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Applications · Robotics

Zhixuan Shen, Yijie Zeng, Shengxiang Luo, Tianrui Li, Haonan Luo

In embodied vision, Goal-Oriented Navigation (GON) requires robots to locate a specific goal within an unexplored environment. The primary challenge of GON arises from the need to construct a Bird's-Eye-View (BEV) map to understand the environment while simultaneously localizing an unobserved goal. Existing map-based methods typically employ self-centered semantic maps, often facing challenges such as reliance on complete maps or inconsistent semantic association. To this end, we propose Plug-and-Play Label Map Diffusion (PLMD), which defines a novel map completion diffusion model based on Denoising Diffusion Probabilistic Models (DDPM). PLMD generates obstacle and semantic labels for unobserved regions through a diffusion-based completion process, thereby enabling goal localization even in partially observed environments. Moreover, it mitigates inconsistent semantic association by leveraging structural consistency between known and unknown obstacle layouts and integrating obstacle priors into the semantic denoising process. By substituting predicted labels for unobserved regions, robots can accurately localize the specified objects. Extensive experiments demonstrate that PLMD \textbf{(I)} effectively expands the region of unknown maps, \textbf{(II)} integrates seamlessly into existing navigation strategies that rely on semantic maps, \textbf{(III)} achieves state-of-the-art performance on three GON tasks.

Deep Learning · Self-Supervised Learning

Sho Oshima, Yuji Okamoto, Taisei Tosaki, Ryosuke Kojima

Graph Contrastive Learning (GCL) is a powerful self-supervised learning framework that performs data augmentation through graph perturbations, with growing applications in the analysis of biological networks such as Gene Regulatory Networks (GRNs). The artificial perturbations commonly used in GCL, such as node dropping, induce structural changes that can diverge from biological reality. This concern has contributed to a broader trend in graph representation learning toward augmentation-free methods, which view such structural changes as problematic and should be avoided. However, this trend overlooks the fundamental insight that structural changes from biologically meaningful perturbations are not a problem to be avoided, but rather a rich source of information, thereby ignoring the valuable opportunity to leverage data from real biological experiments. Motivated by this insight, we propose SupGCL (Supervised Graph Contrastive Learning), a new GCL method for GRNs that directly incorporates biological perturbations from gene knockdown experiments as supervision. SupGCL is a probabilistic formulation that continuously generalizes conventional GCL, linking artificial augmentations with real perturbations measured in knockdown experiments, and using the latter as explicit supervision. On patient-derived GRNs from three cancer types, we train GRN representations with SupGCL and evaluate it in two regimes: (i) embedding space analysis, where it yields clearer disease-subtype structure and improves clustering, and (ii) task-specific fine-tuning, where it consistently outperforms strong graph representation learning baselines on 13 downstream tasks spanning gene-level functional annotation and patient-level prediction.

Probabilistic Methods · Bayesian Models and Methods

Zier Mensch, Lars Holdijk, Samuel Duffield, Maxwell Aifer, Patrick Coles, Max Welling, Miranda C. N. Cheng

Stochastic-gradient MCMC methods enable scalable Bayesian posterior sampling but often suffer from sensitivity to minibatch size and gradient noise. To address this, we propose Stochastic Gradient Lattice Random Walk (SGLRW), an extension of the Lattice Random Walk discretization. Unlike conventional Stochastic Gradient Langevin Dynamics (SGLD), SGLRW introduces stochastic noise only through the off-diagonal elements of the update covariance; this yields greater robustness to minibatch size while retaining asymptotic correctness. Furthermore, as comparison we analyze a natural analogue of SGLD utilizing gradient clipping. Experimental validation on Bayesian regression and classification demonstrates that SGLRW remains stable in regimes where SGLD fails, including in the presence of heavy-tailed gradient noise, and matches or improves predictive performance.

Probabilistic Methods · Everything Else

Yinjie Min, Liuhua Peng, Changliang Zou

Existing evaluations of conformal prediction, such as prediction efficiency and test-conditional coverage, are defined in expectation over the calibration data. In practice, when only one calibration set of limited size is available, the prediction sets can exhibit high variability, especially for methods with localization. We formalize this concern as **set stability**, defined as the variance of the conditional expectation of the set size given the calibration data. To improve stability without requiring additional target-task labels, we propose Stable Localized Conformal Prediction (SLCP), a transfer learning approach that utilizes labeled source-task data and unlabeled target data. Theoretically, we characterize the marginal coverage and stability of SLCP; empirically, it delivers more stable prediction sets than standard conformal prediction methods with localization when calibration data are limited.

