This paper proposes Partially Observable Reference Policy Programming, a novel anytime online approximate POMDP solver which samples meaningful future histories very deeply while simultaneously forcing a gradual policy update. We provide theoretical guarantees for the algorithm's underlying scheme which say that the performance loss is bounded by the average of the sampling approximation errors rather than the usual maximum, a crucial requirement given the sampling sparsity of online planning. Empirical evaluations on two large-scale problems with dynamically evolving environments -- including a helicopter emergency scenario in the Corsica region requiring approximately 150 planning steps -- corroborate the theoretical results and indicate that our solver considerably outperforms current online benchmarks.

Trajectory planning involving multi-agent interactions has been a long-standing challenge in the field of robotics, primarily burdened by the inherent yet intricate interactions among agents. While game-theoretic methods are widely acknowledged for their effectiveness in managing multi-agent interactions, significant impediments persist when it comes to accommodating the intentional uncertainties of agents. In the context of intentional uncertainties, the heavy computational burdens associated with existing game-theoretic methods are induced, leading to inefficiencies and poor scalability. In this paper, we propose a novel game-theoretic interactive trajectory planning method to effectively address the intentional uncertainties of agents, and it demonstrates both high efficiency and enhanced scalability. As the underpinning basis, we model the interactions between agents under intentional uncertainties as a general Bayesian game, and we show that its agent-form equivalence can be represented as a potential game under certain minor assumptions. The existence and attainability of the optimal interactive trajectories are illustrated, as the corresponding Bayesian Nash equilibrium can be attained by optimizing a unified optimization problem. Additionally, we present a distributed algorithm based on the dual consensus alternating direction method of multipliers (ADMM) tailored to the parallel solving of the problem, thereby significantly improving the scalability. The attendant outcomes from simulations and experiments demonstrate that the proposed method is effective across a range of scenarios characterized by general forms of intentional uncertainties. Its scalability surpasses that of existing centralized and decentralized baselines, allowing for real-time interactive trajectory planning in uncertain game settings.

The Dutch railway network is one of the busiest in the world, with delays being a prominent concern for the principal passenger railway operator NS. This research addresses a gap in delay prediction studies within the Dutch railway network by employing an XGBoost Classifier with a focus on topological features. Current research predominantly emphasizes short-term predictions and neglects the broader network-wide patterns essential for mitigating ripple effects. This research implements and improves an existing methodology, originally designed to forecast the evolution of the fast-changing US air network, to predict delays in the Dutch Railways. By integrating Node Centrality Measures and comparing multiple classifiers like RandomForest, DecisionTree, GradientBoosting, AdaBoost, and LogisticRegression, the goal is to predict delayed trajectories. However, the results reveal limited performance, especially in non-simultaneous testing scenarios, suggesting the necessity for more context-specific adaptations. Regardless, this research contributes to the understanding of transportation network evaluation and proposes future directions for developing more robust predictive models for delays.

We study the problem of sampling from a distribution $μ$ with density $\propto e^{-V}$ for some potential function $V:\mathbb R^d\to \mathbb R$ with query access to $V$ and $\nabla V$. We start with the following standard assumptions: (1) The potential function $V$ is $L$-smooth. (2) The second moment $\mathbf{E}_{X\sim μ}[\|X\|^2]\leq M$. Recently, He and Zhang (COLT'25) showed that the query complexity of sampling from such distributions is at least $\left(\frac{LM}{dε}\right)^{Ω(d)}$ where $ε$ is the desired accuracy in total variation distance, and the Poincaré constant can be arbitrarily large. Meanwhile, another common assumption in the study of diffusion based samplers (see e.g., the work of Chen, Chewi, Li, Li, Salim and Zhang (ICLR'23)) strengthens the smoothness condition (1) to the following: (1*) The potential function of *every* distribution along the Ornstein-Uhlenbeck process starting from $μ$ is $L$-smooth. We show that under the assumptions (1*) and (2), the query complexity of sampling from $μ$ can be $\mathrm{poly}(L,d)\cdot \left(\frac{Ld+M}{ε^2}\right)^{\mathcal{O}(L+1)}$, which is polynomial in $d$ and $\frac{1}ε$ when $L=\mathcal{O}(1)$ and $M=\mathrm{poly}(d)$. This improves the algorithm with quasi-polynomial query complexity developed by Huang et al. (COLT'24). Our results imply that the seemly moderate strengthening of the smoothness condition (1) to (1*) can lead to an exponential gap in the query complexity of sampling algorithms. Moreover, we show that together with the assumption (1*) and the stronger moment assumption that $\|X\|$ is $λ$-sub-Gaussian for $X\simμ$, the Poincaré constant of $μ$ is at most $\mathcal{O}(λ)^{2(L+1)}$. As an application of our technique, we obtain improved estimate of the Poincaré constant for mixture of Gaussians with the same covariance.

