UAI 2026 论文列表

Large language models present challenges for principled uncertainty quantification, in part due to their complexity and the diversity of their outputs. Semantic dispersion, or the variance in the meaning of sampled answers, has been proposed as a useful proxy for model uncertainty, but the associated computational cost prohibits its use in latency-critical applications. We show that sampled semantic distributions can be distilled into lightweight student models which estimate a prompt-conditioned density before the language model generates an answer token. The student model predicts a semantic distribution over possible answers; the entropy of this distribution provides a prompt-level uncertainty signal, and the probability density allows answer-level reliability evaluation. Across experiments on TriviaQA and MMLU, we find our student models perform competitively relative to the teacher’s sampled semantic dispersion on a hallucination prediction task, whilst offering additional uncertainty primitives for out-of-domain detection and multiple-choice answer selection. We term this technique Semantic Self-Distillation (SSD), which can serve as a general framework for distilling predictive uncertainty in complex output spaces beyond language.

Policy-based approaches to Bayesian experimental design (BED) allow the learning of deep policy networks that adaptively make intelligent design decisions based on previously collected data. However, the training of such policies is often held back by a fundamental challenge: the double intractability of the expected information gain (EIG). This necessitates expensive or complex approximations that restrict the effort one can invest in optimising the policy itself. To address this, we show that the double intractability of the EIG can be isolated from the policy learning by first solving a score matching problem that is independent of the policy used, then using the learned score approximation to train the policy in a singly intractable manner. This turns the key multiplicative cost into an additive one and reduces the computational burden on the policy training itself, making it far cheaper to train the policy multiple times when needed, e.g. for architecture search, hyperparameter tuning, or avoiding local optima. In our experiments we train multiple competitive policies without inducing a multiplicative cost in likelihood evaluations, which can increase performance by allowing us to select the best policy even without performing hyperparameter or architecture searches.

Link prediction models are increasingly used to recommend interactions in evolving networks, yet their impact on network structure is typically assessed from static snapshots. In particular, observed homophily conflates intrinsic interaction tendencies with amplification effects induced by network dynamics and algorithmic feedback. We propose a temporal framework based on multivariate Hawkes processes that disentangles these two sources and introduce an instantaneous bias measure derived from interaction intensities, capturing current reinforcement dynamics beyond cumulative metrics. We provide a theoretical characterization of the stability and convergence of the induced dynamics, and experiments show that the proposed measure reliably reflects algorithmic feedback effects across different link prediction strategies.

Bayesian optimization is a data-efficient technique that has been shown to be extremely powerful to optimize expensive, black-box, and possibly noisy objective functions. Many applications involve optimizing probabilities and mixtures which naturally belong to the probability simplex, a constrained non-Euclidean domain defined by non-negative entries summing to one. This paper introduces α-GaBO, a novel family of Bayesian optimization algorithms over the probability simplex. Our approach is grounded in information geometry, a branch of Riemannian geometry which endows the simplex with a Riemannian metric and a class of connections. Based on information geometry theory, we construct Matérn kernels that reflect the geometry of the probability simplex, as well as a one-parameter family of geometric optimizers for the acquisition function. We validate our method on benchmark functions and on a variety of real-world applications including mixtures of components, mixtures of classifiers, and a robotic control task, showing its increased performance compared to constrained Euclidean approaches.

Markov chain Monte Carlo (MCMC) sampling of densities restricted to linearly constrained domains is an important task arising in Bayesian treatment of inverse problems in the natural sciences. While efficient algorithms for uniform polytope sampling exist, much less work has dealt with more complex constrained densities. In particular, gradient information as used in unconstrained MCMC is not necessarily helpful in the constrained case, where the gradient may push the proposal’s density out of the polytope. In this work, we propose a novel constrained sampling algorithm, which combines strengths of higher-order information, like the target’s log-density’s gradients and curvature, with the Hit- -Run proposal, a simple mechanism which guarantees the generation of feasible proposals, fulfilling the linear constraints. Our extensive experiments demonstrate improved sampling efficiency on complex constrained densities over various constrained and unconstrained samplers.

