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An evidential time-to-event prediction model based on Gaussian random fuzzy numbers

Ling Huang, Yucheng Xing, Thierry Denoeux, Mengling Feng

TL;DR

In this model, uncertainty on event time is quantified by Gaussian random fuzzy numbers, a newly introduced family of random fuzzy subsets of the real line with associated belief functions, generalizing both Gaussian random variables and Gaussian possibility distributions.

Abstract

We introduce an evidential model for time-to-event prediction with censored data. In this model, uncertainty on event time is quantified by Gaussian random fuzzy numbers, a newly introduced family of random fuzzy subsets of the real line with associated belief functions, generalizing both Gaussian random variables and Gaussian possibility distributions. Our approach makes minimal assumptions about the underlying time-to-event distribution. The model is fit by minimizing a generalized negative log-likelihood function that accounts for both normal and censored data. Comparative experiments on two real-world datasets demonstrate the very good performance of our model as compared to the state-of-the-art.

An evidential time-to-event prediction model based on Gaussian random fuzzy numbers

TL;DR

In this model, uncertainty on event time is quantified by Gaussian random fuzzy numbers, a newly introduced family of random fuzzy subsets of the real line with associated belief functions, generalizing both Gaussian random variables and Gaussian possibility distributions.

Abstract

We introduce an evidential model for time-to-event prediction with censored data. In this model, uncertainty on event time is quantified by Gaussian random fuzzy numbers, a newly introduced family of random fuzzy subsets of the real line with associated belief functions, generalizing both Gaussian random variables and Gaussian possibility distributions. Our approach makes minimal assumptions about the underlying time-to-event distribution. The model is fit by minimizing a generalized negative log-likelihood function that accounts for both normal and censored data. Comparative experiments on two real-world datasets demonstrate the very good performance of our model as compared to the state-of-the-art.
Paper Structure (12 sections, 7 equations, 1 figure, 2 tables)

This paper contains 12 sections, 7 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Gaussian random fuzzy numbers
  4. Lognormal random fuzzy numbers
  5. Model
  6. Evidential time-to-event prediction network
  7. Loss function
  8. Experimental results
  9. Illustrative example on simulated dataset
  10. Comparative results on real-world datasets
  11. Conclusion
  12. Acknowledgment

Figures (1)

  • Figure 1: Simulated data, actual regression function (blue broken lines), and predictions obtained from the trained model. Predicted values $\log(y)$ are depicted by red solid lines, while belief prediction intervals (BPIs) at levels $\alpha \in \{0.5, 0.9, 0.99\}$ are represented by shaded areas in blue, green, and orange. The first and second rows are data with censoring intervals $[-1,0]$ and $[-2,0]$, respectively. The first and second columns are data with 10% and 70% censoring rates, respectively.