AISTATS 2026 论文列表

This paper uses a minimum divergence framework to introduce a new way of calculating model weights that can be used to average probabilistic predictions from statistical and machine learning models. The method is general and can be applied regardless of whether the models under consideration are fit to data using frequentist, Bayesian, or some other fitting method. The proposed method is motivated in two different ways and is shown empirically to perform better than or on a par with standard model averaging methods, including model stacking and model averaging that relies on Akaike-style negative exponentiated model weighting, especially when the sample size is small. Our theoretical analysis explains why the method has a small-sample advantage.

Off-policy learning enables training policies from logged interaction data. Most prior work considers the batch setting, where a policy is learned from data generated by a single behavior policy. In real systems, however, policies are updated and redeployed repeatedly, each time training on all previously collected data while generating new interactions for future updates. This sequential off-policy learning setting is common in practice but remains largely unexplored theoretically. In this work, we present and study a simple algorithm for sequential off-policy learning, combining Logarithmic Smoothing (LS) estimation with online PAC-Bayesian tools. We further show that a principled adjustment to LS improves performance and accelerates convergence under mild conditions. The algorithms introduced generalize previous work: they match state-of-the-art offline approaches in the batch case and substantially outperform them when policies are updated sequentially. Empirical evaluations highlight both the benefits of the sequential framework and the strength of the proposed algorithms.

Survival analysis deals with modeling the time until an event occurs, and accurate probability estimates are crucial for decision-making, particularly in the competing-risks setting where multiple events are possible. While recent work has addressed calibration in standard survival analysis, the competing-risks setting remains under-explored as it is harder (the calibration applies to both probabilities across classes and time horizon). We show that existing calibration measures are not suited to the competing-risk setting and that recent models do not give well-behaved probabilities. To address this, we introduce a dedicated framework with two novel calibration measures that are minimized for oracle estimators (i.e., both measures are proper). We also introduce some methods to estimate, test, and correct the calibration. Our recalibration methods yield better probabilities while preserving discrimination.

Enumerating Minimal Unsatisfiable Subsets (MUSes) is a fundamental task in constraint satisfaction problems (CSPs). Its major challenge is the exponential growth of the search space, which becomes particularly severe when satisfiability checks are expensive. Recent machine learning approaches reduce this cost for Boolean satisfiability problems but rely on explicit variable-constraint relationships, limiting their application domains. This paper proposes a domain-agnostic method to accelerate MUS enumeration using Hypergraph Neural Networks (HGNNs). The proposed method incrementally builds a hypergraph with constraints as vertices and MUSes enumerated until the current step as hyperedges, and employs an HGNN-based agent trained via reinforcement learning to minimize the number of satisfiability checks required to obtain an MUS. Experimental results demonstrate the effectiveness of our approach in accelerating MUS enumeration, showing that our method can enumerate more MUSes within the same satisfiability check budget compared to conventional methods.

Although average gain optimality is a commonly adopted performance measure in Markov Decision Processes (MDPs), it is often too asymptotic. Further incorporating measures of immediate losses leads to the hierarchy of bias optimalities, all the way up to Blackwell optimality. In this paper, we investigate the problem of identifying policies of such optimality orders. To that end, for each order, we construct a learning algorithm with vanishing probability of error. Furthermore, we characterize the class of MDPs for which identification algorithms can stop in finite time. That class corresponds to the MDPs with a unique Bellman optimal policy, and does not depend on the optimality order considered. Lastly, we provide a tractable stopping rule that when coupled to our learning algorithm triggers in finite time whenever it is possible to do so.

