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Heteroscedastic Neural Networks for Path Loss Prediction with Link-Specific Uncertainty

Jonathan Ethier

TL;DR

The paper tackles the problem of path loss prediction with reliable uncertainty estimates by employing heteroscedastic neural networks trained with Gaussian negative log-likelihood to jointly predict mean path loss and link-specific variance. It systematically compares three parameter-sharing architectures and validates them on large blind drive-test datasets, finding that the shared-parameter model offers the best training stability and predictive performance, including well-calibrated 95% prediction intervals. The approach yields RMSE around 7.4 dB and calibrated intervals (PICP ~95%) with informative width (MPIW ~29.6 dB), outperforming a homoscedastic baseline and providing spatially varying uncertainty to support RF planning and diagnostics. Spatial uncertainty maps and diagnostic insights reveal where training data are deficient, enabling targeted data collection and feature enhancement for improved reliability in real-world deployments.

Abstract

Traditional and modern machine learning-based path loss models typically assume a constant prediction variance. We propose a neural network that jointly predicts the mean and link-specific variance by minimizing a Gaussian negative log-likelihood, enabling heteroscedastic uncertainty estimates. We compare shared, partially shared, and independent-parameter architectures using accuracy, calibration, and sharpness metrics on blind test sets from large public RF drive-test datasets. The shared-parameter architecture performs best, achieving an RMSE of 7.4 dB, 95.1 percent coverage for 95 percent prediction intervals, and a mean interval width of 29.6 dB. These uncertainty estimates further support link-specific coverage margins, improve RF planning and interference analyses, and provide effective self-diagnostics of model weaknesses.

Heteroscedastic Neural Networks for Path Loss Prediction with Link-Specific Uncertainty

TL;DR

The paper tackles the problem of path loss prediction with reliable uncertainty estimates by employing heteroscedastic neural networks trained with Gaussian negative log-likelihood to jointly predict mean path loss and link-specific variance. It systematically compares three parameter-sharing architectures and validates them on large blind drive-test datasets, finding that the shared-parameter model offers the best training stability and predictive performance, including well-calibrated 95% prediction intervals. The approach yields RMSE around 7.4 dB and calibrated intervals (PICP ~95%) with informative width (MPIW ~29.6 dB), outperforming a homoscedastic baseline and providing spatially varying uncertainty to support RF planning and diagnostics. Spatial uncertainty maps and diagnostic insights reveal where training data are deficient, enabling targeted data collection and feature enhancement for improved reliability in real-world deployments.

Abstract

Traditional and modern machine learning-based path loss models typically assume a constant prediction variance. We propose a neural network that jointly predicts the mean and link-specific variance by minimizing a Gaussian negative log-likelihood, enabling heteroscedastic uncertainty estimates. We compare shared, partially shared, and independent-parameter architectures using accuracy, calibration, and sharpness metrics on blind test sets from large public RF drive-test datasets. The shared-parameter architecture performs best, achieving an RMSE of 7.4 dB, 95.1 percent coverage for 95 percent prediction intervals, and a mean interval width of 29.6 dB. These uncertainty estimates further support link-specific coverage margins, improve RF planning and interference analyses, and provide effective self-diagnostics of model weaknesses.

Paper Structure

This paper contains 14 sections, 7 equations, 2 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Problem Formulation
  4. Architecture Variants
  5. Performance Metrics
  6. Dataset Description, Preprocessing, and Model Features
  7. Architecture Performance Analysis
  8. Model Optimization Strategy
  9. Training Stability
  10. Accuracy, Calibration, and Sharpness on Blind Test Sets
  11. Assessment of Normality
  12. Spatial Distribution of Predictive Uncertainty: A Use Case
  13. Uncertainty as Model Diagnostics
  14. Conclusions

Figures (2)

  • Figure 1: NLL (a) training and (b) validation loss using different architectures
  • Figure 2: Illustrative heatmap showing spatially dependent 95% confidence intervals (width ranging from 25 to 45 dB). Black regions represent areas inside buildings where path loss is not predicted, as training data is outdoor-only. Larger intervals indicate higher uncertainty, showing 20 dB variation across the map compared to a fixed 27 dB for the homoscedastic approach.