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Adapting GT2-FLS for Uncertainty Quantification: A Blueprint Calibration Strategy

Yusuf Guven, Tufan Kumbasar

TL;DR

This work tackles uncertainty quantification for deep learning by leveraging General Type-2 Fuzzy Logic Systems (GT2-FLSs) to produce prediction intervals. It introduces a blueprint calibration strategy that enables post-hoc adaptation of a GT2-FLS trained at a single coverage level (e.g., $φ_d=99\%$) to any target coverage $φ_d$ without retraining, using α-plane calibration and two methods: a look-up table and a derivative-free search. The approach yields calibrated GT2-FLSs (C-GT2-FLS) that achieve comparable or better coverage to models trained directly for the target $φ_d$, albeit with wider intervals, and with significantly reduced computational overhead. These results support scalable, practical deployment of GT2-FLS-based UQ in high-dimensional settings.

Abstract

Uncertainty Quantification (UQ) is crucial for deploying reliable Deep Learning (DL) models in high-stakes applications. Recently, General Type-2 Fuzzy Logic Systems (GT2-FLSs) have been proven to be effective for UQ, offering Prediction Intervals (PIs) to capture uncertainty. However, existing methods often struggle with computational efficiency and adaptability, as generating PIs for new coverage levels $(φ_d)$ typically requires retraining the model. Moreover, methods that directly estimate the entire conditional distribution for UQ are computationally expensive, limiting their scalability in real-world scenarios. This study addresses these challenges by proposing a blueprint calibration strategy for GT2-FLSs, enabling efficient adaptation to any desired $φ_d$ without retraining. By exploring the relationship between $α$-plane type reduced sets and uncertainty coverage, we develop two calibration methods: a lookup table-based approach and a derivative-free optimization algorithm. These methods allow GT2-FLSs to produce accurate and reliable PIs while significantly reducing computational overhead. Experimental results on high-dimensional datasets demonstrate that the calibrated GT2-FLS achieves superior performance in UQ, highlighting its potential for scalable and practical applications.

Adapting GT2-FLS for Uncertainty Quantification: A Blueprint Calibration Strategy

TL;DR

This work tackles uncertainty quantification for deep learning by leveraging General Type-2 Fuzzy Logic Systems (GT2-FLSs) to produce prediction intervals. It introduces a blueprint calibration strategy that enables post-hoc adaptation of a GT2-FLS trained at a single coverage level (e.g., ) to any target coverage without retraining, using α-plane calibration and two methods: a look-up table and a derivative-free search. The approach yields calibrated GT2-FLSs (C-GT2-FLS) that achieve comparable or better coverage to models trained directly for the target , albeit with wider intervals, and with significantly reduced computational overhead. These results support scalable, practical deployment of GT2-FLS-based UQ in high-dimensional settings.

Abstract

Uncertainty Quantification (UQ) is crucial for deploying reliable Deep Learning (DL) models in high-stakes applications. Recently, General Type-2 Fuzzy Logic Systems (GT2-FLSs) have been proven to be effective for UQ, offering Prediction Intervals (PIs) to capture uncertainty. However, existing methods often struggle with computational efficiency and adaptability, as generating PIs for new coverage levels typically requires retraining the model. Moreover, methods that directly estimate the entire conditional distribution for UQ are computationally expensive, limiting their scalability in real-world scenarios. This study addresses these challenges by proposing a blueprint calibration strategy for GT2-FLSs, enabling efficient adaptation to any desired without retraining. By exploring the relationship between -plane type reduced sets and uncertainty coverage, we develop two calibration methods: a lookup table-based approach and a derivative-free optimization algorithm. These methods allow GT2-FLSs to produce accurate and reliable PIs while significantly reducing computational overhead. Experimental results on high-dimensional datasets demonstrate that the calibrated GT2-FLS achieves superior performance in UQ, highlighting its potential for scalable and practical applications.

Paper Structure

This paper contains 12 sections, 21 equations, 3 figures, 2 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Learning GT2-FLSs for UQ
  3. Inference of Zadeh-type GT2-FLSs
  4. Learnable Parameter Sets
  5. DL Framework
  6. Adapting GT2-FLS for UQ: The blueprint
  7. Post-hoc Calibration Method-1: Look-up Table
  8. Post-hoc Calibration Method-2: A search algorithm
  9. Performance Analysis
  10. Design of Experiments
  11. Performance Evaluation
  12. Conclusion and Future Work

Figures (3)

  • Figure 1: The blue and yellow curves represent the calibration curves ($g^{-1}$) of the Parkinson's Motor (PM) and Powerplant (PP) datasets, respectively, where ${\color{red}\alpha_{\text{PM}}^*}$ and ${\color{red}\alpha_{\text{PP}}^*}$ indicate the critical $\alpha^*$ achieving 90% coverage, selected directly from the calibration curves without retraining the model. The calibration curves were obtained as follows: The baseline GT2-FLS was trained to generate PIs with $\phi_d=99\%$ through the TRS of its $\alpha_0$ plane$[\underline{y}(\boldsymbol{x}, {\alpha_0}), \overline{y}({\boldsymbol{x}, \alpha_0})]$. After training, $\alpha$-planes were quantized as $[0.01, 0.1, 0.2, \dots, 1]$. For each quantized $\alpha$-plane, the bounds $[\underline{y}(\boldsymbol{x},{\alpha}), \overline{y}(\boldsymbol{x},{\alpha})]$ were obtained, and the correspond empiric coverage $(\phi_{\alpha})$ was calculated on the calibration dataset. Linear interpolation was applied via the interp1 function to construct smooth calibration curves.
  • Figure 2: Illustrations of a Z-GT2-FS with an $\alpha$ - plane
  • Figure 3: Illustration of the PIs generated by GT2-FLS and C-GT2-FLS for the PP dataset: C-GT2-FLS($95$%): Calibrated for $\phi_d=95$ from a trained GT2-FLS ($99$%); GT2-FLS($95$%): Trained GT2-FLS for $\phi_d=$95$\%$.