UAI 2026 Papers

Real-world learning tasks often encounter uncertainty due to covariate shift and noisy or inconsistent labels. However, existing robust learning methods merge these effects into a single distributional uncertainty set. In this work, we introduce a novel structured credal learning framework that explicitly separates these two sources. Specifically, we derive geometric bounds on the total variation diameter of structured credal sets and demonstrate how this quantity decomposes into contributions from covariate shift and expected label disagreement. This decomposition reveals a *gating effect*: covariate modulates how much label disagreement contributes to the joint uncertainty such that seemingly benign covariate shifts can substantially increase the effective uncertainty. We also establish finite-sample concentration bounds in a fixed covariate regime and demonstrate that this quantity can be efficiently estimated. Lastly, we show that robust optimization over these structured credal sets reduces to a tractable discrete min–max problem, avoiding ad-hoc robustness parameters. Overall, our approach provides a principled and practical foundation for robust learning under combined covariate and label mechanism ambiguity.

Physics models are inherently imperfect due to misspecified or missing mechanisms, resulting in systematic discrepancies between model predictions and real-world observations. The Kennedy–O’Hagan (KOH) framework addresses this issue through explicit discrepancy modeling. However, its non-amortized, per-instance formulation limits scalability across families of related systems. We introduce Amortized Physics-Informed Calibration (APIC), a population-level extension of KOH that leverages Neural Processes to perform scalable Bayesian inference across realizations. Our framework employs a two-branch latent architecture to disentangle instance-specific physical parameters from shared, state-dependent structural discrepancies. By integrating differentiable physics into an amortized inference backbone, APIC enables rapid calibration of unseen realizations from sparse observations while quantifying uncertainty. Experiments on the damped spring oscillator, the Lotka–Volterra system, and the advection–diffusion PDE with misspecified physics demonstrate improved parameter recovery and consistent identification of the systemic discrepancy structure compared to other calibration approaches.

Training neural networks to jointly predict mean and uncertainty estimates from noisy observations can be unstable, prompting a series of independent stabilization efforts. We argue that these interventions highlight a common underlying issue where gradient steps are poorly aligned with the geometry of the loss landscape. To better align updates with local curvature, we derive Fisher8, an output-layer gradient correction that reorients and rescales updates using Fisher geometry rather than Euclidean geometry. Unlike past stabilizers, Fisher8 introduces no data-dependent hyperparameters beyond learning rate and admits an approximate KL trust radius between successive predictive distributions. We show that prior stabilizers converge on overlapping components of this geometric correction. Across multidimensional regression and representation-learning tasks, Fisher8 obtains superior likelihood–error tradeoffs, predicts calibrated uncertainty estimates, and learns rich uncertainty-aware feature spaces.

This paper proposes a causal independence principle for *value*—the *value Causal Markov Condition* (v-CMC)—and develops the conceptual and mathematical foundations of a "causal value theory" linking causality and utility. After motivating a local formulation of the v-CMC, we introduce a probability–value duality that translates standard causal-inference results into the value setting. In particular, we formulate local, global, and decomposition versions of the v-CMC and prove their equivalence. We also define v-separation and show that it is sound and complete for conditional value independence. Furthermore, we derive a Bellman-type recursion as a special case of the v-CMC, thereby generalizing standard Bellman recursion from linear chains to causal DAGs. Finally, we show how the v-CMC supports modular transfer and updating of utility information across causal contexts and develop algorithms for causally structured utility elicitation and canonical influence-diagram construction.

We study Hedonic Project Games, a model in which agents select projects with divisible rewards while holding subjective preferences over coalition composition. This framework addresses a key gap in existing models: agents simultaneously care about who they collaborate with and what they work on. We extend this framework to an online learning setting in which rewards and preferences are initially unknown and learned through repeated interactions. We develop a decentralized variance-reduced stochastic policy-gradient method that provably converges to approximate Nash equilibria using single-sample gradient estimates, and an unbiased momentum variant that achieves faster convergence at the cost of additional curvature computation. We provide sample-complexity guarantees for both methods and show that exploiting the game’s additive pairwise structure reduces the interactions required to reach an approximate equilibrium by a polynomial factor in the number of agents. Experiments on synthetic instances and a real-world crowdsourcing dataset validate the theoretical convergence rates and demonstrate the advantages of momentum-based variance reduction over momentum-free baselines.

