Hierarchical Moment-Preserving Coresets

Experimental Evaluation Suite

This repository contains all code to reproduce the experiments in:

Beyond Coverage: Task-Specific Moment Preservation for Optimal Coreset Selection

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Quick Start

# Install dependencies
pip install -r requirements.txt

# Run synthetic experiments (1-8)
python run_all_experiments.py 1 2 3 4 5 6 7 8

# Run REAL-WORLD experiments (9-10)
python run_all_experiments.py 9 10

# Run specific experiment
python run_all_experiments.py 9   # S&P 500 finance
python run_all_experiments.py 10  # PhysioNet EEG

# Generate figures
python generate_figures.py

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Installation

# Basic install (synthetic experiments only)
pip install numpy scipy pandas scikit-learn matplotlib seaborn

# Full install (includes real-world data support)
pip install numpy scipy pandas scikit-learn matplotlib seaborn mne

# Or use requirements.txt
pip install -r requirements.txt

Required Libraries by Experiment

Experiment	Libraries Needed
1-8 (Synthetic)	numpy, scipy, pandas, scikit-learn
9 (S&P 500)	pandas (+ manual data download)
10 (EEG)	mne (auto-downloads data)
Figures	matplotlib, seaborn

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Real-World Data Setup

S&P 500 Stock Data (Experiment 9)

Source: https://www.kaggle.com/datasets/andrewmvd/sp-500-stocks

1. Download sp-500-stocks.zip from Kaggle
2. Extract to data/sp500/ folder
3. Verify: data/sp500/sp500_stocks.csv exists

paper_experiments/
└── data/
    └── sp500/
        ├── sp500_stocks.csv      # Required (~200MB)
        ├── sp500_companies.csv   # Not required
        └── sp500_index.csv       # Not required

What's in the data:

• Daily OHLCV data for 500+ S&P 500 stocks
• Date range: 2010-2022+
• We use: Adjusted Close prices → Daily returns

PhysioNet EEG Data (Experiment 10)

Source: https://physionet.org/content/eegmmidb/1.0.0/

• Automatically downloaded by MNE-Python on first run
• 109 subjects, 64 channels, motor/imagery tasks
• ~1.9GB total (downloaded incrementally per subject)
• Cached in ~/mne_data/

# Install MNE
pip install mne

# Just run - data downloads automatically
python run_all_experiments.py 10

First run note: May take 5-10 minutes to download data for first few subjects.

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Repository Structure

paper_experiments/
├── utils/
│   ├── __init__.py
│   ├── coreset_methods.py        # All coreset selection algorithms
│   └── metrics.py                # Evaluation metrics
│
├── Synthetic Experiments:
│   ├── exp_1_moment_preservation.py  # Core moment quality
│   ├── exp_2_covariance_tasks.py     # QDA, PCA, Mahalanobis
│   ├── exp_3_generative_models.py    # FID, MMD for GANs/VAEs
│   ├── exp_4_signal_processing.py    # ICA/BSS (synthetic signals)
│   ├── exp_5_finance_outliers.py     # Finance (synthetic)
│   ├── exp_6_real_signals.py         # EEG/audio (synthetic)
│   ├── exp_7_ablations.py            # Ablation studies
│   └── exp_8_runtime.py              # Computational analysis
│
├── Real-World Experiments:
│   ├── exp_5_finance_real.py     # S&P 500 Stock Data
│   └── exp_6_eeg_real.py         # PhysioNet EEGMMI
│
├── run_all_experiments.py        # Master runner
├── generate_figures.py           # Paper figures
├── paper_draft.tex               # LaTeX paper draft
├── requirements.txt              # Python dependencies
└── README.md                     # This file

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Experiments Overview

#	Name	Data	Key Metric
1	Moment Preservation	Synthetic	Cov/Kurt Error
2	Covariance Tasks	Synthetic	QDA Accuracy
3	Generative Models	Synthetic	FID Score
4	Signal Processing	Synthetic	SIR (dB)
5	Finance Outliers	Synthetic	VaR Error
6	Real Signals	Synthetic	Separation quality
7	Ablations	Synthetic	Various
8	Runtime	Synthetic	Time (s)
9	S&P 500 Finance	REAL	Outlier Precision, VaR Error
10	PhysioNet EEG	REAL	ICA Source Correlation

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Key Methods

Baseline Methods

• Random: Uniform random sampling (unbiased)
• K-means++: D² sampling for coverage
• Herding: Kernel herding for mean matching

Our Methods

• Covariance: Greedy covariance matching (best for 2nd-order tasks)
• HMP: Hierarchical Moment-Preserving (balanced)
• HMP-Kurt: Heavy kurtosis weighting (best for ICA)

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Expected Results

Synthetic Data (Quick Test)

Method          : Cov Error    Kurt Error
-------------------------------------------
Random          : 0.4266       0.9884
K-means++       : 1.9825       7.6249  ← 10x WORSE!
Covariance      : 0.0388       1.0006  ← BEST for cov
HMP-Kurt        : 0.1735       0.8580  ← Best balanced

Real-World S&P 500

• Covariance method: ~85% outlier precision
• Random: ~70% outlier precision
• Improvement: +15-20%

Real-World EEG

• HMP-Kurt: Best ICA source separation
• Covariance-only: Destroys kurtosis needed for ICA
• Validates theory on real neural signals

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License

MIT License. See LICENSE file for details.