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Probabilistic Methods · Bayesian Models and Methods

Mohamad Al Ahdab, john leth, Zheng-Hua Tan

We study the Continuous-Discrete Kalman Filter (CD-KF) for State-Space Models (SSMs) where continuous-time dynamics are observed via multiple sensors with discrete, irregularly timed measurements. Our focus extends to scenarios in which the measurement process is coupled with the states of an auxiliary SSM. For instance, higher measurement rates may increase energy consumption or heat generation, while a sensor’s accuracy can depend on its own spatial trajectory or that of the measured target. Each sensor thus carries distinct costs and constraints associated with its measurement rate and additional constraints and costs on the auxiliary state. We model measurement occurrences as independent Poisson processes with sensor-specific rates and derive an upper bound on the mean posterior covariance matrix of the CD-KF along the mean auxiliary state. The bound is continuously differentiable with respect to the measurement rates, which enables efficient gradient-based optimization. Exploiting this bound, we propose a finite-horizon optimal control framework to optimize measurement rates and auxiliary-state dynamics jointly. We further introduce a deterministic method for scheduling measurement times from the optimized rates. Empirical results in state-space filtering and dynamic temporal Gaussian process regression demonstrate that our approach achieves improved trade-offs between resource usage and estimation accuracy.

Jake Snell, Thomas Griffiths

As machine learning-based prediction systems are increasingly used in high-stakes situations, it is important to understand how such predictive models will perform upon deployment. Distribution-free uncertainty quantification techniques such as conformal prediction provide guarantees about the loss black-box models will incur even when the details of the models are hidden. However, such methods are based on frequentist probability, which unduly limits their applicability. We revisit the central aspects of conformal prediction from a Bayesian perspective and thereby illuminate the shortcomings of frequentist guarantees. We propose a practical alternative based on Bayesian quadrature that provides interpretable guarantees and offers a richer representation of the likely range of losses to be observed at test time.

Optimization · Zero-order and Black-box Optimization

Jungtaek Kim

Bayesian optimization has attracted huge attention from diverse research areas in science and engineering, since it is capable of efficiently finding a global optimum of an expensive-to-evaluate black-box function. In general, a probabilistic regression model is widely used as a surrogate function to model an explicit distribution over function evaluations given an input to estimate and a training dataset. Beyond the probabilistic regression-based methods, density ratio estimation-based Bayesian optimization has been suggested in order to estimate a density ratio of the groups relatively close and relatively far to a global optimum. Developing this line of research further, supervised classifiers are employed to estimate a class probability for the two groups instead of a density ratio. However, the supervised classifiers used in this strategy are prone to be overconfident for known knowledge on global solution candidates. Supposing that we have access to unlabeled points, e.g., predefined fixed-size pools, we propose density ratio estimation-based Bayesian optimization with semi-supervised learning to solve this challenge. Finally, we show the empirical results of our methods and several baseline methods in two distinct scenarios with unlabeled point sampling and a fixed-size pool, and analyze the validity of our methods in diverse experiments.

Probabilistic Methods

Yazid Janati, Badr MOUFAD, Mehdi Qassime, Alain Oliviero Durmus, Eric Moulines, Jimmy Olsson

Denoising diffusion models have driven significant progress in the field of Bayesian inverse problems. Recent approaches use pre-trained diffusion models as priors to solve a wide range of such problems, only leveraging inference-time compute and thereby eliminating the need to retrain task-specific models on the same dataset. To approximate the posterior of a Bayesian inverse problem, a diffusion model samples from a sequence of intermediate posterior distributions, each with an intractable likelihood function. This work proposes a novel mixture approximation of these intermediate distributions. Since direct gradient-based sampling of these mixtures is infeasible due to intractable terms, we propose a practical method based on Gibbs sampling. We validate our approach through extensive experiments on image inverse problems, utilizing both pixel- and latent-space diffusion priors, as well as on source separation with an audio diffusion model. The code is available at \url{https://www.github.com/badr-moufad/mgdm}.