Synthetic tabular data generation addresses data scarcity and privacy constraints in a variety of domains. Tabular Prior-Data Fitted Network (TabPFN), a recent foundation model for tabular data, has been shown capable of generating high-quality synthetic tabular data. However, TabPFN is autoregressive: features are generated sequentially by conditioning on the previous ones, depending on the order in which they appear in the input data. We demonstrate that when the feature order conflicts with causal structure, the model produces spurious correlations that impair its ability to generate synthetic data and preserve causal effects. We address this limitation by integrating causal structure into TabPFN’s generation process through two complementary approaches: Directed Acyclic Graph (DAG)-aware conditioning, which samples each variable given its causal parents, and a partially directed acyclic graph (PDAG)-based strategy for scenarios with partial causal knowledge. We evaluate these approaches on controlled benchmarks and six CSuite datasets, assessing structural fidelity, distributional quality, and Average Treatment Effect (ATE) preservation. Across most settings, DAG-aware conditioning improves the quality and stability of synthetic data relative to vanilla TabPFN. Under partial causal knowledge, the oracle partially directed acyclic graph (oracle-PDAG), which orients only the edges into the colliders, shows moderate gains, while the benefit of a Completed Partially Directed Acyclic Graph (CPDAG) discovered from data depends on how well the causal structure is recovered. These results indicate that reliable causal structure, even partial, can be injected into TabPFN at inference time, without parameter updates, to improve synthetic data quality.

In safety-critical classification, the cost of failure is often asymmetric. Yet Bayesian deep learning summarises epistemic uncertainty with a single scalar, mutual information (MI), which cannot distinguish whether a model’s ignorance involves a benign or safety-critical class. We decompose MI into a per-class vector 𝒞_k(x)=σ_k^2/(2μ_k), with μ_k = 𝔼[p_k] and σ_k^2 = Var[p_k] across posterior samples. The decomposition follows from a second-order Taylor expansion of the entropy; the 1/μ_k weighting corrects boundary suppression and makes 𝒞_k comparable across rare and common classes. By construction ∑_k 𝒞_k ≈MI, and a companion skewness diagnostic flags inputs where the approximation degrades. After characterising the axiomatic properties of 𝒞_k, we validate it on three tasks: (i) selective prediction for diabetic retinopathy, where critical-class 𝒞_k reduces selective risk by 34.7

Kernel methods compare inputs through feature maps. Quantum kernels follow the same principle: input data are encoded into quantum states, which define quantum feature representations in Hilbert spaces. Kernel values are then obtained by estimating inner products between these states using suitable quantum circuit measurements. As a result, quantum kernels may be intractable to compute classically while remaining efficiently computable on quantum hardware, potentially leading to a quantum advantage. However, designing effective quantum kernels remains a major challenge. Many quantum kernels, such as the fidelity kernel, suffer from exponential concentration. This results in near-identity kernel matrices that fail to capture meaningful data correlations and lead to overfitting and poor generalization. In this paper, we propose a novel strategy for constructing quantum kernels that achieve good generalization performance, drawing inspiration from benign overfitting in classical machine learning. We introduce the concept of Local-Global quantum kernels, which combine two components: a local quantum kernel based on measurements of small subsystems, and a global quantum kernel derived from full-system measurements. To support the effectiveness of the proposed construction, we show theoretically and empirically that Local-Global quantum kernels exhibit benign overfitting.

Quantile regression provides a powerful tool for summarizing the conditional distribution of a real-valued random variable (r.v.) of interest Y as a function of covariates Z in cases where it shows a large dispersion with high probability, going beyond the situation where standard least square regression is informative/predictive. This article aims to extend this methodology to the pairwise setting, where the variable to be explained is a similarity score between two independent observations (e.g., pixelated ID photos used as input to biometric systems), and the explanatory variables consist of the pair of covariates attached to these observations, such as age or hair color. We establish theoretical guarantees for solutions of this statistical learning problem, considered here as empirical minimizers of a pairwise version of the pinball loss. Leveraging sharp concentration results for U-processes, we prove generalization bounds and identify mild conditions under which fast learning rates can be achieved. Confirming the probabilistic analysis, experiments based on simulation data also provide solid empirical evidence of the validity of the methodology promoted here for pairwise quantile regression. Finally, its usefulness from an application perspective is demonstrated by a detailed study aimed at analyzing errors in similarity scoring for facial recognition.

