🤖 machine learning

Evidential Fusion Network for Multimodal Survival Prediction under Missing Modalities

The paper proposes the Evidential Missing Modality Survival Fusion (EMMS) model, which leverages Dempster-Shafer theory and Gaussian Random Fuzzy Numbers to achieve state-of-the-art, calibrated multimodal survival predictions under missing data conditions by treating absent modalities as vacuous evidence without requiring generative imputation.

Original authors: Yucheng Xing, Hailan Mo, Zi Wang, Ling Huang, Mengling Feng

Published 2026-06-23

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CC BY 4.0

Original authors: Yucheng Xing, Hailan Mo, Zi Wang, Ling Huang, Mengling Feng

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are a doctor trying to predict how long a patient might live with a specific type of cancer. To make the best guess, you usually want two types of information:

The "Picture" (Pathology): A microscopic photo of the tumor tissue.
The "Code" (Genomics): A list of the patient's gene activity.

In a perfect world, you'd have both. But in the real world, things go wrong. Sometimes the tissue sample runs out before you can take the picture, or the gene test is too expensive and gets skipped. This leaves you with only half the story.

Most current computer models try to guess the missing half. They say, "Oh, you don't have a picture? No problem, I'll imagine what the picture probably looks like based on the genes." The problem is, this is like a chef guessing the taste of a missing ingredient. Sometimes the guess is right, but often the computer "hallucinates" (makes up) details that don't exist, which can lead to dangerous mistakes in high-stakes medical decisions.

Other models just ignore the missing piece and try to make do with what they have, but they act like they are just as confident as if they had the full picture. This is dangerous because they don't admit, "Hey, I'm missing a huge piece of the puzzle, so I shouldn't be this sure."

The Solution: The "Honest" AI (EMMS)

The authors of this paper propose a new system called EMMS (Evidential Missing Modality Survival Fusion). Instead of guessing missing data or pretending everything is fine, EMMS uses a clever mathematical trick based on Dempster–Shafer theory (think of it as a "confidence accounting system").

Here is how it works, using simple analogies:

1. The "Empty Box" Strategy

When a piece of data is missing (e.g., no gene test), EMMS doesn't try to fill the box with a fake item. Instead, it puts an empty box labeled "I know nothing about this."

Old way: Try to fill the box with a guess (risky).
EMMS way: Leave it empty but mark it clearly. This empty box is called "vacuous evidence." It tells the system, "This input contributes zero information, so don't let it mess up the other good information."

2. The "Team Meeting" (Fusion)

Imagine the Pathology team and the Genomics team are meeting to decide a patient's prognosis.

If both teams are there, they combine their notes to make a strong, confident decision.
If the Genomics team is absent, the Pathology team still gives their report.
Crucially: Because the Genomics team is missing, the final decision comes with a loud warning label: "This prediction is based on only half the data, so we are less certain."

The system calculates a "confidence score." If data is missing, the score drops naturally. It doesn't force a high-confidence answer when it doesn't have the facts.

3. Two Types of "Uncertainty"

The paper explains that the system tracks two kinds of doubt:

Aleatoric Uncertainty (Noise): The natural randomness in the data (e.g., "Even with perfect data, biology is messy").
Epistemic Uncertainty (Ignorance): The doubt caused by missing information (e.g., "I don't know the answer because I'm missing the gene test").
EMMS is special because it can tell the difference between "The data is noisy" and "I don't have the data."

What Did They Find?

The researchers tested this system on four different types of cancer data (Breast, Stomach, Kidney, and Lung). They simulated situations where up to 60% of the data was missing.

Better Accuracy: Even when data was missing, EMMS made better predictions than other methods that tried to guess the missing parts or just ignored the problem.
Honest Confidence: When the system was unsure (because data was missing), it admitted it. Other systems kept acting confident even when they were wrong.
No Extra Cost: Unlike other methods that try to "reconstruct" missing data (which takes a lot of computer power), EMMS is fast. It doesn't need to do extra work to fill in the blanks; it just handles the blanks gracefully.

The Bottom Line

This paper presents a smarter way for AI to handle incomplete medical records. Instead of making up facts or pretending to know everything, the system admits when it's missing information and adjusts its confidence accordingly. It's like a doctor who says, "Based on what I have, here is my best guess, but please note that I'm missing a key test, so we should be careful."

Technical Summary: Evidential Fusion Network for Multimodal Survival Prediction under Missing Modalities

Problem Statement

Accurate survival prediction is critical for precision oncology, yet the deployment of multimodal models in real-world clinical settings is frequently hindered by missing modalities. In practice, complete morpho-molecular profiles (combining whole-slide images and transcriptomic data) are often unavailable due to tissue exhaustion, sequencing costs, or heterogeneous infrastructure.

Existing approaches face two primary limitations:

Imputation-based methods (e.g., SMIL, M3Care) reconstruct missing data via generative modeling. While effective on average, they risk "hallucinating" non-existent biological signals and incur high computational costs, which is problematic for high-stakes clinical decisions.
Imputation-free methods (e.g., EmbraceNet) aggregate only available embeddings but often treat missingness merely as a masking or dropout issue. They fail to explicitly quantify the epistemic uncertainty (lack of knowledge) induced by absent modalities, often resulting in miscalibrated confidence levels that do not reflect the model's ignorance.

