Dynamic Aware: Adaptive Multi-Mode Out-of-Distribution Detection for Trajectory Prediction in Autonomous Vehicles

1. Problem Statement

Autonomous vehicles (AVs) rely heavily on trajectory prediction models to ensure safety. However, these models often fail when encountering Out-of-Distribution (OOD) scenarios—rare traffic scenes, aggressive maneuvers, or environmental uncertainties not present in training data.

• Limitations of Existing Methods:
  • Frame-wise approaches: Most current OOD detection methods focus on perception (object detection) and operate on a frame-by-frame basis, ignoring spatiotemporal correlations in agent trajectories.
  • Static Thresholds: Recent work framed OOD detection as a Quickest Change Detection (QCD) problem using CUSUM algorithms. However, these methods assume a single, static error distribution.
  • The Core Issue: The authors identify that prediction errors are multi-modal (exhibiting distinct low-error and high-error regimes) and that the active error mode evolves dynamically over time. A single global threshold is suboptimal: it is either too conservative (causing long detection delays in complex scenes) or too sensitive (causing false alarms in simple scenes).

2. Methodology: Mode-Aware CUSUM (MA-CUSUM)

The paper proposes MA-CUSUM, an adaptive framework that explicitly models the temporal evolution of error modes to dynamically adjust detection thresholds.

A. Empirical Observation

Analysis of real-world benchmarks (ApolloScape, NGSIM, nuScenes) reveals:

• Prediction errors follow a Gaussian Mixture Model (GMM) with two latent components: a low-risk mode (low error) and a high-risk mode (high error).
• The active mode switches over time depending on the driving context (e.g., frequent switches in urban intersections vs. stable modes on highways).
• These mode transitions are latent and cannot be reliably inferred from raw scene statistics (e.g., agent count or speed) alone.

B. Algorithm Overview

MA-CUSUM processes prediction error streams ($\epsilon_t$) in three sequential steps per time step:

1. Mode Estimation (MAP):

   • Uses Maximum A Posteriori (MAP) estimation to infer the current latent error mode ($\hat{M}_t \in \{0, 1\}$) based on the current prediction error $\epsilon_t$ and the pre-trained GMM.
   • This step is computationally lightweight ($O(1)$) and strictly online.

2. Adaptive Threshold Update:

   • Calculates a mode-specific threshold $\theta_t^{(\hat{M}_t)}$.
   • Estimates the local error variance $\hat{\sigma}(\hat{M}_t)$ over a sliding window of recent steps matching the estimated mode.
   • The threshold is scaled by this variance ($h \propto \sigma$) and smoothed over time to prevent instability. Crucially, the low-error mode is assigned a higher threshold to absorb transient fluctuations, while the high-error mode uses a lower threshold for rapid sensitivity.

3. CUSUM Update & Detection:

   • Computes a log-likelihood ratio (LLR) based on the estimated mode and the available knowledge of the post-change (OOD) distribution.
   • Accumulates evidence in a CUSUM statistic $S_t$.
   • Triggers an alarm when $S_t$ exceeds the adaptive threshold $\theta_t^{(\hat{M}_t)}$.

C. Knowledge Paradigms

The framework is robust to varying levels of knowledge regarding the OOD distribution ($g$):

• Full Knowledge: Exact $g$ is known.
• Partial Knowledge: Only coarse statistics (mean/variance) of $g$ are known.
• Unknown Knowledge: No parametric form of $g$ is known; uses a robust shift-based approximation.

3. Key Contributions

1. Systematic Evidence: First to demonstrate across multiple benchmarks that trajectory prediction errors exhibit time-evolving multi-modal distributions, invalidating the assumption of a single static error distribution.
2. MA-CUSUM Algorithm: Introduces a novel algorithm that dynamically identifies the active error regime and adapts detection thresholds accordingly, preserving the efficiency of classical CUSUM while adding mode awareness.
3. Modularity & Efficiency: The method is model-agnostic, requiring only streaming prediction residuals (no ground truth or model internals). It introduces negligible computational overhead (one-timestamp delay) compared to standard CUSUM.
4. Comprehensive Evaluation: Validated on large-scale datasets (ApolloScape, NGSIM, nuScenes) and diverse models (GRIP++, FQA), showing consistent improvements over state-of-the-art baselines.

4. Experimental Results

The authors evaluated MA-CUSUM against likelihood-based methods (IGMM, NLL), sequential detectors (Z-Score, Chi-Square), and the baseline Global CUSUM.

• Detection Accuracy: MA-CUSUM achieved the highest AUROC (0.93–0.95) and AUPR across all models and datasets.
  • On the FQA model, it improved AUPR by 157.6% compared to Global CUSUM, significantly reducing false positives during rare OOD events.
• Delay vs. False Alarm Trade-off:
  • MA-CUSUM consistently achieved lower detection delays at the same false alarm rates compared to Global CUSUM.
  • Under Markovian and Arbitrary switching dynamics (most realistic for AVs), MA-CUSUM reduced the Worst-Case Average Detection Delay (WADD) by 30–40%.
• Robustness:
  • The method maintained stable False Alarm Rates (FAR) even under "Unknown Knowledge" settings where the post-change distribution was not fully specified.
  • It outperformed computationally expensive Uncertainty Quantification (UQ) methods (like Deep Ensembles and MC-Dropout) while being ~7x faster (5.1ms vs 29–38ms per frame).

5. Significance

• Safety Critical: By reducing detection delay in hazardous scenarios without increasing false alarms, MA-CUSUM enables AVs to react faster to distribution shifts, preventing potential accidents caused by overconfident but incorrect predictions.
• Theoretical Advancement: It bridges the gap between statistical change detection and the complex, non-stationary nature of real-world traffic, proving that "one-size-fits-all" detection is suboptimal.
• Practical Deployment: The low computational cost and lack of dependency on model internals make it highly suitable for real-time, onboard deployment in production autonomous vehicles.

In conclusion, the paper establishes that context-aware, adaptive thresholding based on latent error modes is essential for robust OOD detection in trajectory prediction, offering a principled and efficient solution for next-generation autonomous driving safety systems.