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Invariant Transformation and Resampling based Epistemic-Uncertainty Reduction

Sha Hu

TL;DR

This work observed that when inferring multiple samples based on invariant transformations of an input, inference errors can show partial independences due to epistemic uncertainty, and proposes a "resampling"based inferencing that applies to a trained AI model with multiple transformed versions of an input, and aggregates inference outputs to a more accurate result.

Abstract

An artificial intelligence (AI) model can be viewed as a function that maps inputs to outputs in high-dimensional spaces. Once designed and well trained, the AI model is applied for inference. However, even optimized AI models can produce inference errors due to aleatoric and epistemic uncertainties. Interestingly, we observed that when inferring multiple samples based on invariant transformations of an input, inference errors can show partial independences due to epistemic uncertainty. Leveraging this insight, we propose a "resampling" based inferencing that applies to a trained AI model with multiple transformed versions of an input, and aggregates inference outputs to a more accurate result. This approach has the potential to improve inference accuracy and offers a strategy for balancing model size and performance.

Invariant Transformation and Resampling based Epistemic-Uncertainty Reduction

TL;DR

This work observed that when inferring multiple samples based on invariant transformations of an input, inference errors can show partial independences due to epistemic uncertainty, and proposes a "resampling"based inferencing that applies to a trained AI model with multiple transformed versions of an input, and aggregates inference outputs to a more accurate result.

Abstract

An artificial intelligence (AI) model can be viewed as a function that maps inputs to outputs in high-dimensional spaces. Once designed and well trained, the AI model is applied for inference. However, even optimized AI models can produce inference errors due to aleatoric and epistemic uncertainties. Interestingly, we observed that when inferring multiple samples based on invariant transformations of an input, inference errors can show partial independences due to epistemic uncertainty. Leveraging this insight, we propose a "resampling" based inferencing that applies to a trained AI model with multiple transformed versions of an input, and aggregates inference outputs to a more accurate result. This approach has the potential to improve inference accuracy and offers a strategy for balancing model size and performance.
Paper Structure (11 sections, 1 theorem, 15 equations, 5 figures)

This paper contains 11 sections, 1 theorem, 15 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Resampling A Trained AI model
  3. Mathematical Formulations
  4. Invariant Transformations
  5. Resampling Theorem
  6. Epistemic Uncertainty Reduction with Resampling
  7. Discussions
  8. Simulation Results with MIMO Detection
  9. Inference Errors
  10. Performance Enhancements
  11. Summary

Key Result

Theorem 1

Assume there are $M$ estimates of a scalar variable $s$, denoted as $s_m \!=\! s \!+\! z_m$, and $z_m$ represents a zero-mean estimation error with identical variance $\text{var}(z_m)\! =\! \sigma^2$. Further, the correlation between any two errors satisfies $\text{cov}(\boldsymbol{z}_m,\boldsymbol{ subject to $\sum_{m=0}^{M-1} \beta_m \!=\! 1$. The minimum variance of estimation error in $\bar{s}

Figures (5)

  • Figure 1: Resampling a trained MIMO detector with multiple inference samples generated from conjugates, flips, and permutations for an input $(\boldsymbol{y}, \boldsymbol{H})$.
  • Figure 2: Conventional supervised-learning based training (a) and inferencing (b), and the proposed resampling based inferencing with multiple samples generated from an input observation. In case $f$ is unknown, $\text{Char}(f)$ is excluded from the inputs to the model.
  • Figure 3: The variance decrements in relation to $\rho_{mn}\!=\!\rho$ for $m\!\ne\!n$.
  • Figure 4: The distribution of inference errors and example samples.
  • Figure 5: Uncoded BER and BLER for $8\!\times\! 8$ MIMO and 256QAM modulation under ETU-70Hz channel.

Theorems & Definitions (3)

  • Definition 1: Mapping Characteristic
  • Definition 2: Invariant Transformation
  • Theorem 1