UAI 2026 论文列表

We investigate Gaussian Process (GP) bandit optimization utilizing quantum kernels. While quantum kernels enable embedding data into high-dimensional Hilbert spaces—potentially offering enhanced expressivity or a "quantum advantage"—this property can pose challenges in bandit learning. Specifically, employing full quantum kernels naïvely may lead to increased model complexity and, consequently, higher cumulative regret impacting the learnability. To address this, we explore the use of projected quantum kernels and classical kernel approximation techniques, which effectively reduce feature dimensionality while preserving essential quantum properties. We demonstrate that these approaches can yield improved regret bounds by strategically balancing approximation error and information gain. Empirical results show that they significantly outperform models based on full quantum kernels in bandit optimization tasks. Additionally, we analyze how to select the optimal model complexity to achieve a favorable trade-off between expressivity and learnability. Our methods also substantially reduce computational costs by simplifying kernel-based inference to linear models, since only a finite set of reduced features is required.

Time series out-of-distribution generalization requires forecasters to remain reliable when deployment dynamics differ from training conditions due to covariate shift, concept shift, and temporal dependence. Probably Approximately Correct Bayesian domain adaptation provides computable certificates by decomposing target risk into a source risk term, a source-to-target mismatch term, and a complexity term, but standard analyses rely on independent sampling and distributional stability, assumptions that are violated in time series by serial dependence and nonstationary shift. We propose a model-agnostic online martingale Probably Approximately Correct Bayesian framework that yields finite-sample certificates under temporal dependence and distribution shift. The certificate replaces independent-sample concentration with martingale concentration that adapts to loss scale and predictable variation. We use the certificate as a surrogate regularizer for online calibration by training a gated residual Bayesian head on top of a fixed forecasting backbone, producing a corrective update that reverts to the backbone prediction when the gate is closed. Online calibration combines a source risk anchor, a posterior-shift penalty, and a time-adaptive mismatch term computed from target windows observed before forecasting. It follows a predict-then-update protocol in which outcomes become available only after forecasting and are used to update subsequent predictions. Experiments across convolutional, attention-based, and large language model-based forecasters show improved stability and accuracy under covariate and concept shift.

Discrete diffusion models offer a powerful framework for solving complex reasoning tasks, particularly through compositional generation, which combines multiple pre-trained experts to generalize beyond their individual training data. Recent theoretical corrections introduce time-dependent mixing weights to better align composed diffusion dynamics with the intended target. However, these methods are fundamentally limited by working on a per-sample basis, treating each generated state monolithically and ignoring the potential spatial or functional specializations of different experts. In this work, we address this limitation by proposing FactorDiff - a factor-wise composition framework for diffusion models. We posit that samples can be further decomposed into smaller factors, and propose a sampling process that dynamically routes each factor to the most relevant expert. We instantiate this framework with spatial/pixel-level compositions and validate it on the ARC-AGI benchmark, demonstrating that simple factor-specific routing consistently outperforms complex global scalar weighting schemes on tasks that require logical consistency and spatial disentanglement.

We introduce the task of clustering trajectories in offline reinforcement learning (RL) datasets to address the multi-modal nature of offline data. Such datasets often contain trajectories from diverse policies, and treating them as a single distribution can obscure structure and increase distributional shift. We formalize trajectory clustering by linking the KL-divergence of offline trajectory distributions with mixtures of policy-induced distributions. To solve this, we propose Policy-Guided K-means (PG-Kmeans) and Centroid-Attracted Autoencoder (CAAE). PG-Kmeans iteratively trains behavior cloning policies and assigns trajectories based on generation probabilities, while CAAE learns continuous latent representations regularized by a learnable codebook to achieve end-to-end clustering. We prove finite-step convergence of PG-Kmeans and analyze the ambiguity of optimal solutions caused by policy-induced conflicts. Experiments on D4RL and GridWorld show that PG-Kmeans and CAAE partition trajectories into coherent clusters and offer a framework for structuring offline data, with applications in data selection, curriculum learning, and policy transfer.

