CASPER-t

Covering Approximation Space Permutation Elimination Rule (t-statistic form) a reliability-weighted topological feature selector, packaged as a drop-in scikit-learn transformer.

Keep a small, confident subset of features instead of all of them without paying for it in accuracy. On 9 benchmark datasets CASPER-t retains a median 60 % of features while tracking full-feature accuracy to within ~1–2 points.

pip install casper-fs

How it works

CASPER-t treats each feature's usefulness as a measured quantity with an error bar, and keeps a feature only when its measured contribution clears a reliability margin not merely when it looks large once.

flowchart LR
    A["X, y"] --> B["Jenks<br/>discretization"]
    B --> C["L₁ tolerance<br/>relation"]
    C --> D["select ε*<br/>(covering radius)"]
    D --> E["γ-PFI<br/>N permutations"]
    E --> F["tᶠ = (Δγ − Q1) / SEM > κ"]
    F --> G["selected<br/>subset"]

1. Discretize each feature by unsupervised Jenks natural breaks.

2. Build an L₁ tolerance relation and pick the covering radius ε* that maximises the γ dependency degree (just below saturation).

3. Score every feature by the drop in γ under N permutations (γ-PFI). A permutation-importance signal native to the covering approximation space.

4. Retain a feature only when that drop clears the first quartile of the feature-wise distribution by a reliable margin:

   tᶠ = (mean(Δγ_f) − Q1) / SEM_f > κ (default κ = 1.5)

Everything is refit on the training split it is given, so it is leakage-free inside a scikit-learn Pipeline / cross-validation loop.

Benchmark

Protocol. Nested cross-validation on 9 datasets, evaluated across 8 classifiers, against 13 feature-selection baselines (filter, wrapper, embedded, and rough-set families). Baselines are compared at matched cardinality. Each is truncated to CASPER-t's own per-fold feature count. So, every method is judged on the same feature budget.

The headline is parsimony. CASPER-t discards 25–51 % of the features yet stays within a point or two of using everything and matches or beats the full set on 4 of 9 datasets (banknote, diabet, htru2, sonar).

Accuracy is the mean over 8 classifiers × outer folds. K is the mean per-fold subset size, p is the number of candidate features.

On honest terms. At a matched feature budget no single selector dominates the field. CASPER-t's mean Accuracy rank is mid-pack (≈ 7.7 of 14 methods), and its value is the combination of a principled topological criterion with a reliability gate that yields compact subsets. Every rank, dispersion (fold std and across-classifier std), and per-fold number behind these figures is shipped in detailed_tables/, nothing is averaged away.

Quickstart

from casper import CasperT
from sklearn.pipeline import Pipeline
from sklearn.svm import SVC
from sklearn.model_selection import cross_val_score
from sklearn.datasets import load_breast_cancer

X, y = load_breast_cancer(return_X_y=True)

# standalone
sel = CasperT(kappa=1.5, n_permutations=30, random_state=42).fit(X, y)
print(sel.get_support().sum(), "features selected")     # -> 13 of 30
print(sel.eps_star_, sel.t_stats_)                      # diagnostics

# leakage-free inside a Pipeline (refits per fold)
pipe = Pipeline([("casper", CasperT()), ("clf", SVC())])
cross_val_score(pipe, X, y, cv=5)

Requires Python ≥ 3.9, numpy, scipy, scikit-learn. Install from a clone with pip install ..

API

CasperT(kappa=1.5, n_permutations=30, max_bins=7, target_gvf=0.80, max_topological=3000, random_state=42)

Fitted attributes: support_, delta_gamma_, sem_, t_stats_, eps_star_, gamma_base_, q1_. Standard SelectorMixin API: fit, transform, get_support, get_feature_names_out.

Reproducing the article

pipeline/gamma_pfi_uhem.py is the full nested-CV pipeline used for the paper (all baselines, statistics, and per-fold outputs); pipeline/make_tables.py regenerates the LaTeX tables from those outputs.

Detailed results (detailed_tables/)

The article's tables report means only, for readability. These files hold the same numbers with their dispersion and at fold-level granularity:

Method ids: V1_tstat = CASPER-t; *_matchK = baselines truncated at CASPER-t's per-fold cardinality; *_native = rough-set baselines at their own stopping point; ALL = full feature set.

Changelog

0.1.3 — Fixed a bug in tstat_support (the t_f reliability rule): a zero-variance or near-zero-variance feature (SEM_f ≈ 0) could get a spurious, arbitrarily large t-statistic from the + 1e-9 denominator guard whenever Q1 < 0, causing it to be auto-selected regardless of kappa even though it carries no measurable signal. tstat_support now falls back to the point estimate (Δγ_f) when SEM_f is ~0, rather than dividing by it. If you're on <=0.1.2 and your feature set can contain constant or extremely low-variance columns (e.g. one-hot/multi-hot encodings with rare categories), upgrade and re-run — your selected-feature set may change.

Citation

If you use CASPER-t, please cite the article:

@article{casper_t,
  title  = {A Topological Feature Selection Framework via Generalized Covering
            Approximation Spaces with Permutation Importance},
  authors = {Uğur Yiğit, Kenan Evren Boyabatlı, Ebrar Karakurt, Esma Nur Elgün and
Ertan Sönmez},
journal = {Preprint - Appearing}
  year   = {2026}
}

License

MIT — see LICENSE.