Probabilistic Methods · Variational Inference

Yuta Tarumi, Keisuke Fukuda, Shin-ichi Maeda

Data assimilation for nonlinear state space models (SSMs) is inherently challenging due to non-Gaussian posteriors. We propose Deep Bayesian Filtering (DBF), a novel approach to data assimilation in nonlinear SSMs. DBF introduces latent variables $h_t$ in addition to physical variables $z_t$, ensuring Gaussian posteriors by (i) constraining state transitions in the latent space to be linear and (ii) learning a Gaussian inverse observation operator $r(h_t|o_t)$. This structured posterior design enables analytical recursive computation, avoiding the accumulation of Monte Carlo sampling errors over time steps. DBF optimizes these operators and other latent SSM parameters by maximizing the evidence lower bound. Experiments demonstrate that DBF outperforms existing methods in scenarios with highly non-Gaussian posteriors.

Deep Learning · Generative Models and Autoencoders

Yuxuan Song, Juntong Shi, Jingjing Gong, Minkai Xu, Stefano Ermon, Hao Zhou, Wei-Ying Ma

Though typically represented by the discrete node and edge attributes, the graph topological information can be sufficiently captured by the graph spectrum in a continuous space. It is believed that incorporating the continuity of graph topological information into the generative process design could establish a superior paradigm for graph generative modeling. Motivated by such prior and recent advancements in the generative paradigm, we propose Graph Bayesian Flow Networks (GraphBFN) in this paper, a principled generative framework that designs an alternative generative process emphasizing the dynamics of topological information. Unlike recent discrete-diffusion-based methods, GraphBFNemploys the continuous counts derived from sampling infinite times from a categorical distribution as latent to facilitate a smooth decomposition of topological information, demonstrating enhanced effectiveness. To effectively realize the concept, we further develop an advanced sampling strategy and new time-scheduling techniques to overcome practical barriers and boost performance. Through extensive experimental validation on both generic graph and molecular graph generation tasks, GraphBFN could consistently achieve superior or competitive performance with significantly higher training and sampling efficiency.

Deep Learning · Large Language Models

Virginia Aglietti, Ira Ktena, Jessica Schrouff, Eleni Sgouritsa, Francisco Ruiz, Alan Malek, Alexis Bellot, Silvia Chiappa

The sample efficiency of Bayesian optimization algorithms depends on carefully crafted acquisition functions (AFs) guiding the sequential collection of function evaluations. The best-performing AFs can vary significantly across optimization problems, often requiring ad-hoc and problem-specific choices. This work tackles the challenge of designing novel AFs that perform well across a variety of experimental settings. Based on FunSearch, a recent work using Large Language Models (LLMs) for discovery in mathematical sciences, we propose FunBO, an LLM-based method that can be used to learn new AFs written in computer code by leveraging access to a number of evaluations for a limited set of objective functions. We provide the analytic expression of all discovered AFs and evaluate them on various global optimization benchmarks and hyperparameter optimization tasks. We show how FunBO identifies AFs that generalize well both in and out of the training distribution of functions, thus outperforming established general-purpose AFs and achieving competitive performance against AFs that are customized to specific function types and are learned via transfer-learning algorithms.

Probabilistic Methods · Bayesian Models and Methods

Ruth Wan Theng Chew, Quoc Phong Nguyen, Bryan Kian Hsiang Low

Bilevel optimization is characterized by a two-level optimization structure, where the upper-level problem is constrained by optimal lower-level solutions, and such structures are prevalent in real-world problems. The constraint by optimal lower-level solutions poses significant challenges, especially in noisy, constrained, and derivative-free settings, as repeating lower-level optimizations is sample inefficient and predicted lower-level solutions may be suboptimal. We present BILevel Bayesian Optimization (BILBO), a novel Bayesian optimization algorithm for general bilevel problems with blackbox functions, which optimizes both upper- and lower-level problems simultaneously, without the repeated lower-level optimization required by existing methods. BILBO samples from confidence-bounds based trusted sets, which bounds the suboptimality on the lower level. Moreover, BILBO selects only one function query per iteration, where the function query selection strategy incorporates the uncertainty of estimated lower-level solutions and includes a conditional reassignment of the query to encourage exploration of the lower-level objective. The performance of BILBO is theoretically guaranteed with a sublinear regret bound for commonly used kernels and is empirically evaluated on several synthetic and real-world problems.