This paper develops principled updating rules for possibilistic inference, where uncertainty about a fixed parameter is represented by a possibility function, the maxitive analogue of a probability distribution, and comparisons are made pointwise via a partial order. From two complementary foundations, an information-conservation viewpoint and an axiomatic viewpoint, we derive the same canonical update: the posterior is the prior-likelihood product followed by supremum normalisation. The two derivations agree for an arbitrary loss, differing only in where the learning-rate parameter enters. This parameter controls epistemic strength and is not identifiable from the normalising evidence alone, clarifying the role of analogous learning-rate parameters in generalised Bayesian updating.

Typical semi-supervised learning (SSL) methods rely on distributional assumptions, and their performance degrades when these are violated. While PNU learning, a risk rewriting method, offers a distribution-free alternative, it is restricted to binary classification and its variance optimality remains unclear. In this paper, we propose a generalized framework that constructs unbiased risk estimators using linear combinations of component risks, subsuming PNU learning and extending to multiclass classification. We derive the minimum achievable variance, demonstrating our estimator can attain lower variance than PNU in asymmetric loss scenarios. Furthermore, we establish a generalization bound directly linking this variance reduction to improved learning performance. Based on these theoretical insights, we introduce two practical SSL methods that empirically match or outperform existing approaches on binary and multiclass benchmarks.

Epidemic spread on graphs involves local infection dynamics and directional propagation through population movement. Current epidemic graph neural networks combine these aspects using a single symmetric aggregation operator, which limits the learning of their distinct timescales and fails to capture the asymmetry of real epidemic spread. This leads to node representations collapsing to a common state, losing diversity necessary for distinguishing infection stages. To address these issues, we propose EpiRDN, which discretizes the reaction-diffusion equation on graphs and learns its components end-to-end. EpiRDN features a local reaction network for region-level transitions and an anisotropic diffusion operator that utilizes asymmetric attention for directional infection flow. A feature-conditioned damping coefficient balances preserving local identity and neighborhood aggregation. We demonstrate that feature diversity in EpiRDN decays at most geometrically with depth, providing a significant advantage over existing methods. Experiments on four real-world datasets related to influenza and COVID-19 show consistent improvements, especially at longer forecasting horizons.

Positive–Unlabeled (PU) learning critically depends on assumptions about how positive instances are labeled, yet the labeling mechanism is typically unknown in practice. Misspecification of the labeling mechanism can therefore lead to systematic bias and unstable learning. We formulate labeling mechanism identification as a statistical inference problem under an unknown class prior using only positive and unlabeled data. We propose a two-stage testing framework that first constructs a family of empirical positive sets through false discovery rate (FDR)-controlled multiple testing at multiple FDR levels, and then performs bootstrap-based selected completely at random (SCAR) consistency tests on each empirical positive set, whose evidence is aggregated via a Bonferroni correction to produce a global decision.We establish that each empirical positive set admits provably controlled contamination, and further show that the Bonferroni-aggregated bootstrap test provides valid inference. Experiments on synthetic and real-world datasets demonstrate that the proposed framework reliably distinguishes SCAR from selected at random (SAR) mechanisms and improves the robustness of downstream PU learning.

Evaluating the causal effect of a treatment on an outcome is a central objective in causal inference. While the average causal effect summarizes the mean impact of treatment, the central moments of the individual causal effect (ICE) characterize the shape of the ICE distribution, thereby revealing the extent and structure of treatment effect heterogeneity across individuals. This paper investigates the identification and bounding of the central moments of the ICE using only the marginal central moments of each potential outcome (PO). Compared with existing approaches that require knowledge of the full marginal distributions of the POs, marginal moment information is often substantially easier to obtain in empirical applications. Finally, we illustrate the practical relevance of our results through two empirical case studies.