Probabilistic Methods · Bayesian Models and Methods

Kaizheng Wang, Yuhang Wu, Assaf Zeevi

We study adaptive querying for learning user-dependent quantities of interest, such as responses to held-out items and psychometric indicators, within tight question budgets. Classical Bayesian design and computerized adaptive testing typically rely on restrictive parametric assumptions or expensive posterior approximations, limiting their use in heterogeneous, high-dimensional, and cold-start settings. We introduce a persona-induced latent variable model that represents a user's state through membership in a finite dictionary of AI personas, each offering response distributions produced by a large language model. This yields expressive priors with closed-form posterior updates and efficient finite-mixture predictions, enabling scalable Bayesian design for sequential item selection. Experiments on synthetic data and WorldValuesBench demonstrate that persona-based posteriors deliver accurate probabilistic predictions and an interpretable adaptive elicitation pipeline.

Probabilistic Methods · Bayesian Models and Methods

Horace Yiu, Leandro Sánchez-Betancourt, Alvaro Cartea, Gerardo Duran-Martin

We derive a robust update rule for the online infinite hidden Markov model (iHMM) for when the streaming data contains outliers and the model is misspecified. Leveraging recent advances in generalised Bayesian inference, we define robustness via the posterior influence function (PIF), and provide conditions under which the online iHMM has bounded PIF. Imposing robustness inevitably induces an adaptation lag for regime switching. Our method, which is called Batched Robust iHMM (BR-iHMM), balances adaptivity and robustness with two additional tunable parameters. Across limit order book data, hourly electricity demand, and a synthetic high-dimensional linear system, BR-iHMM reduces one-step-ahead forecasting error by up to 67% relative to competing online Bayesian methods. Together with theoretical guarantees of bounded PIF, our results highlight the practicality of our approach for both forecasting and interpretable online learning.

Probabilistic Methods · Bayesian Models and Methods

Kenyon Ng, Edwin Fong, David Frazier, Jeremias Knoblauch, Susan Wei

Bayesian inference provides principled uncertainty quantification but is often limited by challenges of prior and likelihood elicitation. The martingale posterior (MGP) (Fong et al, 2023) offers an alternative by replacing these requirements with a predictive rule. Additionally MGP focuses inference on parameters defined through a loss function. This framework is especially resonant in the era of foundation transformers; practitioners increasingly leverage models like TabPFN for their state-of-the-art capabilities, yet often require epistemic uncertainty for a scientific estimand $\theta$ that need not parametrize the model’s implicit latent model. The MGP provides the mechanism to recover these posterior distributions. We introduce TabMGP, an MGP built on TabPFN for tabular data. TabMGP produces credible sets with near-nominal coverage and often outperforms both handcrafted MGP constructions and standard Bayesian baselines.

Applications · Chemistry, Physics, and Earth Sciences

Jaemin Seo, Su Rin Lee, JaeYong Lee

Deep learning methods based on backward stochastic differential equations (BSDEs) have emerged as competitive alternatives to physics-informed neural networks (PINNs) for solving high-dimensional partial differential equations (PDEs). By leveraging probabilistic representations, BSDE approaches can avoid the curse of dimensionality and often admit second-order-free training objectives that do not require explicit Hessian evaluations. It has recently been established that the commonly used Euler–Maruyama (EM) time discretization induces an intrinsic bias in BSDE training losses. While high-order schemes such as Heun can fully eliminate this bias, such schemes re-introduce second-order spatial derivatives and incur substantial computational overhead. In this work, we provide a principled analysis of EM-induced loss bias and propose an unbiased, second-order-free training framework that preserves the computational advantages of BSDE methods.

Probabilistic Methods · Everything Else

Kaizheng Wang, Ghifari Adam Faza, Fabio Cuzzolin, Siu Lun Chau, David Moens, Hans Hallez

Credal predictors are epistemic-uncertainty-aware models that produce a convex set of probabilistic predictions. They provide a principled framework for quantifying predictive epistemic uncertainty (EU) and have been shown to improve model robustness across a range of settings. However, most state-of-the-art (SOTA) methods primarily define EU as disagreement induced by random training initializations, which mainly reflects sensitivity to optimization randomness rather than uncertainty from more substantive sources. In response, we formulate EU as disagreement between models trained under different degrees of relaxation of the i.i.d. assumption between the training and test distributions. Building on this idea, we propose *CreDRO*, which learns an ensemble of plausible models via distributionally robust optimization. As a result, CreDRO captures EU arising not only from training randomness but also from informative disagreement due to potential train–test distribution shifts. Empirically, CreDRO consistently outperforms SOTA credal approaches on downstream tasks, including out-of-distribution detection on extensive benchmarks and selective classification in medical settings.

