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Conformal Prediction for Manifold-based Source Localization with Gaussian Processes

Vadim Rozenfeld, Bracha Laufer Goldshtein

TL;DR

This work tackles uncertainty quantification in acoustic source localization under adverse conditions by integrating a semi-supervised manifold-based Gaussian process regression (MMGP) with Transductive Conformal Prediction (TCP) to produce prediction intervals with finite-sample guarantees. The MMGP fuses per-node manifold GPs into a unified model, enabling robust localization from limited labeled data and unlabeled samples, while CP provides valid coverage for the resulting intervals. Empirical results in simulated reverberant rooms show that GPR-CP achieves the target coverage with narrower intervals than baselines like standard GPR and Jackknife+, and performance degrades gracefully with higher reverberation or lower SNR. The approach offers practical, statistically sound uncertainty quantification for robot audition and related audio localization systems in realistic environments.

Abstract

We address the problem of uncertainty quantification (UQ) in the localization of a sound source within adverse acoustic environments. Estimating the position of the source is influenced by various factors, such as noise and reverberation, leading to significant uncertainty. Quantifying this uncertainty is essential, particularly when localization outcomes impact critical decision-making processes, such as in robot audition, where the accuracy of location estimates directly influences subsequent actions. Despite this, common localization methods offer point estimates without quantifying the estimation uncertainty. To address this, we employ conformal prediction (CP)-a framework that delivers statistically valid prediction intervals (PIs) with finite-sample guarantees, independent of the data distribution. However, commonly used Inductive CP (ICP) methods require a large amount of labeled data, which can be difficult to obtain in the localization setting. To mitigate this limitation, we incorporate a semi-supervised manifold-based localization method using Gaussian process regression (GPR), with an efficient Transductive CP (TCP) technique, specifically designed for GPR. We demonstrate that our method generates statistically valid PIs across different acoustic conditions, while producing smaller intervals compared to baselines.

Conformal Prediction for Manifold-based Source Localization with Gaussian Processes

TL;DR

This work tackles uncertainty quantification in acoustic source localization under adverse conditions by integrating a semi-supervised manifold-based Gaussian process regression (MMGP) with Transductive Conformal Prediction (TCP) to produce prediction intervals with finite-sample guarantees. The MMGP fuses per-node manifold GPs into a unified model, enabling robust localization from limited labeled data and unlabeled samples, while CP provides valid coverage for the resulting intervals. Empirical results in simulated reverberant rooms show that GPR-CP achieves the target coverage with narrower intervals than baselines like standard GPR and Jackknife+, and performance degrades gracefully with higher reverberation or lower SNR. The approach offers practical, statistically sound uncertainty quantification for robot audition and related audio localization systems in realistic environments.

Abstract

We address the problem of uncertainty quantification (UQ) in the localization of a sound source within adverse acoustic environments. Estimating the position of the source is influenced by various factors, such as noise and reverberation, leading to significant uncertainty. Quantifying this uncertainty is essential, particularly when localization outcomes impact critical decision-making processes, such as in robot audition, where the accuracy of location estimates directly influences subsequent actions. Despite this, common localization methods offer point estimates without quantifying the estimation uncertainty. To address this, we employ conformal prediction (CP)-a framework that delivers statistically valid prediction intervals (PIs) with finite-sample guarantees, independent of the data distribution. However, commonly used Inductive CP (ICP) methods require a large amount of labeled data, which can be difficult to obtain in the localization setting. To mitigate this limitation, we incorporate a semi-supervised manifold-based localization method using Gaussian process regression (GPR), with an efficient Transductive CP (TCP) technique, specifically designed for GPR. We demonstrate that our method generates statistically valid PIs across different acoustic conditions, while producing smaller intervals compared to baselines.
Paper Structure (10 sections, 1 theorem, 25 equations, 3 figures, 1 table)

This paper contains 10 sections, 1 theorem, 25 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Guaranteed coverage prediction intervals for Source Localization
  3. Problem Formulation
  4. Multiple Manifold Gaussian Process
  5. Conformal Prediction with Gaussian Process Regression
  6. Experiments and Results
  7. Experimental settings
  8. Evaluation
  9. Results
  10. Conclusions

Key Result

Theorem 1

(Marginal CP coverage guarantee vovk2005algorithmic). Suppose $(\mathbf{h}_1, p_1), \ldots ,(\mathbf{h}_{n_L}, p_{n_L}), (\mathbf{h}_{t}, p_{t})$ are exchangeable, then the PI eq:predictive_interval satisfies:

Figures (3)

  • Figure 1: MMGP localization integrated with GPR-CP to derive the PI $\Gamma^{\delta}(\mathbf{h}_t)$ for test position $p_t$, with relevant equations in red.
  • Figure 2: The simulated room setup.
  • Figure 3: PI widths for $99\%$ coverage at $T_{60}=700$ ms and SNR$=15$ dB. Left: X-coordinate. Right: Y-coordinate.

Theorems & Definitions (1)

  • Theorem 1