We address the classical problem of constructing confidence intervals (CIs) for the mean of a distribution, given N i.i.d. samples, such that the CI contains the true mean with probability at least 1 - δ, where δ∈ (0,1). We characterize three distinct learning regimes based on the minimum achievable limiting width of any CI as the sample size N_δ→∞ and δ→ 0. In the first regime, where N_δ grows slower than log(1/δ), the limiting width of any CI equals the width of the distribution’s support, precluding meaningful inference. In the second regime, where N_δ scales as log(1/δ), we precisely characterize the minimum limiting width, which depends on the scaling constant. In the third regime, where N_δ grows faster than log(1/δ), complete learning is achievable, and the limiting width of the CI collapses to zero and CI converges to the true mean. We demonstrate that CIs derived from concentration inequalities based on Kullback-Leibler (KL) divergences achieve asymptotically optimal performance, attaining the minimum limiting width in both the sufficient and the complete learning regimes for distributions in three families: single-parameter exponential, bounded support and known bound on (1+ϵ)^ th moment. Additionally, these results extend to one-sided CIs, with the width notion adjusted appropriately. Finally, we generalize our findings to settings with random per-sample costs, motivated by practical applications such as stochastic simulators and cloud service selection. Instead of a fixed sample size, we consider a cost budget C_δ, identifying analogous learning regimes and characterizing the optimal CI construction policy.

Network alignment (i.e., graph matching) is a fundamental, though computationally challenging, problem that seeks to identify correspondences between vertices in network data. We present Community-Enhanced Semi-seeded Network Alignment (CESSNA), a novel algorithm that integrates community structure and partial seed information to improve matching efficiency and accuracy. CESSNA decomposes the global matching problem into smaller, community-based blocks, enabling efficient block-wise gradient descent and reducing computational complexity to that of the largest non-seeded community. The method flexibly incorporates both true and inferred communities, maintaining robustness even in the presence of noise and limited seed data. Experiments on synthetic and real-world datasets demonstrate that CESSNA consistently outperforms traditional seeded and unseeded graph matching approaches, achieving up to a 46-fold increase in accuracy over state-of-the-art methods without any seeds on the Wikipedia dataset. Furthermore, we present an innovative application of CESSNA to microbiome data, showing the capacity of this approach for robust, multiscale graph comparison in complex network data. These findings highlight the potential of CESSNA for addressing a broad spectrum of non-traditional network alignment problems, and emphasize CESSNA’s ability to accomplish efficient and accurate network alignment and its utility for uncovering new insights in biologically hierarchical data.

We study early-stopped mirror descent (ESMD) for high-dimensional Gaussian linear regression over arbitrary convex bodies and design matrices, where the task is to minimize the in-sample mean squared error. Our main result shows that some of the sharpest risk bounds for the least squares estimator (LSE), based on the local Gaussian width, extend to ESMD. We derive sufficient conditions on the potential, expressed via the Minkowski functional, under which our result holds. These conditions allow us to construct new potentials and analyze existing ones. Our results then yield general sufficient conditions for minimax optimality of ESMD, provide a systematic comparison with the LSE, and establish the tightest known risk bound in the ℓ_1-constrained setting.

Randomized trials are typically designed to detect average treatment effects but often lack the statistical power to uncover individual-level treatment effect heterogeneity, limiting their value for personalized decision-making. To address this, we propose the QR-learner, a model-agnostic learner that estimates conditional average treatment effects (CATE) within the trial population by leveraging external data from other trials or observational studies. The proposed method is robust: it can reduce the mean squared error relative to a trial-only CATE learner, and is guaranteed to recover the true CATE even when the external data are not aligned with the trial. Moreover, we introduce a procedure that combines the QR-learner with a trial-only CATE learner and show that it asymptotically matches or exceeds both component learners in terms of mean squared error. We examine the performance of our approach in simulation studies and apply the methods to a real-world dataset, demonstrating improvements in both CATE estimation and statistical power for detecting heterogeneous effects.

Networks are popular representations of complex data. In particular, differentially private synthetic networks are much in demand. Here, instead of starting from a network, we start with the complex data set itself and construct both a network representation and a corresponding synthetic network generator. We build a network model directly based on the underlying complex system data, capturing its structure and attributes. Using a random connection model, we devise an effective algorithmic approach for generating attributed synthetic networks which is ϵ-differentially private at the vertex level, while preserving utility. We provide theoretical guarantees for the accuracy of the private synthetic networks using the fused Gromov-Wasserstein distance.