High-dimensional images and measurements may indicate extreme and rare behavior, such as advanced stages of cancer or material failure, and understanding these distributions is important for many disciplines. Classically, extreme value theory (EVT) provides a theoretical framework for extrapolating based on extremeness of magnitude of measurements and is used to model the tail of a distribution from limited observations. We propose a framework for learning representations from high dimensional observations that are amenable to analysis using classical EVT. Specifically, we propose extending the max-stability property of EVT to φ-stability, which generalizes the max operator to a more general operator φ that has practical applications in high dimensional cases. We base φ-stability on representation learning techniques such that the resulting representations lend themselves to analysis by EVT and can model high-dimensional observations of extreme characteristics. This enables our method to extrapolate to observations of extreme behavior in the observation domain. We then extend our method to infinite dimensional observations such as time series. Empirical results indicate the utility of using max-stability for representations to extrapolate beyond the training data.

We study constraint-based structure learning of Markov networks and Bayesian networks in the presence of an unreliable conditional independence oracle that makes at most a bounded number of errors. For Markov networks, we observe that a low maximum number of vertex-wise disjoint paths implies that the structure is uniquely identifiable even if the number of errors is (moderately) exponential in the number of vertices. For Bayesian networks, however, we prove that one cannot tolerate any errors to always identify the structure even when many commonly used graph parameters like treewidth are bounded. Finally, we give algorithms for structure learning when the structure is uniquely identifiable.

We evaluate the ability of the current generation of large language models (LLMs) to help a decision-making agent facing an exploration-exploitation tradeoff. While previous work has largely study the ability of LLMs to solve combined exploration-exploitation tasks, we take a more systematic approach and use LLMs to explore and exploit in silos in various (contextual) bandit tasks. We find that reasoning models show the most promise for solving exploitation tasks, although they are still too expensive or too slow to be used in many practical settings. Motivated by this, we study tool use and in-context summarization using non-reasoning models. We find that these mitigations may be used to substantially improve performance on medium-difficulty tasks, however even then, all LLMs we study perform worse than a simple linear regression, even in non-linear settings. On the other hand, we find that LLMs do help at exploring large action spaces with inherent semantics, by suggesting suitable candidates to explore.

Scientific experiments are often designed to maximize information gain, yet in many applications the primary objective is to support reliable downstream decision-making. Existing decision-aware experimental design and active learning methods typically assume well-specified outcome models and implicitly rely on the stability of the optimal decision under real-world perturbations. In practice, however, experimental outcomes are frequently influenced by hidden or weakly modeled effects, which can substantially alter decision optimality and lead to misleading conclusions. We study sequential adversarially robust decision-aware experimental design, where data acquisition has to take into account information gain against plausible worst-case unexpected effects, modeled here as variation in adversarial variables. Building on Bayesian decision theory, we formalize an adversarially robust optimal decision under this setting and derive a principled Bayesian experimental design criterion. The criterion explicitly targets decision stability rather than nominal optimality. Experiments on synthetic and real-world scientific datasets show that conventional decision-aware design can converge rapidly to high confidence yet fragile decisions, while our robustness-aware approach yields decisions that are significantly more stable and reliable under adversarial variation.

We investigate the identifiability of nonlinear canonical correlation analysis (CCA) in a multi-view setup, in which each view is generated by applying an unknown nonlinear map to a linear mixture of shared latent variables plus view-private noise. Rather than pursuing exact unmixing, which is known to be ill-posed under general nonlinear mixing, we instead reframe multi-view CCA as a basis-invariant subspace identification problem. Under suitable latent priors and spectral separation conditions, we prove that the pairwise population CCA objective recovers correlated signal subspaces up to view-wise orthogonal ambiguity. For N ≥ 3 views, their multi-view aggregation provably isolates the jointly correlated subspaces shared across all views while eliminating view-private variation. We further establish finite-sample statistical consistency guarantees by translating the concentration of empirical cross-covariances into explicit subspace error bounds via spectral perturbation theory. Experiments on synthetic and rendered image datasets support our theoretical findings and illustrate the necessity of the assumed conditions.