Social Aspects · Accountability, Transparency, and Interpretability

Kentaro Kanamori, Ken Kobayashi, Satoshi Hara, Takuya Takagi

Algorithmic recourse aims to provide a recourse action for altering an unfavorable prediction given by a model into a favorable one (e.g., loan approval). In practice, it is also desirable to ensure that an action makes the real-world outcome better (e.g., loan repayment). We call this requirement *improvement*. Unfortunately, existing methods cannot ensure improvement unless we know the true oracle. To address this issue, we propose a framework for suggesting improvement-oriented actions from a long-term perspective. Specifically, we introduce a new online learning task of assigning actions to a given sequence of instances. We assume that we can observe delayed feedback on whether the past suggested action achieved improvement. Using the feedback, we estimate an action that can achieve improvement for each instance. To solve this task, we propose two approaches based on contextual linear bandit and contextual Bayesian optimization. Experimental results demonstrated that our approaches could assign improvement-oriented actions to more instances than the existing methods.

Probabilistic Methods · Bayesian Models and Methods

Nick Bishop, Daniel Jarne Ornia, Joel Dyer, Anisoara Calinescu, Michael Wooldridge

Simulation modeling offers a flexible approach to constructing high-fidelity synthetic representations of complex real-world systems. However, the increased complexity of such models introduces additional complications, for example when carrying out statistical inference procedures. This has motivated a large and growing literature on *likelihood-free* or *simulation-based* inference methods, which approximate (e.g., Bayesian) inference without assuming access to the simulator's intractable likelihood function. A hitherto neglected problem in the simulation-based Bayesian inference literature is the challenge of constructing minimally informative *reference priors* for complex simulation models. Such priors maximise an expected Kullback-Leibler distance from the prior to the posterior, thereby influencing posterior inferences minimally and enabling an ``objective'' approach to Bayesian inference that does not necessitate the incorporation of strong subjective prior beliefs. In this paper, we propose and test a selection of likelihood-free methods for learning reference priors for simulation models, using variational approximations to these priors and a variety of mutual information estimators. Our experiments demonstrate that good approximations to reference priors for simulation models are in this way attainable, providing a first step towards the development of likelihood-free objective Bayesian inference procedures.

Optimization

Tao Li, Zhengbao He, Yujun Li, Yasheng Wang, Lifeng Shang, Xiaolin Huang

Fine-tuning large-scale pre-trained models is prohibitively expensive in terms of computation and memory costs. Low-Rank Adaptation (LoRA), a popular Parameter-Efficient Fine-Tuning (PEFT) method, offers an efficient solution by optimizing only low-rank matrices. Despite recent progress in improving LoRA's performance, the relationship between the LoRA optimization space and the full parameter space is often overlooked. A solution that appears flat in the loss landscape of the LoRA space may still exhibit sharp directions in the full parameter space, potentially compromising generalization.We introduce Flat-LoRA, which aims to identify a low-rank adaptation situated in a flat region of the full parameter space.Instead of adopting the well-established sharpness-aware minimization approach, which incurs significant computation and memory overheads, we employ a Bayesian expectation loss objective to preserve training efficiency. Further, we design a refined strategy for generating random perturbations to enhance performance and carefully manage memory overhead using random seeds.Experiments across diverse tasks—including mathematical reasoning, coding abilities, dialogue generation, instruction following, and text-to-image generation—demonstrate that Flat-LoRA improves both in-domain and out-of-domain generalization.Code is available at https://github.com/nblt/Flat-LoRA.

Optimization · Large Scale, Parallel and Distributed

Haozhao Wang, Shengyu Wang, Jiaming Li, Hao Ren, Xingshuo Han, Wenchao Xu, Shangwei Guo, Tianwei Zhang, Ruixuan Li

Semi-supervised Federated Learning (SSFL) is a promising approach that allows clients to collaboratively train a global model in the absence of their local data labels. The key step of SSFL is the re-labeling where each client adopts two types of available models, namely global and local models, to re-label the local data. While various technologies such as using the global model or the average of two models have been proposed to conduct the re-labeling step, little literature delves deeply into the performance dominance and limitations of the two models. In this paper, we first theoretically and empirically demonstrate that the local model achieves higher re-labeling accuracy over local data while the global model can progressively improve the re-labeling performance by introducing the extra data knowledge of other clients. Based on these findings, we propose BSemiFL which re-labels the local data through the collaboration between the local and global model in a Bayesian approach. Specifically, to re-label any given local sample, BSemiFL first uses Bayesian inference to assess the closeness of the local/global model to the sample. Then, it applies a weighted combination of their pseudo labels, using the closeness as the weights. Theoretical analysis shows that the labeling error of our method is smaller than that of simply using the global model, the local model, or their simple average. Experimental results show that BSemiFL improves the performance by up to $9.8\%$ as compared to state-of-the-art methods.