Directed acyclic graphs (DAGs) are widely used to represent complex causal relationships in real-world systems. The goal of causal discovery is to learn the underlying DAG from data generated by these systems. While *Greedy Equivalence Search* (GES) is a well-established score-based algorithm for causal discovery, the GES family often suffers from scalability and sample complexity issues due to its large search space and susceptibility to local optima. In this paper, we introduce *parent deletion*, a novel, simple, yet powerful operator for score-based causal discovery. This operator is theoretically sound and effectively alleviates these limitations. Moreover, its simplicity enables seamless compatibility with existing score-based methods, and extensive experiments demonstrate consistent improvements across a wide range of settings. The source code used in this study is available at https://github.com/LGAI-Research/breaking-bad.

The structural causal bandit (SCB) framework offers a graphical approach to identifying suboptimal actions by leveraging prior knowledge of the underlying causal structure. While theoretically appealing, there has been limited guidance on how to systematically transfer information across heterogeneous datasets from multiple environments. In this paper, we study the structural causal bandit under transportability, where prior knowledge from source environments is integrated to accelerate learning in a target deployment environment. We show that exploiting causal invariances across environments improves sample efficiency in identifying the optimal action.

We establish the first convergence guarantees for the plain vector-form Adam optimizer under heavy-tailed stochastic noise. While several Adam variants are known to achieve optimal iteration complexity in bounded-variance nonconvex optimization, little is understood about their behavior when stochastic gradients admit only a bounded p-th central moment for some p ∈ (1,2], a setting increasingly observed in modern deep learning. To address this gap, we generalize the recent online-to-nonconvex conversion framework to accommodate heavy-tailed martingale-difference noise. Building on this generalized framework, we develop a discounted regret analysis for Adam, without restrictive parameter coupling. Our results show that Adam converges to (ρ,ϵ)-stationary points under heavy-tailed noise. However, it exhibits a suboptimal iteration complexity and p-dependent convergence, a suboptimality that persists even in the bounded-variance case (p=2). When the domain radius is known and used to control the online-learner output, a standard setup in related literature, the convergence rate improves to match the optimal complexity. These findings provide new theoretical insight into the robustness and limitations of Adam in heavy-tailed regimes.

We present nearly optimal algorithms for simultaneously estimating the means of multiple distributions given a fixed total sample budget while ensuring uniform confidence intervals for the distributions. Our algorithms are based on the well-known _explore-then-commit_ policy from the bandit literature along with an additional refinement phase between the exploration phase and the commit phase. Our algorithms achieve regret Õ( (logσ_min^-1)^0.5 T^-1.5) when the rewards are subgaussian and Õ(σ_min^-1T^-1.5) regret when the rewards have bounded fourth moment, where T is the horizon and σ_min^2 is the minimum among the variances of the distributions of the G arms. We also provide lower bounds on the regret that nearly match the upper bounds for a constant G in both these cases. IImportantly, we show that the dependence on σ_min in both cases is necessary, resolving a long-standing open problem of [Carpentier et al]. We also study the setting where the distributions are hypercontractive. This distribution class includes the family of Gaussian distributions but also includes several families of heavy-tailed distributions. We propose an algorithm for hypercontractive reward distributions that achieves a Õ(T^-1.5) regret, independent of σ_min, and show a nearly matching lower bound for Gaussians.

Probabilistic model checking for Markov decision processes (MDPs) provides quantitative guarantees, but often offers limited insight into why undesired outcomes occur. Probability-raising (PR) causality addresses this by identifying states whose visitation increases the probability of reaching designated states. Existing PR-cause identification methods, however, use MDP modifications ill-suited for learning: the gap between conditional and unconditional reachability probabilities can be hard to detect from samples, and construction requires reachability probabilities of the original MDP, which are unavailable when transition probabilities are unknown. We study unknown MDPs and propose a learning approach with probabilistic guarantees for PR-cause identification. Our key ingredient is a restart-based MDP modification that reduces PR-cause checking to two conditional reachability queries without using reachability values of the original MDP. We prove correctness, establish sample-complexity bounds, and develop an anytime learning-and-checking algorithm based on two-sided value iteration that progressively classifies states as causal, non-causal, or undecided. Experiments on two benchmarks demonstrate reliable and fast identification of PR causes.