Computer vision models are increasingly used as measurement tools to estimate population-level quantities from large image collections, but prediction errors introduce bias and the resulting estimates lack statistical guarantees required in scientific applications. Prior work uses a Monte Carlo framework to combine model predictions with ground-truth annotations by sampling some images for humans to label and is able to provide unbiased estimates with controllable accuracy, but primarily addresses single-scalar estimation. We study the more general problem of multi-target estimation, where many quantities (e.g., class counts or proportions) must be estimated simultaneously, and adapt sampling and estimation strategies from survey sampling to this setting. Evaluations on five detection and segmentation datasets with 7–80 classes show that importance sampling excels with moderate annotation budgets or fewer targets, whereas uniform sampling with control variates is superior when estimating many targets or operating with minimal labels. Additionally, a subset-based ratio estimator remains highly competitive across all regimes. Ultimately, our framework effectively combines biased model predictions and limited human labels into rigorous scientific measurements.

How can we make graph positive-unlabeled (PU) learning interpretable? Existing methods jointly process node features and edge information, which obscures their interaction and makes predictions difficult to interpret. In this paper, we propose a novel interpretable graph PU learning framework that explicitly decouples feature and edge processing, enabling multi-level interpretability. Our framework first produces a core prediction from node features using probabilistic circuits (PCs) and then refines it using edge information, providing graph-level interpretability by exposing how graph structure affects predictions. For feature-based prediction, we construct two PCs through a careful split of the training nodes, yielding node-level interpretability by highlighting which nodes support the separation of positive and negative instances. Finally, by leveraging the tractability of PCs, we obtain feature-level interpretability via feature attribute marginalization, which quantifies attribute impact and importance while revealing interactions and dependencies. Experiments on 10 datasets show that our framework achieves strong performance while substantially improving interpretability. The code is available at https://github.com/hagad1/graphpu-cpu.

Ordinal classification (OC) arises in high-stakes domains such as medicine and finance, where uncertainty quantification must account for the severity of ordinal errors. Conformal prediction (CP) provides distribution-free prediction sets with marginal coverage guarantees; however, its practical effectiveness depends critically on the choice of nonconformity function. We introduce a CP method for ordinal classification based on the ranked probability score (RPS), a proper scoring rule defined over cumulative predictive distributions. Although it reflects ordinal risk quite naturally, it has largely been neglected in conformal ordinal prediction (COP). When used as a measure of nonconformity, RPS yields median-centered contiguous prediction sets by construction. The method is model-agnostic, supports both assessed and grouped ordered categorical outcomes, and permits efficient implementation compared to greedy interval selection procedures. Across multiple ordinal image and tabular datasets, RPS-based CP produces contiguous prediction sets and strikes a favorable balance between prediction set width and the magnitude of ordinal miscoverage relative to existing CP methods.

Unobserved confounding is a fundamental obstacle in causal inference problems. In the graphical modeling literature, a general theory has been developed that allows identification in the presence of hidden variables, with some limitations. In particular, Pearl’s celebrated front-door criterion allows nonparametric identification in the presence of unobserved common causes of the treatment and the outcome, however it requires the presence of an unconfounded variable that mediates all causal influence from the treatment to the outcome. This stringent requirement limits the applicability of the front-door criterion. We propose proximal generalizations of the front-door criterion, allowing both arbitrary treatment/outcome confounding, and unobserved confounders of the mediator, provided informative proxies for the latter type of confounders are observed. In addition to deriving three new identification strategies in this setting, we provide plug-in and influence function-based estimation strategies for the resulting functionals, and evaluate their performance through simulations.

Many real-world reinforcement learning (RL) problems evolve in continuous time, where decisions occur at irregular, event-driven intervals rather than at fixed discrete steps. We study episodic continuous-time Markov Decision Processes (MDPs) in which decision epochs are governed by a homogeneous Poisson process and the reward and transition dynamics vary smoothly over time. We consider both a fixed number of jumps per episode and a fixed time budget with a random number of Poisson decision epochs. Under a Lipschitz continuity assumption in time, we exploit local smoothness through discretization and extend both UCRL <cit.> and Q-learning <cit.> to this setting, proving 𝒪̃(T^2/3) regret bounds for both model-based and model-free algorithms. Finally, we establish matching Ω̃(T^2/3) minimax lower bounds, showing that the rate is optimal up to logarithmic factors. These results provide the first tight regret guarantees for Lipschitz-smooth continuous-time episodic MDPs with Poisson decision epochs.