We present Entropic Variational Inference Auto-encoding (EVIA), a novel framework that extends classical variational approaches—including WAEs and AAEs, by incorporating entropy regularization. This regularization yields an entropic objective characterized by a closed-form Gibbs posterior, established via the Donsker–Varadhan representation. Consequently, this formulation facilitates efficient sampling strategy, allowing the model to perform high-fidelity autoencoding while jointly ensuring accurate distributional alignment. Empirical results demonstrate EVIA’s strong, consistent performance across diverse generative modeling tasks, including posterior estimation, variational inference, and image inpainting.

We study a novel machine learning problem: Positive-Unlabeled Regression (PUR), which extends the classical Positive-Unlabeled (PU) learning framework to regression setting with a non-negative, discrete target variable. This setting arises naturally in applications where only some positive quantitative outcomes are reported, while the absence of a label may either indicate a true zero outcome or an unreported positive value. Applications include predicting the number of diseases a patient may have, the number of complications following an illness, or the advancement stage of a disease. We formalize the PUR problem and highlight the limitations of naive approaches that either use reported target variable or discard unlabeled data. To account for the inherent bias in such strategies, we propose two principled methods. The first is based on calibration of regression estimates using posterior probabilities from classical PU learning. The second builds on an empirical risk minimization framework, restating the target risk as a weighted function dependent on the instance-specific propensity score. We demonstrate both theoretically and empirically that the proposed approaches yield improved performance over standard baselines.

We study linear contextual bandits under adversarial corruption and heavy-tailed noise with finite (1+ϵ)-th moments for some ϵ∈ (0,1]. Existing work that addresses both adversarial corruption and heavy-tailed noise relies on a finite variance assumption and suffers from computational inefficiency. We propose the first computationally efficient algorithm based on online mirror descent that is robust to both adversarial corruption and heavy-tailed noise. While the existing algorithm incurs 𝒪(tlog T) computational cost per round, our algorithm reduces this to 𝒪(1) per round. We establish an additive regret bound consisting of a term depending on the (1+ϵ)-moment bound of the noise and a term depending on the total amount of corruption. This bound unifies and extends previous guarantees for (generalized) linear contextual bandits under adversarial corruption and heavy-tailed noise. In particular, when ϵ = 1, it recovers existing guarantees under finite-variance assumptions. When no corruption is present, it achieves the same regret rate as existing results for linear contextual bandits with heavy-tailed noise in the general setting. Moreover, the algorithm requires only upper bounds on the noise moment and the total amount of corruption, while still guaranteeing sublinear regret.

Latent-variable energy-based models (LV-EBMs) assign a single normalized energy to joint pairs of observed data and latent variables, offering expressive generative modeling while capturing hidden structure. We recast maximum-likelihood training as a saddle problem over distributions on the latent and joint manifolds and view the inner updates as coupled Wasserstein gradient flows. The resulting algorithm alternates overdamped Langevin updates for a joint negative pool and for conditional latent particles with stochastic parameter ascent, requiring no discriminator or auxiliary networks. We prove existence and convergence under standard smoothness and dissipativity assumptions, with decay rates in KL divergence and Wasserstein-2 distance. The saddle-point view further yields an ELBO strictly tighter than bounds obtained with restricted amortized posteriors. Our method is evaluated on numerical approximations of physical systems and performs competitively against comparable approaches.

We propose a spectral learning method for stochastic nonlinear dynamical systems represented with embedded latent transfer operators in deep feature spaces. We instantiate the method as Deep Spectral Encoder (DSE), an operator-based latent state-space model in which a time-invariant neural encoder implements learnable nonlinear feature maps from observations, and these features define Markovian latent states whose temporal evolution and observation mapping are described by the transfer and observation operators, respectively. Functional canonical correlation analysis in a learnable Galerkin-projected feature space provides state coordinates from past and future observations, and the two linear operators are estimated on the state coordinates as ridge-regularized closed-form solutions that coincide with Galerkin projections of the associated covariance operators. On this representation, we generalize sequential Bayesian filtering and Koopman spectral mode decomposition in feature space. Experiments on several scenarios show stable and superior performance with sequential Bayesian filtering and dynamic mode decomposition baselines even under noise and partial observability.