Causal identification functionals often require integration over conditional densities of continuous variables, such as those arising in nonparametric identification theory of total and mediated causal effects in DAGs with hidden variables. Estimating these densities and evaluating the resulting integrals can be statistically and computationally demanding. A common workaround is to discretize the continuous variable and replace integrals with finite sums. Although convenient, discretization alters the population-level functional and can induce non-negligible approximation bias, even when identification is correct. Under smoothness conditions, we show that the resulting coarsening error is first order in the bin width and arises at the level of the target functional, distinct from statistical estimation error. We propose a simple debiased coarsened functional that evaluates the outcome regression at within-bin conditional means, eliminating the leading coarsening error term and yielding a second-order approximation error. We derive plug-in and one-step estimators for this debiased coarsened functional. Simulations demonstrate substantial bias reduction and near-nominal confidence interval coverage, even under coarse binning. Our results provide a simple framework for controlling the impact of variable discretization on both parameter approximation and statistical estimation.

Here we introduce Partially Observed Structural Causal Models (POSCMs) as an extension of structural causal models (SCMs) to settings where upstream contexts co-determine both the interaction structure and downstream mechanisms on observed variables. POSCMs thus provide a self-contained causal modeling framework for endogenous graphs, allowing for an intervention hierarchy spanning node- and edge-level contexts and endogenous variable interventions. To define edge interventions, we separate node mechanisms into edge-local transmission channels that can be modified without changing the source node or the rest of the target mechanism. We provide an identifiability theory that clarifies which intervention families would suffice to disentangle structure formation from mechanisms. We then empirically validate these theoretical results in two external simulators: a biophysically detailed virtual human retina and a gene-regulatory analogue. The experiments reproduce non-identifiability under latent context, expose structure-mechanism confounding under latent edges, and recover pathway-level input-output relationships under targeted interventions, consistent with our positive Markov kernel identifiability results. Together, POSCMs provide an intervention-oriented framework for causal systems in which contexts, graph structure, mechanisms, and measurements are jointly generated and only partially observed.

True causal relationships are rarely known, and inferring causal graphs from data is hard. A fundamental challenge is how to assess whether a given causal graph is good in the absence of a ground truth. We propose falsifying candidate causal graphs based on whether they can explain the propagation of an outlier event. Our approach leverages a key principle: weak outliers rarely cause strong ones. While this principle has previously been used in root cause analysis to identify root causes without prior knowledge of the graph, we turn it on its head and use it to falsify candidate causal graphs whose implied outlier propagation is inconsistent with the data. To this end, we present the first statistical tests for the hypothesis that a candidate graph is the true causal graph, and show they have false positive control, power guarantees against incorrect causal graphs, and can operate with a single outlier sample.

Uncovering the causal mechanisms of complex real-world systems remains a significant challenge, as these systems often entail high data collection costs and involve unknown interventions. We introduce MetaCaDI, the first framework to cast the identification of unknown interventions as a meta-learning problem, explicitly leveraging a jointly learned causal graph. MetaCaDI is a Bayesian framework that learns a shared causal structure across multiple environments and is optimized to rapidly adapt to new, few-shot intervention target identification tasks. A key innovation is our model’s analytical adaptation, which uses a closed-form solution to bypass expensive and potentially unstable gradient-based bilevel optimization. Extensive experiments on synthetic and complex gene expression data demonstrate that MetaCaDI significantly outperforms state-of-the-art methods. It excels at identifying intervention targets from as few as 3 samples—where existing methods collapse to random chance—while robustly recovering the shared causal graph, proving its effectiveness in data-scarce scenarios.