Probabilistic Methods · Everything Else

Sacha Braun, David Holzmüller, Michael Jordan, Francis Bach

Evaluating conditional coverage remains one of the most persistent challenges in assessing the reliability of predictive systems. Although conformal methods can give guarantees on marginal coverage, no method can guarantee to produce sets with correct conditional coverage, leaving practitioners without a clear way to interpret local deviations. To overcome sample-inefficiency and overfitting issues of existing metrics, we cast conditional coverage estimation as a classification problem. Conditional coverage is violated if and only if any classifier can achieve lower risk than the target coverage. Through the choice of a (proper) loss function, the resulting risk difference gives a conservative estimate of natural miscoverage measures such as L1 and L2 distance, and can even separate the effects of over- and under-coverage, as well as handle non-constant target coverages. We call the resulting family of metrics excess risk of the target coverage (ERT). We show experimentally that the use of modern classifiers provides much higher statistical power than simple classifiers underlying established metrics like CovGap. Additionally, we use our metric to benchmark different conformal prediction methods. Finally, we release an open-source package for ERT as well as previous conditional coverage metrics. Together, these contributions provide a new lens for understanding, diagnosing, and improving the conditional reliability of predictive systems.

Probabilistic Methods · Monte Carlo and Sampling Methods

Xiaoyu Wang, Jonathan Huggins

Stochastic gradient Langevin dynamics combined with Gibbs updates (SGLD-Gibbs) provides a highly scalable approach to approximate Bayesian inference in latent variable models. However, it remains unclear how to tune the algorithm's hyperparameters in a principled manner to ensure the uncertainty estimates are statistically meaningful. In this work, we address this gap in tuning guidance by developing a statistical scaling limit theory for SGLD-Gibbs. We derive a joint asymptotic limit for the global parameters and latent variables under appropriate space-time rescaling. We show that global parameters converge to a diffusion-type limit, while individual latent variables converge to a jump process reflecting their intermittent Gibbs updates. This joint jump-diffusion structure reveals how latent-variable randomness contributes to the stationary distribution of the global parameters. We leverage our results to provide explicit guidance on hyperparameter tuning for SGLD-Gibbs that ensures meaningful uncertainty quantification. Our empirical results show that SGLD-Gibbs with our tuning guidance leads to better parameter estimates and uncertainty quantification than stochastic variational inference.

Theory · Probabilistic Methods

Santo Thies, Viktor Bengs, Timo Kaufmann, Sebastian Vollmer, Eyke Hüllermeier

Calibration, the alignment of predicted probabilities with true outcome frequencies, is essential for reliable decision-making. While extensively studied for classification and regression, calibration has not been formally addressed for probabilistic label ranking, where the goal is to predict a distribution over orderings of a label set. Naively treating rankings as classes ignores their structure and fails to capture important modalities such as pairwise and top-k predictions. We formalize calibration for label ranking and develop a hierarchy of notions covering full rankings, sub-rankings, and top-k rankings. We prove that full-rank calibration implies the others but not conversely, and sub-ranking and top-k calibration are incomparable. Empirically, we find popular label ranking models are often poorly calibrated, with substantial differences between sub-ranking and top-k metrics. Applying our framework to RLHF reward models, we find that calibration correlates strongly but not perfectly with benchmark accuracy, suggesting it captures a meaningful quality dimension beyond top-1 accuracy. These findings motivate future work on understanding the downstream effects of miscalibration and developing methods to correct it.