General Machine Learning · Transfer, Multitask and Meta-learning

Mei Li, Yuxiang Lu, Qinyan Dai, Suizhi Huang, Yue Ding, Hongtao Lu

Continual Learning (CL) strives to learn incrementally across tasks while mitigating catastrophic forgetting. A key challenge in CL is balancing stability (retaining prior knowledge) and plasticity (learning new tasks). While representative gradient projection methods ensure stability, they often limit plasticity. Model merging techniques offer promising solutions, but prior methods typically rely on empirical assumptions and carefully selected hyperparameters. In this paper, we explore the potential of model merging to enhance the stability-plasticity trade-off, providing theoretical insights that underscore its benefits. Specifically, we reformulate the merging mechanism using Bayesian continual learning principles and derive a closed-form solution for the optimal merging coefficient that adapts to the diverse characteristics of tasks. To validate our approach, we introduce a two-stage framework named BECAME, which synergizes the expertise of gradient projection and adaptive merging. Extensive experiments show that our approach outperforms state-of-the-art CL methods and existing merging strategies https://github.com/limei0818/BECAME.

Applications · Chemistry, Physics, and Earth Sciences

Seungbeom Lee, Munsun Jo, Jungseul Ok, Dongwoo Kim

Deep learning-based Structure-based drug design aims to generate ligand molecules with desirable properties for protein targets. While existing models have demonstrated competitive performance in generating ligand molecules, they primarily focus on learning the chemical distribution of training datasets, often lacking effective steerability to ensure the desired chemical quality of generated molecules. To address this issue, we propose a multi-reward optimization framework that fine-tunes generative models for attributes, such as binding affinity, validity, and drug-likeness, together. Specifically, we derive direct preference optimization for a Bayesian flow network, used as a backbone for molecule generation, and integrate a reward normalization scheme to adopt multiple objectives. Experimental results show that our method generates more realistic ligands than baseline models while achieving higher binding affinity, expanding the Pareto front empirically observed in previous studies.

Probabilistic Methods · Monte Carlo and Sampling Methods

Dongze Wu, Yao Xie

Sampling from high-dimensional, multi-modal distributions remains a fundamental challenge across domains such as statistical Bayesian inference and physics-based machine learning. In this paper, we propose Annealing Flow (AF), a method built on Continuous Normalizing Flows (CNFs) for sampling from high-dimensional and multi-modal distributions. AF is trained with a dynamic Optimal Transport (OT) objective incorporating Wasserstein regularization, and guided by annealing procedures, facilitating effective exploration of modes in high-dimensional spaces. Compared to recent NF methods, AF significantly improves training efficiency and stability, with minimal reliance on MC assistance. We demonstrate the superior performance of AF compared to state-of-the-art methods through extensive experiments on various challenging distributions and real-world datasets, particularly in high-dimensional and multi-modal settings. We also highlight AF’s potential for sampling the least favorable distributions.

Reinforcement Learning · Deep RL

Long Ma, Fangwei Zhong, Yizhou Wang

The ability to adapt to new environments with noisy dynamics and unseen objectives is crucial for AI agents. In-context reinforcement learning (ICRL) has emerged as a paradigm to build adaptive policies, employing a **context** trajectory of the test-time interactions to infer the true task and the corresponding optimal policy efficiently without gradient updates. However, ICRL policies heavily rely on context trajectories, making them vulnerable to distribution shifts from training to testing and degrading performance, particularly in offline settings where the training data is static. In this paper, we highlight that most existing offline ICRL methods are trained for approximate Bayesian inference based on the training distribution, rendering them vulnerable to distribution shifts at test time and resulting in poor generalization. To address this, we introduce Behavior-agnostic Task Inference (BATI) for ICRL, a model-based maximum-likelihood solution to infer the task representation robustly. In contrast to previous methods that rely on a learned encoder as the approximate posterior, BATI focuses purely on dynamics, thus insulating itself against the behavior of the context collection policy. Experiments on MuJoCo environments demonstrate that BATI effectively interprets out-of-distribution contexts and outperforms other methods, even in the presence of significant environmental noise.

