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BVFLMSP : Bayesian Vertical Federated Learning for Multimodal Survival with Privacy

Abhilash Kar, Basisth Saha, Tanmay Sen, Biswabrata Pradhan

Abstract

Multimodal time-to-event prediction often requires integrating sensitive data distributed across multiple parties, making centralized model training impractical due to privacy constraints. At the same time, most existing multimodal survival models produce single deterministic predictions without indicating how confident the model is in its estimates, which can limit their reliability in real-world decision making. To address these challenges, we propose BVFLMSP, a Bayesian Vertical Federated Learning (VFL) framework for multimodal time-to-event analysis based on a Split Neural Network architecture. In BVFLMSP, each client independently models a specific data modality using a Bayesian neural network, while a central server aggregates intermediate representations to perform survival risk prediction. To enhance privacy, we integrate differential privacy mechanisms by perturbing client side representations before transmission, providing formal privacy guarantees against information leakage during federated training. We first evaluate our Bayesian multimodal survival model against widely used single modality survival baselines and the centralized multimodal baseline MultiSurv. Across multimodal settings, the proposed method shows consistent improvements in discrimination performance, with up to 0.02 higher C-index compared to MultiSurv. We then compare federated and centralized learning under varying privacy budgets across different modality combinations, highlighting the tradeoff between predictive performance and privacy. Experimental results show that BVFLMSP effectively includes multimodal data, improves survival prediction over existing baselines, and remains robust under strict privacy constraints while providing uncertainty estimates.

BVFLMSP : Bayesian Vertical Federated Learning for Multimodal Survival with Privacy

Abstract

Multimodal time-to-event prediction often requires integrating sensitive data distributed across multiple parties, making centralized model training impractical due to privacy constraints. At the same time, most existing multimodal survival models produce single deterministic predictions without indicating how confident the model is in its estimates, which can limit their reliability in real-world decision making. To address these challenges, we propose BVFLMSP, a Bayesian Vertical Federated Learning (VFL) framework for multimodal time-to-event analysis based on a Split Neural Network architecture. In BVFLMSP, each client independently models a specific data modality using a Bayesian neural network, while a central server aggregates intermediate representations to perform survival risk prediction. To enhance privacy, we integrate differential privacy mechanisms by perturbing client side representations before transmission, providing formal privacy guarantees against information leakage during federated training. We first evaluate our Bayesian multimodal survival model against widely used single modality survival baselines and the centralized multimodal baseline MultiSurv. Across multimodal settings, the proposed method shows consistent improvements in discrimination performance, with up to 0.02 higher C-index compared to MultiSurv. We then compare federated and centralized learning under varying privacy budgets across different modality combinations, highlighting the tradeoff between predictive performance and privacy. Experimental results show that BVFLMSP effectively includes multimodal data, improves survival prediction over existing baselines, and remains robust under strict privacy constraints while providing uncertainty estimates.

Paper Structure

This paper contains 39 sections, 5 theorems, 98 equations, 8 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Survival Analysis Using Machine Learning or Deep Learning:
  4. Multimodal Survival Analysis:
  5. Survival Analysis using Bayesian Neural Network:
  6. Vertical Federated Learning:
  7. Differential Privacy:
  8. Problem Statement
  9. Methodology
  10. Survival Analysis
  11. Multimodal Survival Analysis
  12. Bayesian Neural Networks
  13. Kullback-Leibler Divergence Regularization
  14. Loss Function
  15. Vertical Federated Learning
  16. ...and 24 more sections

Key Result

Lemma 1

In a Gaussian mechanism $\mathcal{Q}$ with noise scale $\sigma$ and batch sampling $p$, privacy loss's log-moment ($\alpha_{\mathcal{Q}_{i}}(\lambda)$) is bounded as: For all i $\in$ 1(1)$\tau$. $\blacktriangleleft$$\blacktriangleleft$

Figures (8)

  • Figure 1: Architecture of BVFLMSP.
  • Figure 2: Loss and accuracy curves for two modalities (Clinical + miRNA).
  • Figure 3: Loss and accuracy curves for three modalities (Clinical + miRNA + DNAm).
  • Figure 4: Loss and accuracy curves for two clients (Clinical + miRNA )
  • Figure 5: Loss and accuracy curves for three clients (Clinical + miRNA + DNAm)
  • ...and 3 more figures

Theorems & Definitions (9)

  • Definition 1
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Theorem 1
  • proof
  • Theorem 2: Convergence of BVFLMSP
  • proof
  • proof : Proof of Theorem \ref{['thm:main']}.