Probabilistic Methods · Variational Inference

Sylvia Liu, Valeria Vitelli, Carlo Mannino, Arnoldo Frigessi, Ida Scheel

We propose the Pseudo-Mallows distribution over the set of all permutations of $n$ items, to approximate the posterior distribution of the Bayesian Mallows model. The Bayesian Mallows model has been successfully used for recommender systems to learn personal preferences from highly incomplete users data. However current inference algorithms do not scale, preventing its use in real-time applications. The Pseudo-Mallows distribution is a product of univariate discrete Mallows-like distributions, where the quality of the approximation depends on the order of the $n$ items in the factorization sequence. In a variational setting, we optimize the variational order parameter by minimising a marginalized KL-divergence, conjecturing a certain form of the optimal variational order that depends on the data, and proposing an approximation algorithm for this discrete optimization. Empirical evidence and some theory support our conjecture. We demonstrate on clicking data that variational inference via the Pseudo-Mallows distribution allows much faster probabilistic preference learning compared to alternative MCMC-based options.

Probabilistic Methods · Variational Inference

Tiago Silva, Esmeralda S. Whitammer, Salem Lahlou

We consider the problem of sampling compositional and discrete objects from a given unnormalized posterior distribution. Notably, recent studies have shown that this problem can be efficiently solved by learning a deterministic Markov Decision Process (MDP) that progressively builds each object in proportion to the posterior. In this work, however, we demonstrate that the Markovian assumption can both hamper signal propagation during training and catastrophically reduce the learned sampler's expressivity due to state aliasing. To address these issues, we propose lifting the MDP with a learnable latent dynamics that allows the underlying policy to depend on the entire past trajectory---and not only on the current state. In view of this, we refer to the resulting method as \emph{path-dependent discrete amortized inference}. Importantly, we provably extend existing learning algorithms for amortized samplers to our setting. In experiments on standard benchmark problems, we also show that our approach often leads to faster learning convergence and improved state space exploration relatively to prior techniques.

Social Aspects · Robustness

Kuheli Pratihar, Debdeep Mukhopadhyay

Large language models generate text through probabilistic token sampling, a mechanism increasingly leveraged for inference-time watermarking to verify AI-generated content. We present an information-theoretic framework that characterizes the trade-off between robustness to text editing and detectability by keyless observers, where detectability bounds are information-theoretic and computational attainability depends on detector access. Central to our analysis is an additive, usable Kullback-Leibler (KL) information budget that governs hypothesis testing separability between watermarked and unwatermarked outputs subject to a stealth constraint. This budget induces a hierarchy of detectability across watermark families: distribution-preserving schemes exhibit zero statistical drift, while probability-modifying schemes at both token and sentence levels accumulate detectable signal with sequence length. When text editing is modeled as a noise process, the usable KL budget contracts quadratically with edit rate for token-level schemes and according to an induced semantic flip rate for sentence-level schemes. These contraction laws reveal an irreducible trilemma among robustness, stealth, and reliable verification. Guided by these limits, we propose a hybrid watermarking strategy that selects among distribution-preserving, semantic-level, and token-level methods based on anticipated editing regimes. Experiments on Llama-2-7B and Mistral-7B under paraphrasing attacks corroborate theoretical predictions and confirm that the hybrid strategy is empirically near-Pareto across evaluated edit regimes.

Probabilistic Methods · Bayesian Models and Methods

Pierre-Louis Ruhlmann, Michael Arbel, Florence Forbes, Pedro Luiz Coelho Rodrigues

Simulation-based inference (SBI) is transforming experimental sciences by enabling parameter estimation in complex non-linear models from simulated data. A persistent challenge, however, is model misspecification: simulators are only approximations of reality, and mismatches between simulated and real data can yield biased or overconfident posteriors. We address this issue by introducing Flow Matching Corrected Posterior Estimation (FMCPE), a framework that leverages the flow matching paradigm to refine simulation-trained posterior estimators using a small set of calibration samples. Our approach proceeds in two stages: first, a posterior approximator is trained on abundant simulated data; second, flow matching transports its predictions toward the true posterior supported by real observations, without requiring explicit knowledge of the misspecification. This design enables FMCPE to combine the scalability of SBI with robustness to distributional shift. Across synthetic benchmarks and real-world datasets, we show that our proposal consistently mitigates the effects of misspecification, delivering improved inference accuracy and uncertainty calibration compared to standard SBI baselines, while remaining computationally efficient.

