PIDReg: Explainable Multimodal Regression via Information Decomposition

Overview

Framework of Partial Information Decomposition for Multimodal Regression (PIDReg), illustrated with video and audio modalities, where $P(X_{1})$, $P(X_{2})$, and $P(Y)$ denote empirical data distributions that may deviate from Gaussianity (e.g., skewed or heavy-tailed).

PIDReg adaptively fuses two input modalities by learning how much each modality should contribute to prediction, rather than relying on fixed or hand-tuned weights. During training, PIDReg operates in the joint latent space of the modalities and decomposes the information into:

• 🔺 Unique Information
  Modality-specific information that is captured by one modality but not the other.

• 🔶 Redundant Information
  Overlapping information between modalities.

• 🔴 Synergistic Information
  Information that emerges when both modalities are considered jointly, interactions that neither modality can provide alone.

By explicitly estimating these components, PIDReg can (i) quantify what each modality is truly contributing, and (ii) weight modalities accordingly during regression.

Key Features

🌈	Feature	Description
①	Dynamic Fusion Weights	Learns optimal fusion weights via PID-based decomposition, eliminating hand-crafted balancing.
②	Information Bottleneck	Enforces compact yet informative latent representations for each modality.
③	Conditional MI Minimization	Minimizes redundancy to enhance modality-specific informativeness.
④	Adaptive λ-Learning	Automatically adjusts information bottleneck strength through learnable λ parameters.
⑤	PID Stability Detection	Detects stabilization of PID terms and freezes weights to prevent overfitting.

Installation

1. Repository preparation:

git clone https://github.com/zhaozhaoma/PIDReg.git
cd PIDReg

2. Install dependencies:

pip install -r requirements.txt

3. Ensure you have CUDA-compatible PyTorch installed for GPU acceleration

Data Format

To make PIDReg directly runnable, we include a curated sample dataset (./data/sample.csv). This file contains 5,000 rows subsampled from the original Superconductivity dataset used in our experiments. Each row in sample.csv follows a unified and intuitive column layout:

Index Range	Description	Modality
0–80	Feature dimensions for the first input source	Modality 1
81–166	Feature dimensions for the second input source	Modality 2
167	Continuous target variable used for regression	Target Variable

Model Components

File	Purpose	Key Functionalities
PIDRegModel.py	Core model definition	• Implements modality-specific information bottlenecks • Computes PID-based fusion weights for adaptive modality contribution • Incorporates Gaussian reconstruction and Cauchy–Schwarz divergence regularizations
PIDRegTrainer.py	Training orchestration	• Uses dual optimizers (one for model parameters, one for λ) • Integrates a scheduler for adaptive learning rate control • Performs PID stability detection and automatic fusion-weight freezing once convergence reached
CMICalculator.py	Conditional mutual information module	• Estimates conditional mutual information (CMI) between modalities and targets • Guides training toward reducing information leakage and enhancing modality specificity
csv_data_loader.py	Data processing and preparation	• Automatically splits data into train / validation / test sets • Applies standard scaling to both features and target • Supports flexible dataset paths and batch construction

Usage

1. Basic Training

python main.py --data_path ./data --n_epochs 200 --batch_size 256

2. Advanced Configuration

python main.py \
    --data_path ./data \
    --result_dir ./results \
    --batch_size 256 \
    --n_epochs 200 \
    --window_size 5 \
    --early_stopping 30 \
    --lambda_lr 0.1 \
    --hidden_dim 256 \
    --latent_dim 64

Citation

If you utilize PIDReg in your work, we would appreciate your citation of the following paper 📃:

@article{ma2025explainable,
  title={Explainable Multimodal Regression via Information Decomposition},
  author={Ma, Zhaozhao and Yu, Shujian},
  journal={arXiv preprint arXiv:2512.22102},
  year={2025}
}

Contact

For any questions or feedback, please feel free to reach out to us via email: zhaozhaoma@zju.edu.cn

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