We introduce Prior-Fitted Functional Flows, a generative foundation model for pharmacokinetics that enables zero-shot population synthesis and individual forecasting without manual parameter tuning. We learn functional vector fields, explicitly conditioned on the sparse, irregular data of an entire study population. This enables the generation of coherent virtual cohorts as well as forecasting of partially observed patient trajectories with calibrated uncertainty. We construct a new open-access literature corpus to validate our priors, and demonstrate state-of-the-art predictive accuracy on extensive real-world datasets. Our code repository a, pretrained model, data and examples are available online.

Active inference casts decision-making as inference, with the Expected Free Energy (EFE) providing an objective that unifies goal-seeking and information-gathering behavior. Recent work showed that EFE minimization can be reformulated as Variational Free Energy (VFE) minimization on a generative model augmented with epistemic priors, but left open how this formulation relates to other inference-based planning methods and whether it admits efficient message-passing implementations. Here we address both questions. First, we show that active inference is variational inference with specific entropy corrections to the VFE. Different planning-as-inference methods correspond to different corrections, each yielding a distinct objective; active inference is the variant whose corrections yield the Expected Free Energy. Second, we derive a message-passing scheme by introducing a channel reparameterization that re-localizes the entropy corrections into a standard Bethe free energy. Experiments on three grid-world environments with distinct uncertainty profiles show that the dynamics channel drives spatial information gathering when observations are decisive, the observation channel is critical when observations are merely suggestive, and only the full active inference objective performs robustly across all regimes.

Conformal prediction **(CP)** is a distribution-free framework for achieving probabilistic guarantees on black-box models. **CP** is generally applied to a model post-training. Recent research efforts, on the other hand, have focused on optimizing CP efficiency **during training**. We formalize this concept as the problem of **conformal risk minimization** (CRM). In this direction, **conformal training** **(ConfTr**) by (Stutz et. al (2022)) is a CRM technique that seeks to minimize the expected prediction set size of a model by simulating **CP** in-between training updates. In this paper, we provide a novel analysis for the **ConfTr** gradient estimation method, revealing a strong source of sample inefficiency that introduces training instability and limits its practical use. To address this challenge, we propose **variance-reduced conformal training** **(VR-ConfTr)**, a CRM method that carefully incorporates a novel variance reduction technique in the gradient estimation of the **ConfTr** objective function. Through extensive experiments on various benchmark datasets, we demonstrate that **VR-ConfTr** consistently achieves faster convergence and smaller prediction sets compared to baselines.

Bayesian inference of Bayesian network structures is often performed by sampling directed acyclic graphs along an appropriately constructed Markov chain. We present two techniques to improve sampling. First, we give an efficient implementation of basic moves, which add, delete, or reverse a single arc. Second, we expedite summing over parent sets, an expensive task required for more sophisticated moves: we devise a preprocessing method to prune possible parent sets so as to approximately preserve the sums. Our empirical study shows that our techniques can yield substantial efficiency gains compared to previous methods.

Efficient selection among multiple generative models is increasingly important in modern generative AI, where sampling from suboptimal models is costly. This problem can be viewed as a *multi-armed bandit (MAB)* task. Under diversity-aware evaluation scores, a non-degenerate mixture of generators can outperform any individual model, distinguishing this MAB setting from classical best-arm identification. Prior approaches incorporate an Upper Confidence Bound (UCB) exploration bonus into the mixture objective. However, across multiple datasets and evaluation metrics, we observe that the UCB term consistently slows convergence and reduces sample efficiency. In contrast, a simple *Mixture-Greedy* strategy without explicit UCB-type optimism converges faster and achieves even better performance, particularly for widely used metrics such as FID and Vendi where tight confidence bounds are difficult to construct. We provide theoretical insight explaining this behavior: under structural conditions, diversity-aware objectives induce *implicit exploration* by favoring interior mixtures, leading to sampling of all arms and sublinear regret guarantees for diversity-based objectives. These results suggest that in diversity-aware multi-armed bandits, e.g., for generative model selection, exploration can arise intrinsically from the objective’s geometry. The project code is available at https://github.com/bhrdbn/Mixture-Greedy.