Furthermore, current models struggle to distinguish between aleatoric uncertainty (intrinsic data noise) and epistemic uncertainty (uncertainty due to missing information), providing only a "best guess" without signaling reliability.

Methodology

The authors propose the Evidential Missing Modality Survival Fusion (EMMS) model, a framework designed to handle incomplete multimodal observations without data reconstruction. The core components are:

1. Theoretical Foundation: Dempster–Shafer Theory and GRFNs

EMMS is grounded in Dempster–Shafer evidential theory. Instead of predicting a single survival time, each modality's prediction is represented as survival evidence parameterized by Gaussian Random Fuzzy Numbers (GRFNs).

A GRFN, denoted as $\tilde{Y} \sim \tilde{N}(\mu, \sigma^2, h)$ $\tilde{Y} \sim \tilde{N} (μ, σ^{2}, h)$ , models the survival time distribution where:
- $\mu$ : Location parameter (most plausible event-time estimate).
- $\sigma^2$ : Aleatoric uncertainty (data variability).
- $h$ : Epistemic strength (inverse of epistemic uncertainty/ignorance).
Vacuous Evidence: Crucially, when a modality is missing, the model sets its epistemic strength $h=0$ . This causes the GRFN to degenerate into "vacuous evidence," representing complete ignorance. This formulation avoids approximating missing inputs; instead, it explicitly encodes their absence as zero evidential contribution.

2. Unimodal Branches

The model processes two modalities independently before fusion:

Pathology Branch: Whole-slide images (WSIs) are tessellated into patches, encoded via a pretrained patch encoder, and aggregated into a slide-level representation using the TITAN slide encoder. This feature is mapped to survival evidence via a prototype-based evidential formulation using radial basis function kernels.
Genomics Branch: Transcriptomic profiles are processed through a similar framework to generate survival evidence modeled as a GRFN.

3. Evidential Fusion

The model fuses the evidence from available modalities using Dempster's combination rule.

Handling Missingness: A binary availability indicator ( $r \in \{0, 1\}$ ) determines if a modality is present. If $r=0$ , the modality contributes vacuous evidence ( $h=0$ ).
Weighted Aggregation: The fused GRFN parameters ( $\mu_f, \sigma^2_f, h_f$ ) are calculated via a closed-form, evidence-weighted aggregation. Modalities with higher epistemic strength contribute more to the final prediction.
Graceful Degradation: When a modality is missing, the fusion naturally reduces to the available modality without interference. The total epistemic strength ( $h_f$ ) accumulates additively, serving as an interpretable metric of overall confidence. A reduction in $h_f$ explicitly reflects the uncertainty induced by missing data.

4. Loss Function

The training objective combines:

Survival Loss ( $L_{surv}$ ): A generalized negative log-likelihood for GRFNs that supervises both uncensored and right-censored samples using belief and plausibility bounds.
Alignment Loss ( $L_{align}$ ): A symmetric Kullback–Leibler (KL) divergence term applied only when both modalities are present, acting as a lightweight cross-modal consistency regularizer.

Key Contributions

Vacuous Evidence Formulation: The paper introduces a method to treat missing modalities as vacuous evidence ( $h=0$ ) within a GRFN framework. This prevents the model from hallucinating data or being contaminated by missing inputs, while naturally increasing the epistemic uncertainty of the prediction.
Uncertainty Quantification: EMMS explicitly distinguishes between aleatoric and epistemic uncertainty. The total evidential strength serves as a built-in, interpretable metric for the confidence of the prediction under incomplete observations.
Computational Efficiency: Unlike imputation-based methods, EMMS requires no generative phase or latent-space retrieval for missing data, introducing no additional computational overhead compared to imputation-free baselines.
Closed-Form Fusion: The use of Dempster–Shafer theory allows for principled, closed-form aggregation of multimodal evidence, ensuring that missing inputs exert no influence on available data.

Experimental Results

The authors evaluated EMMS on four cancer cohorts from The Cancer Genome Atlas (TCGA): BRCA, LUAD, STAD, and KIRC.

Performance under Complete Data: In the 0% missing modality setting, EMMS achieved state-of-the-art (SOTA) performance in terms of Concordance Index (C-index) and Integrated Brier Score (IBS) across most datasets, outperforming baselines like DisPro, MUSE, and Flex-MoE.
Robustness under Missing Data: Under a 60% missing modality rate, EMMS consistently outperformed all baselines across all datasets and evaluation settings (pathology-only, genomics-only, and complete-modality). It demonstrated superior robustness where other models showed significant performance degradation.
Calibration: Calibration plots indicated that EMMS predictions remained closer to the ideal diagonal line compared to baselines, with a lower Mean Absolute Deviation (MAD). This suggests the model provides more reliable confidence estimates.
Efficiency: Training time comparisons showed that EMMS is comparable in speed to the imputation-free baseline MUSE and significantly faster than the imputation-based DisPro.

Significance and Claims

The paper claims that EMMS provides a scalable, computation-effective, and theoretically grounded solution for personalized medicine in realistic clinical settings where data completeness cannot be guaranteed.

By leveraging Dempster–Shafer theory, the model bridges the gap between predictive performance and uncertainty awareness. It allows clinical decision support systems to "signal their own ignorance" when data is missing, distinguishing between noise and lack of knowledge. The authors emphasize that this approach achieves SOTA discrimination and calibration without the risks of data hallucination or the computational burden of generative imputation, making it a viable candidate for deployment in heterogeneous clinical environments.