dataset is shipped as shape_sensitivity_demo for downstream examples without requiring users to re-run the sweep.

Usage

janusplot_shape_sensitivity(
  shapes = NULL,
  n_grid = c(50L, 100L, 200L, 500L),
  sigma_grid = c(0.02, 0.05, 0.1, 0.2, 0.4),
  n_rep = 200L,
  cutoffs = janusplot_shape_cutoffs(),
  parallel = FALSE,
  seed = 2026L,
  verbose = interactive()
)

Arguments

shapes: Character vector of ground-truth names from janusplot_shape_sensitivity_shapes(). Default NULL → all 14.
n_grid: Integer vector of sample sizes. Default c(50L, 100L, 200L, 500L).
sigma_grid: Numeric vector of noise levels (fraction of the y-range). Default c(0.02, 0.05, 0.10, 0.20, 0.40).
n_rep: Integer. Replicates per cell. Default 200L.
cutoffs: Named list of classification thresholds; see janusplot_shape_cutoffs().
parallel: Logical. If TRUE and future.apply is installed, dispatch replicates in parallel. The caller is responsible for configuring future::plan() (e.g. future::plan(future::multisession)).
seed: Integer. Base seed — each fit uses seed + row_index so results are reproducible and cell-permutation-invariant.
verbose: Logical. Print progress messages to the console. Default is interactive().

Value

A data frame with one row per fit. Columns:

truth: Ground-truth shape name.
n: Sample size for this fit.
sigma: Noise level for this fit.
seed: RNG seed used.
predicted: Classifier output at the fine (24-category) level.
correct: Logical — does predicted == truth?
archetype_truth: Expected archetype for truth.
archetype_pred: Archetype of predicted.
archetype_correct: Logical — archetype-level correctness.
monotonicity_index: Monotonicity index M (see janusplot_shape_metrics()).
convexity_index: Convexity index C (see janusplot_shape_metrics()).
n_turn, n_inflect: Recovered turning-point and inflection counts.
error: "gam_fit_failed" when mgcv::gam() errored; NA otherwise.

Examples

# Tiny-run smoke test (< 2 seconds): 3 shapes x 2 n x 2 sigma x 5 reps.
res <- janusplot_shape_sensitivity(
  shapes     = c("linear_up", "u_shape", "wave"),
  n_grid     = c(100L, 200L),
  sigma_grid = c(0.05, 0.20),
  n_rep      = 5L,
  verbose    = FALSE
)
head(res)
#>       truth   n sigma seed  predicted correct archetype_truth  archetype_pred
#> 1 linear_up 100  0.05 2027  linear_up    TRUE monotone_linear monotone_linear
#> 2   u_shape 100  0.05 2028    u_shape    TRUE        unimodal        unimodal
#> 3      wave 100  0.05 2029 broad_peak   FALSE            wave        unimodal
#> 4 linear_up 200  0.05 2030  linear_up    TRUE monotone_linear monotone_linear
#> 5   u_shape 200  0.05 2031    u_shape    TRUE        unimodal        unimodal
#> 6      wave 200  0.05 2032 broad_peak   FALSE            wave        unimodal
#>   archetype_correct monotonicity_index convexity_index n_turn n_inflect error
#> 1              TRUE         1.00000000       0.0000000      0         0  <NA>
#> 2              TRUE         0.02660353       0.9768746      1         0  <NA>
#> 3             FALSE        -0.10849908      -0.2416725      1         2  <NA>
#> 4              TRUE         1.00000000       0.0000000      0         0  <NA>
#> 5              TRUE         0.06946110       0.9999646      1         0  <NA>
#> 6             FALSE        -0.07133879      -0.2442866      1         2  <NA>
janusplot_shape_sensitivity_summary(res, level = "archetype")
#>        truth   n sigma accuracy
#> 1  linear_up 100  0.05      0.8
#> 2    u_shape 100  0.05      1.0
#> 3       wave 100  0.05      0.0
#> 4  linear_up 200  0.05      0.8
#> 5    u_shape 200  0.05      1.0
#> 6       wave 200  0.05      0.0
#> 7  linear_up 100  0.20      0.6
#> 8    u_shape 100  0.20      1.0
#> 9       wave 100  0.20      0.0
#> 10 linear_up 200  0.20      0.8
#> 11   u_shape 200  0.20      1.0
#> 12      wave 200  0.20      0.0

Usage

Arguments

Value

See also

Examples