Standard Bayesian approaches for linear time-invariant (LTI) system identification are hindered by parameter non-identifiability; the resulting complex, multi-modal posteriors make inference inefficient and impractical. We solve this problem by embedding canonical forms of LTI systems within the Bayesian framework. We rigorously establish that inference in these minimal parameterizations fully captures all invariant system dynamics (e.g., transfer functions, eigenvalues, predictive distributions of system outputs) while resolving identifiability. This approach unlocks the use of meaningful, structure-aware priors (e.g., enforcing stability via eigenvalues) and ensures conditions for a Bernstein--von Mises theorem -- a link between Bayesian and frequentist large-sample asymptotics that is broken in standard forms. Extensive simulations with modern MCMC methods highlight advantages over standard parameterizations: canonical forms achieve higher computational efficiency, generate interpretable and well-behaved posteriors, and provide robust uncertainty estimates, particularly from limited data.

Equivariant models leverage prior knowledge on symmetries to improve predictive performance, but misspecified architectural constraints can harm it instead. While work has explored learning or relaxing constraints, selecting among pretrained models with varying symmetry biases remains challenging. We examine this model selection task from an uncertainty-aware perspective, comparing frequentist (via Conformal Prediction), Bayesian (via the marginal likelihood), and calibration-based measures to naive error-based evaluation. We find that uncertainty metrics generally align with predictive performance, but Bayesian model evidence does so inconsistently. We attribute this to a mismatch in Bayesian and geometric notions of model complexity for the employed last-layer Laplace approximation, and discuss possible remedies. Our findings point towards the potential of uncertainty in guiding symmetry-aware model selection.

Tensor Network (TN) Kernel Machines speed up model learning by representing parameters as low-rank TNs, reducing computation and memory use. However, most TN-based Kernel methods are deterministic and ignore parameter uncertainty. Further, they require manual tuning of model complexity hyperparameters like tensor rank and feature dimensions, often through trial-and-error or computationally costly methods like cross-validation. We propose Bayesian Tensor Network Kernel Machines, a fully probabilistic framework that uses sparsity-inducing hierarchical priors on TN factors to automatically infer model complexity. This enables automatic inference of tensor rank and feature dimensions, while also identifying the most relevant features for prediction, thereby enhancing model interpretability. All the model parameters and hyperparameters are treated as latent variables with corresponding priors. Given the Bayesian approach and latent variable dependencies, we apply a mean-field variational inference to approximate their posteriors. We show that applying a mean-field approximation to TN factors yields a Bayesian ALS algorithm with the same computational complexity as its deterministic counterpart, enabling uncertainty quantification at no extra computational cost. Experiments on synthetic and real-world datasets demonstrate the superior performance of our model in prediction accuracy, uncertainty quantification, interpretability, and scalability.

--Stochastic Petri Nets (SPNs) are an increasingly popular tool of choice for modeling discrete-event dynamics in areas such as epidemiology and systems biology, yet their parameter estimation remains challenging in general and in particular when transition rates depend on external covariates and explicit likelihoods are unavailable. We introduce a neural-surrogate (neural-network-based approximation of the posterior distribution) framework that predicts the coefficients of known covariate-dependent rate functions directly from noisy, partially observed token trajectories. Our model employs a lightweight 1D Convolutional Residual Network trained end-to-end on Gillespie-simulated SPN realizations, learning to invert system dynamics under realistic conditions of event dropout. During inference, Monte Carlo dropout provides calibrated uncertainty bounds together with point estimates. On synthetic SPNs with 20% missing events, our surrogate recovers rate-function coefficients with an RMSE = 0.108 and substantially runs faster than traditional Bayesian approaches. These results demonstrate that data-driven, likelihood-free surrogates can enable accurate, robust, and real-time parameter recovery in complex, partially observed discrete-event systems.

--In this paper, we propose RFF-GP-HSMM, a fast unsupervised time-series segmentation method that incorporates random Fourier features (RFF) to address the high computational cost of the Gaussian process hidden semi-Markov model (GP-HSMM). GP-HSMM models time-series data using Gaussian processes, requiring inversion of an N N kernel matrix during training, where N is the number of data points. T o address this, the proposed method approximates the Gaussian process with linear regression using RFF, preserving expressive power while eliminating the need for inversion of the kernel matrix. Experiments on the Carnegie Mellon University (CMU) motion-capture dataset demonstrate that the proposed method achieves segmentation performance comparable to that of conventional methods, with approximately 278 times faster segmentation on time-series data comprising 39,200 frames. Segmentation enables the extraction of frequent events and facilitates analysis of their underlying structure, even in complex time-series data that are difficult to analyze manually.

Marginalization -- summing a function over all assignments to a subset of its inputs -- is a fundamental computational problem with applications from probabilistic inference to formal verification. Despite its computational hardness in general, there exist many classes of functions (e.g., probabilistic models) for which marginalization remains tractable, and they can be commonly expressed by polynomial size arithmetic circuits computing multilinear polynomials. This raises the question, can all functions with polynomial time marginalization algorithms be succinctly expressed by such circuits? We give a negative answer, exhibiting simple functions with tractable marginalization yet no efficient representation by known models, assuming $\textsf{FP}\neq\#\textsf{P}$ (an assumption implied by $\textsf{P} \neq \textsf{NP}$). To this end, we identify a hierarchy of complexity classes corresponding to stronger forms of marginalization, all of which are efficiently computable on the known circuit models. We conclude with a completeness result, showing that whenever there is an efficient real RAM performing virtual evidence marginalization for a function, then there are small circuits for that function's multilinear representation.