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Latent Dynamics-Aware OOD Monitoring for Trajectory Prediction with Provable Guarantees

Tongfei Guo, Lili Su

Abstract

In safety-critical Cyber-Physical Systems (CPS), accurate trajectory prediction provides vital guidance for downstream planning and control, yet although deep learning models achieve high-fidelity forecasts on validation data, their reliability degrades under out-of-distribution (OOD) scenarios caused by environmental uncertainty or rare traffic behaviors in real-world deployment; detecting such OOD events is challenging due to evolving traffic conditions and changing interaction patterns, while safety-critical applications demand formal guarantees on detection delay and false-alarm rates, motivating us-following recent work [1]-to formulate OOD monitoring for trajectory prediction as a quickest changepoint detection (QCD) problem that offers a principled statistical framework with established theory; we further observe that the real-world evolution of prediction errors under in-distribution (ID) conditions can be effectively modeled by a Hidden Markov Model (HMM), and by leveraging this structure we extend the cumulative Maximum Mean Discrepancy approach to enable detection without requiring explicit knowledge of the post-change distribution while still admitting provable guarantees on delay and false alarms, with experiments on three real-world driving datasets demonstrating reduced detection delay and robustness to heavy-tailed errors and unknown post-change conditions.

Latent Dynamics-Aware OOD Monitoring for Trajectory Prediction with Provable Guarantees

Abstract

In safety-critical Cyber-Physical Systems (CPS), accurate trajectory prediction provides vital guidance for downstream planning and control, yet although deep learning models achieve high-fidelity forecasts on validation data, their reliability degrades under out-of-distribution (OOD) scenarios caused by environmental uncertainty or rare traffic behaviors in real-world deployment; detecting such OOD events is challenging due to evolving traffic conditions and changing interaction patterns, while safety-critical applications demand formal guarantees on detection delay and false-alarm rates, motivating us-following recent work [1]-to formulate OOD monitoring for trajectory prediction as a quickest changepoint detection (QCD) problem that offers a principled statistical framework with established theory; we further observe that the real-world evolution of prediction errors under in-distribution (ID) conditions can be effectively modeled by a Hidden Markov Model (HMM), and by leveraging this structure we extend the cumulative Maximum Mean Discrepancy approach to enable detection without requiring explicit knowledge of the post-change distribution while still admitting provable guarantees on delay and false alarms, with experiments on three real-world driving datasets demonstrating reduced detection delay and robustness to heavy-tailed errors and unknown post-change conditions.
Paper Structure (19 sections, 2 theorems, 14 equations, 5 figures, 6 tables, 1 algorithm)

This paper contains 19 sections, 2 theorems, 14 equations, 5 figures, 6 tables, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. Related Work
  3. Trajectory Prediction under Distributional Shift
  4. OOD Detection and Sequential Change Detection
  5. Problem Formulation
  6. Trajectory Prediction
  7. OOD Detection as Quickest Change-Point Detection
  8. Modeling the Non-Stationarity of Prediction Errors
  9. Empirical Evidence for Dynamic-Switching Errors
  10. HMM Error Model
  11. Pre- and Post-Change Error Models
  12. Method: Kernel-based Detection
  13. Experimental Setup
  14. Results
  15. How does DC-MMD compare with baselines across predictors and driving domains?
  16. ...and 4 more sections

Key Result

Theorem 1

For any given $b>0$, $m\in \mathbb{N}$, and properly chosen $\zeta$ such that $\zeta < D(\lambda^{(1)}, \lambda^{(0)})$, the WADD of Algorithm alg:hmm_kernel_cusum satisfies where $a=\sqrt{\frac{2-2\Delta^{(0)} + 4 R^{(0)}}{(m-1)(1-\Delta^{(0)})}}$, and $d=D(\lambda^{(1)}, \lambda^{(0)}) -\zeta$.

Figures (5)

  • Figure 1: Benchmarking trajectory prediction across real-world driving datasets. Examples from nuScenes (top), ApolloScape (middle), and NGSIM (bottom) illustrate the diversity in agent interactions and scene dynamics.
  • Figure 2: Non-stationary switching behavior of prediction errors across three driving environments: NGSIM (Highway), nuScenes (Mixed Urban), and ApolloScape (Unstructured Urban). The $x$-axis represents the time step ($t$) and the $y$-axis denotes the error (log ADE). Preliminary results on other metrics (i.e., FDE and RMSE) show similar behaviors. Background shading indicates the inferred latent error mode: Low-Error Mode ( Blue) and High-Error Mode (Red). The two modes are separated via MAP estimation under a Gaussian mixture model posterior, which assigns each observation to the component with the highest posterior responsibility.
  • Figure 3: WADD–MTFA trade-off curves across driving domains. Each curve traces one detection method under two models: GRIP++ (top) and FQA (bottom) prediction. WADD ↓ = faster detection; MTFA ↑ = fewer false alarms.
  • Figure 4: Latent-dynamic performance across benchmarks. Each radar axis represents a progressively weaker stationarity assumption, arranged clockwise: S (strictly stationary) $\to$WS (weakly stationary) $\to$NS (non-stationary). The Global Profile (left) overlays all six methods; individual panels isolate each method's footprint with per-axis average WADD annotated (at MTFA $\approx 2$ ; 500 runs). Larger area $\Leftrightarrow$ WADD$\downarrow$ (faster change-point response).
  • Figure 5: Robustness to heavy-tailed distribution. Left: Detection delay (WADD) at $\text{MTFA} \approx 2$. DC-MMD (Ours) maintains the lowest delay across all distributions: Gaussian (light-tailed, blue), Laplace (moderate-tailed, tan), and Student-$t$ (heavy-tailed, red).

Theorems & Definitions (5)

  • Remark 1: Optional Variance-Normalization
  • Theorem 1: Detection delay
  • proof
  • Theorem 2: False alarm
  • Remark 2: Order-optimality