Probabilistic Methods · Monte Carlo and Sampling Methods

Yu Wang, Jie Ding, Jonathan Huggins

Tuning stochastic gradient methods such as stochastic gradient descent (SGD) and stochastic gradient Langevin dynamics (SGLD) for approximate sampling and uncertainty quantification remains challenging, particularly in relevant settings using a large batch size or when the model is misspecified. Existing theory that provides tuning guidance relies on continuous-time limits or strong statistical assumptions, which can become quantitatively inaccurate in these regimes. We address these shortcomings by proposing a new discrete-time approximations to SG(L)D with and without momentum, which enables accurate predictions of the stationary covariance, iterate average covariance, and integrated autocorrelation time. Moreover, we prove quantitative, non-asymptotic error bounds showing that these estimates are sufficiently accurate for practical tuning and uncertainty quantification. Numerical experiments demonstrate that our theory yields improved tuning guidance across a range of models and data-generating distributions where existing approaches fail, including when using the $\beta$-divergence rather than log-loss to obtain statistically robust inferences.

Probabilistic Methods · Everything Else

Qi Kuang, Bowen Gang, Yin Xia

We propose a unified framework to enhance the power of online multiple hypothesis testing procedures based on $e$-values. While $e$-value-based methods offer robust online False Discovery Rate (FDR) control under minimal assumptions, they often suffer from power loss by discarding evidence that exceeds the rejection threshold. We address this inefficiency via the **S**equential **C**ontrol with **O**vershoot **R**efund for **E**-values (SCORE) framework, which leverages the inequality $\mathbb{I}(y \ge 1) \le y - (y-1)_+$ to reclaim this otherwise ``wasted'' evidence. This simple yet powerful insight yields a unified principle for improving a broad class of online testing algorithms. Building on this framework, we develop SCORE-enhanced versions of several state-of-the-art procedures, including SCORE-LOND, SCORE-LORD, and SCORE-SAFFRON, all of which strictly dominate their original counterparts while preserving valid finite-sample FDR control. Furthermore, under mild assumptions, SCORE permits retroactive updates of alpha‑wealth by using the latest decision twice: first to determine its reward or loss, and then to refresh past wealth. Such a mechanism enables more aggressive testing strategies while maintaining valid FDR control, thereby further improving statistical power. The effectiveness of the proposed methods is validated through extensive simulation and real-data experiments.

Probabilistic Methods · Everything Else

Zhichao Chen, Zhan Zhuang, Yunfei Teng, Eric Wang, Fangyikang Wang, Zhengnan Li, Tianqiao Liu, Haoxuan Li, Zhouchen Lin

Gradual Domain Adaption (GDA) aims to mitigate domain shift by progressively adapting models from the source domain to the target domain via intermediate domains. However, real intermediate domains are often unavailable or ineffective, necessitating the synthesis of intermediate samples. Flow-based models are recently used for this purpose by interpolating between source and target distributions, but their training typically resorts to sample-based log-likelihood estimation, which can discard useful information and thus degrade GDA performance. The key to addressing this limitation is constructing the intermediate domains via samples directly. To this end, we propose an $\underline{\text{E}}$ntropy-regularized $\underline{\text{S}}$emi-dual $\underline{\text{U}}$nbalanced $\underline{\text{O}}$ptimal $\underline{\text{T}}$ransport (E-SUOT) framework to construct intermediate domains. Specifically, we reformulate flow-based GDA as a Lagrangian dual problem and derive an equivalent objective that circumvents the needs for likelihood estimation. However, the dual problem results in the unstable min–max training procedure. To alleviate this issue, we further introduce entropy regularization to convert it into a more stable alternative optimization procedure. Based on this, we propose a novel GDA training framework and provide theoretical analysis in terms of stability and generalization. Finally, extensive experiments are conducted to demonstrate the efficacy of the E-SUOT framework.

Theory · Probabilistic Methods

Haoxin Sun, Zhongzhi Zhang

The forest matrix of a signed graph plays an important role in network science and social opinion dynamics, yet existing algorithms are mainly designed for unsigned graphs and are difficult to extend to signed graphs. In this paper, we study the problem of efficiently estimating the forest matrix of signed graphs with \(n\) nodes and introduce the signed forest matrix theorem, which establishes the relationship between generalized spanning converging forests and the forest matrix. Based on this result, we propose a novel algorithm GSCF, built on a variant of loop-erased random walks, to generate generalized spanning converging forests in expected \(O(n)\) time. We further develop two sampling algorithms, FMDE and FMDE+, for estimating the diagonal of the forest matrix, both with time complexity \(O(ln)\), where \(l\) is the number of samples. Extensive experiments on various signed graphs show that our methods achieve high estimation accuracy, significantly improve computational efficiency, and scale to graphs with over twenty million nodes. Our source code is publicly available on \url{https://anonymous.4open.science/r/SignedForestDiagonal-FA09}.