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

Tongfei Guo; Lili Su

cs.ROMar 15, 2026

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

Authors: Tongfei Guo, Lili Su

Organizations: Department of Electrical and Computer Engineering, Northeastern University, Boston, MA, USA.

Abstract

In safety-critical Cyber-Physical Systems (CPS), trajectory prediction guides downstream planning and control. Deep learning models forecast well on validation data, but their reliability drops in out-of-distribution (OOD) scenarios driven by environmental uncertainty or rare traffic behaviors [1, 2]. Such failures are often silent: forecasts stay spatially plausible while accuracy collapses, and reported uncertainty does not rise [3]. Detection is hard because traffic conditions and interaction patterns keep evolving, yet the safety-critical nature of autonomous driving (AD) demands formal guarantees on detection delay and false-alarm rate. Following [4], we reframe OOD monitoring as quickest changepoint detection (QCD), a principled statistical framework with well-established theory. We find that the evolution of prediction errors on in-distribution (ID) data is well modeled by a Hidden Markov Model (HMM). Building on this, we extend a recent cumulative Maximum Mean Discrepancy approach to our setting. The method needs no detailed prior knowledge of the post-change distribution, yet admits provable delay and false-alarm guarantees. On three real-world driving datasets, it reduces detection delay while staying robust to heavy-tailed distributions and unknown post-change conditions.

Figures & tables

Fig. 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.

Highway — structured, low-density
Scene	Src	Emission		Transition
Scene	Src	$\Delta\mu$	$\bar{\sigma}^{2}$	$p$
Car-following (platoon)	N	Mod.	Easy	0.15
Congested stop-and-go	N	Mod.	Mod.	0.32
Mixed Urban — transitional, Mod. complexity
On-ramp merge	Nu A	Mod.	Mod.	0.55

TABLE I: Latent error dynamics across driving datasets, modeled as HMMs with emission parameters and transition probability. Emission parameters:

\Delta\mu

(mean gap between modes) and

\bar{\sigma}^{2}

(within-mode variance) characterize detection difficulty as Easy (large

\Delta\mu

, small

\bar{\sigma}^{2}

), Moderate (Mod.), or Hard (small

\Delta\mu

, large

\bar{\sigma}^{2}

). Transition parameter:

p

(mode-switching probability) reflects how often the latent state changes. Each marker denotes the dataset source: N = NGSIM, Nu = nuScenes, A = ApolloScape.

Fig. 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.

Category	Method	AUROC $\uparrow$			FPR@95 $\downarrow$
		NGSIM	nuScenes	ApolloScape	NGSIM	nuScenes	ApolloScape
		(Highway)	(Mixed urban)	(Unstructured Urban)	(Highway)	(Mixed urban)	(Unstructured Urban)
Point-wise	NLL [ 27 ]	0.71	0.64	0.58	0.62	0.71	0.78
(UQ-based)	lGMM [ 24 ]	0.74	0.69	0.62	0.57	0.65	0.73
Sequential	G-CUSUM [ 12 ]	0.82	0.76	0.69	0.44	0.52	0.61
	GMM-CUSUM [ 4 ]	0.85	0.79	0.73	0.41	0.48	0.56

TABLE II: OOD detection performance across datasets. Higher AUROC (

\uparrow

) and lower FPR@95 (

\downarrow

) indicate better performance.

Fig. 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 down = faster detection; MTFA up = fewer false alarms.

Dataset	Model	Dev. (m)	ADE (ID / OOD)	$\boldsymbol{\Delta}$ (%)
NGSIM	GRIP++	0.46	0.73 / 1.82	+149
NGSIM	FQA	0.44	0.81 / 2.05	+153
nuScenes	GRIP++	0.52	1.12 / 2.71	+142
nuScenes	FQA	0.49	1.24 / 3.01	+143
ApolloScape	GRIP++	0.55	1.48 / 3.74	+153
ApolloScape	FQA	0.53	1.61 / 4.02	+150

TABLE III: Impact of subtle OOD generation on prediction accuracy. Dev. denotes the average spatial shifts (

{\leq}\,1

m).

\Delta

(%) denotes the error (ADE) increase from ID to OOD setting.

	WADD $\downarrow$			$\Delta$ (%)
Method	Gaussian	Laplace	Student- $t$	LP	ST
DC-MMD (Ours)	17.52	20.50	20.67	+17	+18
Mode-CUSUM	26.87	31.97	34.39	+19	+28
GMM-CUSUM	36.18	43.42	47.03	+20	+30
G-CUSUM	41.35	57.06	62.85	+38	+52
lGMM	47.58	59.95	66.14	+26	+39

TABLE IV: Detection delay (WADD; in time steps) at MTFA

\approx 2

under heavy-tailed emission misspecification.

\Delta

(%) denotes degradation relative to the Gaussian baseline.

Fig. 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).

Fig. 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 ).

Method	Robust	Delay
DC-MMD (Ours)	✓	16.7
Robust CUSUM ( $\kappa$ -shift)	✓	16.4
G-CUSUM (misspecified)		25.8
NLL		32.6

TABLE V: Detection delay (WADD; in time steps) when the post-change distribution is unknown. All methods operate at MTFA

\approx 1

. Results are averaged over 500 independent runs. Robust CUSUM uses a shift-based surrogate with

\kappa{=}2

selected following [ 4 ] .

Method	Complexity (Per Step)	Parameters	Real-Time
NLL [ 27 ]	$\text{O}(1)$	0	$\star\star\star$
G-CUSUM [ 12 ]	$\text{O}(1)$	0	$\star\star\star$
lGMM [ 24 ]	$\text{O}(1)$	Low	$\star\star\star$
Deep Ensembles [ 7 ]	$\text{O}(N)$	$N\times$ Model	$\star$
DC-MMD (Ours)	$\mathbf{\text{O}(1)^{\ddagger}}$	Minimal	$\mathbf{\star\star\star}$

TABLE VI: Computational Complexity and Real-Time Suitability.

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Out-of-Distribution (OOD) data poses a significant threat to machine learning models, often leading to model failure during deployment. All existing OOD detection methods are post-hoc, relying on evaluation metrics such as accuracy and AUC-ROC during inference to indirectly assess the model's response to OOD data by measuring deviations. In contrast to existing approaches, the proposed work shifts the paradigm from OOD detection to OOD prediction by proposing a pre-hoc anticipatory framework called PLSP for OOD prediction. We make several key contributions: (a) a dataset-independent metric called the CREDibility Score (CREDS) is proposed for OOD prediction; (b) credibility curves are introduced to study the maximum credibility a model can attain; and (c) credibility heat maps (and volume under surface) are introduced to characterize pre-hoc model behavior across different datasets. This work provides a novel perspective on signal processing under distributional shifts. Experiments across multiple datasets demonstrate that the proposed metric serves as a valuable measure for improving the robustness of machine learning models toward OOD prediction.

Abstract

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