Transporting causal information across populations is a critical challenge in clinical decision-making. Causal modeling provides criteria for identifiability and transportability, but these require knowledge of the causal graph, which rarely holds in practice. We propose a Bayesian method that combines observational data from the target domain with experimental data from a different domain to identify s-admissible backdoor sets, which enable unbiased estimation of causal effects across populations, without requiring the causal graph. We prove that if such a set exists, we can always find one within the Markov boundary of the outcome, narrowing the search space, and we establish asymptotic convergence guarantees for our method. We develop a greedy algorithm that reframes transportability as a feature selection problem, selecting conditioning sets that maximize the marginal likelihood of experimental data given observational data. In simulated and semi-synthetic data, our method correctly identifies transportability bias, improves causal effect estimation, and performs favorably against alternatives.

Combining a Student-t Process prior with a Student-t likelihood yields a doubly robust regression model whose intractable posterior has prevented its practical use. We introduce the first tractable variational inference framework for this model. Leveraging the Student-t distribution’s scale-mixture representation, we design a structured variational family that affords an analytic evidence lower bound. To overcome the non-conjugacy of this family, which precludes closed-form updates, we devise a novel projection-based optimization: we find the optimum in a simpler, factorized family and analytically project it back onto our structured one. The framework is extended to a scalable sparse, stochastic setting. Empirical results demonstrate strong performance, particularly in the full-batch setting, establishing this robust model as a practical and powerful tool.

By reducing resolution, coarse-grained models greatly accelerate molecular simulations, unlocking access to long-timescale phenomena, though at the expense of microscopic information. Recovering this fine-grained detail is essential for tasks that depend on atomistic accuracy, making backmapping a central challenge in molecular modeling. We introduce split-flows, a novel flow-based approach that reinterprets backmapping as a continuous-time measure transport across resolutions. Unlike existing generative strategies, split-flows establish a direct probabilistic link between resolutions, enabling expressive conditional sampling of atomistic structures and—for the first time—a tractable route to computing mapping entropies, an information-theoretic measure of the irreducible detail lost in coarse-graining. We demonstrate these capabilities on diverse molecular systems, including Chignolin, a lipid bilayer, and alanine dipeptide, highlighting split-flows as a principled framework for accurate backmapping and systematic evaluation of coarse-grained models.

We investigate robustness to strong data corruption in offline sparse reinforcement learning (RL). In our setting, an adversary may arbitrarily perturb a fraction of the collected trajectories from a high-dimensional but sparse Markov decision process, and our goal is to estimate a near-optimal policy. The main challenge is that, in the high-dimensional regime where the number of samples N is smaller than the feature dimension d, exploiting sparsity is essential for obtaining non-vacuous guarantees but has not been systematically studied in offline RL. We analyse the problem under uniform coverage and sparse single-concentrability assumptions. While Least Square Value Iteration (LSVI), a standard approach for robust offline RL, performs well under uniform coverage, we show that integrating sparsity into LSVI is unnatural, and its analysis may break down due to overly pessimistic bonuses. To overcome this, we propose actor–critic methods with sparse robust estimator oracles, which avoid the use of pointwise pessimistic bonuses and provide the first non-vacuous guarantees for sparse offline RL under single-policy concentrability coverage. Moreover, we extend our results to the contaminated setting and show that our algorithm remains robust under strong contamination. Our results provide the first non-vacuous guarantees in high-dimensional sparse MDPs with single-policy concentrability coverage and corruption, showing that learning near-optimal policy remains possible in regimes where traditional robust offline RL techniques may fail.

Offline-to-Online Reinforcement Learning (O2O RL) faces a critical dilemma in balancing the use of a fixed offline dataset with newly collected online experiences. Standard methods, often relying on a fixed data-mixing ratio, struggle to manage the trade-off between early learning stability and asymptotic performance. To overcome this, we introduce the Adaptive Replay Buffer (ARB), a novel approach that dynamically prioritizes data sampling based on a lightweight metric we call ’on-policyness’. Unlike prior methods that rely on complex learning procedures or fixed ratios, ARB is designed to be learning-free and simple to implement, seamlessly integrating into existing O2O RL algorithms. It assesses how closely collected trajectories align with the current policy’s behavior and assigns a proportional sampling weight to each transition within that trajectory. This strategy effectively leverages offline data for initial stability while progressively focusing learning on the most relevant, high-rewarding online experiences. Our extensive experiments on D4RL benchmarks demonstrate that ARB consistently mitigates early performance degradation and significantly improves the final performance of various O2O RL algorithms, highlighting the importance of an adaptive, behavior-aware replay buffer design. Our code is publicly available at <https://github.com/song970407/ARB>.