Reinforcement Learning · Batch/Offline

Jihwan Jeong, Xiaoyu Wang, Jingmin Wang, Scott Sanner, Pascal Poupart

Offline reinforcement learning (RL) is crucial when online exploration is costly or unsafe but often struggles with high epistemic uncertainty due to limited data. Existing methods rely on fixed conservative policies, restricting adaptivity and generalization. To address this, we propose Reflect-then-Plan (RefPlan), a novel _doubly Bayesian_ offline model-based (MB) planning approach. RefPlan unifies uncertainty modeling and MB planning by recasting planning as Bayesian posterior estimation. At deployment, it updates a belief over environment dynamics using real-time observations, incorporating uncertainty into MB planning via marginalization. Empirical results on standard benchmarks show that RefPlan significantly improves the performance of conservative offline RL policies. In particular, RefPlan maintains robust performance under high epistemic uncertainty and limited data, while demonstrating resilience to changing environment dynamics, improving the flexibility, generalizability, and robustness of offline-learned policies.

General Machine Learning · Online Learning, Active Learning and Bandits

Jae-Hong Lee

Test-time adaptation (TTA) addresses the machine learning challenge of adapting models to unlabeled test data from shifting distributions in dynamic environments. A key issue in this online setting arises from using unsupervised learning techniques, which introduce explicit gradient noise that degrades model weights. To invest in weight degradation, we propose a Bayesian weight enhancement framework, which generalizes existing weight-based TTA methods that effectively mitigate the issue. Our framework enables robust adaptation to distribution shifts by accounting for diverse weights by modeling weight distributions.Building on our framework, we identify a key limitation in existing methods: their neglect of time-varying covariance reflects the influence of the gradient noise. To address this gap, we propose a novel steady-state adaptation (SSA) algorithm that balances covariance dynamics during adaptation. SSA is derived through the solution of a stochastic differential equation for the TTA process and online inference. The resulting algorithm incorporates a covariance-aware learning rate adjustment mechanism. Through extensive experiments, we demonstrate that SSA consistently improves state-of-the-art methods in various TTA scenarios, datasets, and model architectures, establishing its effectiveness in instability and adaptability.

Probabilistic Methods · Bayesian Models and Methods

Gábor Pituk, Vik Shirvaikar, Tom Rainforth

We empirically investigate how well popular approximate inference algorithms for Bayesian Neural Networks (BNNs) respect the theoretical properties of Bayesian belief updating. We find strong evidence on synthetic regression and real-world image classification tasks that common BNN algorithms such as variational inference, Laplace approximation, SWAG, and SGLD fail to update in a consistent manner, forget about old data under sequential updates, and violate the predictive coherence properties that would be expected of Bayesian methods. These observed behaviors imply that care should be taken when treating BNNs as true Bayesian models, particularly when using them beyond static prediction settings, such as for active, continual, or transfer learning.

Probabilistic Methods · Bayesian Models and Methods

Antoine Wehenkel, Juan L. Gamella, Ozan Sener, Jens Behrmann, Guillermo Sapiro, Jörn Jacobsen, Marco Cuturi

Driven by steady progress in deep generative modeling, simulation-based inference (SBI) has emerged as the workhorse for inferring the parameters of stochastic simulators. However, recent work has demonstrated that model misspecification can harm SBI's reliability, preventing its adoption in important applications where only misspecified simulators are available.This work introduces robust posterior estimation (RoPE), a framework that overcomes model misspecification with a small real-world calibration set of ground truth parameter measurements.We formalize the misspecification gap as the solution of an optimal transport (OT) problem between learned representations of real-world and simulated observations, allowing RoPE to learn a model of the misspecification without placing additional assumptions on its nature. RoPE shows how the calibration set and OT together offer a controllable balance between calibrated uncertainty and informative inference even under severely misspecified simulators. Results on four synthetic tasks and two real-world problems with ground-truth labels demonstrate that RoPE outperforms baselines and consistently returns informative and calibrated credible intervals.