PerCE: Hierarchical Perturbation-Based Counterfactual Explanations

PerCE generates plausible counterfactual explanations for multivariate time series classification.

"What minimal change to this ECG would cause the model to predict a different diagnosis?"

PerCE answers that question using a hierarchical perturbation strategy guided by permutation-based feature importance, operating at both temporal-segment and channel levels. It anchors every counterfactual to a real training instance (InSample), enabling physiologically plausible results.

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Paper

Bayrak, B. & Bach, K. (2025). PerCE: Hierarchical Perturbation-Based Counterfactual Explanations for Multivariate Time Series Classification. IEEE Access. DOI: 10.1109/ACCESS.2025.3639125

If you use PerCE in your work, please cite:

@article{bayrak2025perce,
  title   = {{PerCE}: Hierarchical Perturbation-Based Counterfactual Explanations
             for Multivariate Time Series Classification},
  author  = {Bayrak, Bet\"{u}l and Bach, Kerstin},
  journal = {IEEE Access},
  year    = {2025},
  doi     = {10.1109/ACCESS.2025.3639125}
}

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Key Results

Evaluated on the open CODE-test ECG dataset (827 12-lead recordings, cardiologist-annotated), PerCE substantially outperforms the InSample baseline:

from perce import evaluate_batch

summary = evaluate_batch(results)
print(f"Validity:  {summary['validity_rate']:.2%}")
print(f"Proximity: {summary['proximity_mean']:.3f} ± {summary['proximity_std']:.3f}")
print(f"Sparsity:  {summary['sparsity_mean']:.3f} ± {summary['sparsity_std']:.3f}")
print(f"Diversity: {summary['diversity']:.3f}")

Metric	InSample baseline	PerCE	Improvement
Validity ↑	0.65 ± 0.35	0.98 ± 0.05	+51%
Proximity ↓	200 ± 150	50 ± 25	−75%
Sparsity ↑	0.70 ± 0.15	0.40 ± 0.12	+43%
Diversity	0.30 ± 0.10	0.20 ± 0.08	(tunable)

Validity: 1.0 = always achieves class change. Proximity: lower = closer to original. Sparsity: lower = fewer segments modified.

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Installation

pip install perce

With ECG demo dependencies (h5py, matplotlib):

pip install "perce[ecg]"

Requirements: Python ≥ 3.9, NumPy ≥ 1.24, SciPy ≥ 1.10, scikit-learn ≥ 1.3. No Java. No external REST API.

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Quick Start

import numpy as np
from perce import PerCEExplainer

# 1. Wrap your model
#    Must accept (N, C, T) and return (N,) class predictions
def my_model(X):
    # PyTorch example:
    # import torch
    # with torch.no_grad():
    #     return net(torch.tensor(X)).argmax(dim=1).numpy()
    return np.zeros(len(X), dtype=int)   # stub

# 2. Fit (store training data for InSample candidate selection) 
exp = PerCEExplainer(
    model=my_model,
    n_segments=10,   # divide each time series into 10 segments
    alpha=0.5,       # segment-level interpolation strength
    beta=0.6,        # channel-level fallback strength
    k=5,             # k-nearest neighbours for candidate selection
)
exp.fit(X_train, y_train)   # X_train shape: (N, C, T)

# 3. Explain a single instance
result = exp.explain(X_query, target_class=1)   # X_query shape: (C, T)
print(result.summary())

# 4. Access everything 
cf  = result.counterfactual       # shape (C, T) — the explanation
print("Valid?    ", result.is_valid)
print("Proximity:", result.proximity_score)
print("Sparsity: ", result.sparsity_score)
print("Channels modified:", result.channels_modified)

Batch explanation

results = exp.explain_batch(X_test, target_classes=1, verbose=True)

from perce import evaluate_batch
summary = evaluate_batch(results)
print(f"Validity rate: {summary['validity_rate']:.2%}")
print(f"Proximity:     {summary['proximity_mean']:.3f} ± {summary['proximity_std']:.3f}")

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How It Works

PerCE follows a three-stage hierarchical algorithm:

Query X (C channels × T time points)
         │
         ▼
① Feature Importance          ② InSample Candidate
  • Channel-level (Ich)          k-NN from target class
  • Segment-level (Iseg)         via DTW distance
  Both: permutation-based,
  model-agnostic
         │                              │
         └──────────────┬───────────────┘
                        ▼
             ③ Hierarchical Perturbation
               For each channel c (most→least important):
                 For each segment s (most→least important):
                   X'[c,s] = (1−α)·X[c,s] + α·Xcand[c,s]
                   If model predicts target → return X'
               Fallback: full-channel replacement (beta)
                        │
                        ▼
             Counterfactual X' ← real ECG pattern,
             minimal changes, high validity

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Why hierarchical?

Traditional perturbation methods modify all features blindly. PerCE focuses on the most informative channels and time windows first, this facilitates producing sparser, more clinically meaningful explanations.

Why InSample?

By anchoring to real training instances, every generated counterfactual is guaranteed to be within the data distribution. No out-of-distribution artifacts.

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Notebooks

Notebook	Description
01_ECG_demo.ipynb	Full pipeline on CODE-test — reproduces Table 1 from paper
02_custom_model.ipynb	How to plug in your own PyTorch / sklearn model
03_evaluation.ipynb	Comprehensive evaluation

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Related Packages

This package is part of a growing XAI ecosystem from NTNU's NorwAI Centre:

Package	What it does	Paper
PerCE	Counterfactual explanations for time series	IEEE Access 2025
PertCF	Counterfactual explanations for tabular data	SGAI 2023
CEval	Evaluation framework for any counterfactual method	IEEE Access 2024

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Repository Structure

perce/
├── perce/
│   ├── __init__.py          # Public API
│   ├── explainer.py         # PerCEExplainer + CounterfactualResult
│   ├── importance.py        # Channel- and segment-level permutation importance
│   ├── neighbors.py         # DTW-based k-NN candidate selection
│   ├── perturbation.py      # Hierarchical interpolation (Algorithm 1)
│   └── metrics.py           # Proximity, Sparsity, Validity, Diversity
├── notebooks/
│   ├── 01_ECG_demo.ipynb
│   ├── 02_custom_model.ipynb
│   └── 03_evaluation.ipynb
├── tests/
│   └── test_perce.py
├── pyproject.toml
└── README.md

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API Reference

PerCEExplainer

Parameter	Default	Description
model	—	Callable: (N, C, T) → (N,) class predictions
n_segments	10	Number of temporal segments
alpha	0.5	Segment-level interpolation weight
beta	0.6	Channel-level fallback interpolation weight
k	5	Nearest neighbours for candidate selection
dtw_window	0.1	Sakoe-Chiba band (fraction of T)
random_state	42	Reproducibility seed

CounterfactualResult

Attribute	Type	Description
.counterfactual	ndarray (C,T)	The generated explanation
.is_valid	bool	Did it achieve the target class?
.proximity_score	float	Normalised DTW distance (lower=better)
.sparsity_score	float	Fraction of segments unchanged (higher=better)
.channels_modified	list[int]	Which channels were touched
.candidate	ndarray (C,T)	InSample anchor used

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Running Tests

git clone https://github.com/b-bayrak/PerCE
cd PerCE
pip install -e ".[dev]"
pytest tests/ -v

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Acknowledgements

This work was supported by the Research Council of Norway through the SFI NorwAI (Norwegian Research Center for AI Innovation), grant number 309834.

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License

MIT © Betül Bayrak