Pre-trained models have become indispensable for efficiently building models across a broad spectrum of downstream tasks. The advantages of pre-trained models have been highlighted by empirical studies on scaling laws, which demonstrate that larger pre-trained models can significantly reduce the sample complexity of downstream learning. However, existing theoretical investigations of pre-trained models lack the capability to explain this phenomenon. In this paper, we provide a theoretical investigation by introducing a novel framework, caulking, inspired by parameter-efficient fine-tuning (PEFT) methods such as adapter-based fine-tuning, low-rank adaptation, and partial fine-tuning. Our analysis establishes that improved pre-trained models provably decrease the sample complexity of downstream tasks, thereby offering theoretical justification for the empirically observed scaling laws relating pre-trained model size to downstream performance, a relationship not covered by existing results.

Reliably labelling data typically requires annotations from multiple human workers. However, humans are far from being perfect. Hence, it is a common practice to aggregate labels gathered from multiple annotators to make a more confident estimate of the true label. Among many aggregation methods, the simple and well-known Majority Vote (MV) selects the class label polling the highest number of votes. However, despite its importance, the optimality of MV’s label aggregation has not been extensively studied. We address this gap in our work by characterising the conditions under which MV achieves the theoretically optimal lower bound on label estimation error. Our results capture the tolerable limits on annotation noise under which MV can optimally recover labels for a given class distribution. This certificate of optimality provides a more principled approach to model selection for label aggregation as an alternative to otherwise inefficient practices that sometimes include higher experts, gold labels, etc., that are all marred by the same human uncertainty despite huge time and monetary costs. Experiments on both synthetic and real-world data corroborate our theoretical findings.

Reinforcement learning with verifiable rewards has emerged as a promising paradigm for enhancing the reasoning capabilities of large language models particularly in mathematics. Current approaches in this domain present a clear trade-off: PPO-style methods (e.g., GRPO/DAPO) offer training stability but exhibit slow learning trajectories due to their trust-region constraints on policy updates, while REINFORCE-style approaches (e.g., CISPO) demonstrate improved learning efficiency but suffer from performance instability as they clip importance sampling weights while still permitting non-zero gradients outside the trust-region. To address these limitations, we introduce DISPO, a simple yet effective REINFORCE-style algorithm that decouples the up-clipping and down-clipping of importance sampling weights for correct and incorrect responses, yielding four controllable policy update regimes. Through targeted ablations, we uncover how each regime impacts training: for correct responses, weights >1 increase the average token entropy (i.e., exploration) while weights <1 decrease it (i.e., distillation) - both beneficial but causing gradual performance degradation when excessive. For incorrect responses, overly restrictive clipping triggers sudden performance collapse through repetitive outputs (when weights >1) or vanishing response lengths (when weights <1). By separately tuning these four clipping parameters, DISPO maintains the exploration-distillation balance while preventing catastrophic failures, achieving 61.04

Probabilistic Circuits (PCs) offer a computationally scalable framework for generative modeling, supporting exact and efficient inference of a wide range of probabilistic queries. While recent advances have significantly improved the expressiveness and scalability of PCs, effectively training their parameters remains a challenge. In particular, a widely used optimization method, full-batch Expectation-Maximization (EM), requires processing the entire dataset before performing a single update, making it ineffective for large datasets. Although empirical extensions to the mini-batch setting, as well as gradient-based mini-batch algorithms, converge faster than full-batch EM, they generally underperform in terms of final likelihood. We investigate this gap by establishing a novel theoretical connection between these practical algorithms and the general EM objective. Our analysis reveals a fundamental issue that existing mini-batch EM and gradient-based methods fail to properly regularize distribution changes, causing each update to effectively "overfit" the current mini-batch. Motivated by this insight, we introduce anemone, a new mini-batch EM algorithm for PCs. Anemone applies an implicit adaptive learning rate to each parameter, scaled by how much it contributes to the likelihood of the current batch. Across extensive experiments on language, image, and DNA datasets, anemone consistently outperforms existing optimizers in both convergence speed and final performance. Code is available at <https://github.com/liuanji/pc-arena.>