Policy learning methods are increasingly used to inform treatment allocation under budget constraints. Most proposed methods assume complete treatment data, yet applications frequently suffer from missingness that can bias estimates and lead to suboptimal policies. We address this gap by extending efficient estimators for average treatment effect (ATE) estimation to policy value and conditional average treatment effect (CATE) estimation under missing at random (MAR) and missing completely conditionally at random (MCCAR) treatment data. Through asymptotic efficiency analysis, we prove that the MAR estimator, which leverages partially-observed units, is both valid and more efficient than the MCCAR estimator when MCCAR assumptions hold. This result provides formal justification for preferring MAR-based estimation in policy learning under both missing data settings. Our comprehensive experiments using synthetic and semi-synthetic datasets confirm that correctly specifying the missingness mechanism is crucial: misspecified estimators remain biased regardless of sample size, while our estimators achieve near-oracle performance when assumptions are satisfied. Our work provides practitioners with theoretically grounded, empirically validated tools for robust policy learning in the presence of missing treatment data.

We present the first analytical study of ECD, focusing on the one-dimensional setting for this first installment. We formalize a stochastic ECD dynamics (sECD) with energy-preserving noise, as well as a quantum analog of the ECD Hamiltonian (qECD), providing the foundation for a quantum algorithm through Hamiltonian simulation in a tractable model where the barrier-crossing mechanism can be computed explicitly. For one-dimensional double-well objectives in the under-guessing regime, we compute the expected dynamical hitting times from a local minimum to the global minimum. We prove that both sECD and qECD exhibit exponential improvements in continuous hitting time relative to their respective gradient-based baselines, stochastic gradient descent (SGD) and quantum tunneling walk (QTW). For objectives with tall barriers, qECD admits a further hitting time improvement over sECD. Mechanistically, ECD sidesteps the exponential cost associated with rare-escape events of SGD from local minima by moving from dissipative to energy-conserving dynamics.

Instrumental variable regression is a common approach for causal inference in the presence of unobserved confounding. However, identifying valid instruments is often difficult in practice. In this paper, we propose a novel method based on possibility theory that performs posterior inference on the treatment effect, conditional on a user-specified set of potential violations of the instrument exogeneity assumption. Our method can provide valid results even when only a single, potentially invalid, instrument is available. Crucially, and in contrast with existing methods, we prove a finite-sample coverage guarantee for the exactly calibrated (validified) uncertainty intervals when the violation set contains the true value, and we provide practical MC/χ^2 approximations. Simulation experiments and real-data applications indicate strong performance of the proposed approach.

In multiwinner approval elections with many candidates, voters may struggle to determine their preferences over the entire slate of candidates. It is therefore of interest to explore which (if any) fairness guarantees can be provided under reduced communication. In this paper, we consider voters with one-dimensional preferences: voters and candidates are associated with points in ℝ, and each voter’s approval set forms an interval of ℝ. We put forward a probabilistic preference model, where the voter set consists of different groups; each group is associated with a distribution over an interval of ℝ, so that each voter draws the endpoints of her approval interval from the distribution associated with her group. We present an algorithm for computing committees that provide Proportional Justified Representation + (PJR+), which proceeds by querying voters’ preferences, and show that, in expectation, it makes 𝒪(log k) queries per voter, where k is the desired committee size.

Neural network verification and data privacy are inherently in tension: verification demands full access to model parameters and input data, yet both are increasingly restricted by privacy regulations and intellectual property constraints. This tension has left robustness verification impractical in privacy-sensitive domains. In this work, we address this gap with SecureCROWN, the first framework for privacy-preserving neural network robustness verification. Built upon secure two-party computation (2PC), our framework enables a model owner and a data owner to jointly compute certified robustness bounds—revealing only the final result while provably protecting both parties’ private data under the semi-honest security model. A key challenge is securely computing the conditional operations in Linear Bound Propagation, where the data-dependent branching is incompatible with standard secure computation protocols. We eliminate branching by formulating conditional logic as continuous arithmetic operations. Additionally, we introduce a Newton–Raphson refinement method to improve numerical stability. Extensive analysis and experiments show that SecureCROWN strictly matches plaintext verification results, while completing in 0.1–200s across varied model sizes and communication settings (LAN/WAN), demonstrating the feasibility of privacy-preserving neural network verification.