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Optimization · Zero-order and Black-box Optimization

Yonghan Yang, Ye Yuan, Zipeng Sun, Linfeng Du, Bowei He, Haolun Wu, Can Chen, Xue Liu

Offline black-box optimization aims to discover novel designs with high property scores using only a static dataset, a task fundamentally challenged by the out-of-distribution (OOD) extrapolation problem. Existing approaches typically bifurcate into inverse methods, which struggle with the ill-posed nature of mapping scores to designs, and forward methods, which often lack the distributional expressivity to quantify uncertainty effectively. In this work, we propose \textbf{SPADE} (\textbf{S}upport-\textbf{P}roximity \textbf{A}ugmented \textbf{D}iffusion \textbf{E}stimation), a novel framework that reimagines forward surrogate modeling through the lens of conditional generative modeling. SPADE models the forward likelihood $p(y|\boldsymbol{x})$ using a diffusion model, but with two critical enhancements to tailor it for optimization: (1) a \emph{Calibrated Diffusion Estimation} module that enforces global consistency in statistical moments and pairwise rankings, and (2) a \emph{Support-Proximity Regularization} mechanism that implicitly internalizes the data manifold constraint $p(\boldsymbol{x})$ via kNN-based density estimation. Theoretically, we prove that our regularization is first-order equivalent to maximizing a Bayesian posterior with a valid design prior. Empirically, SPADE achieves state-of-the-art performance across Design-Bench tasks and an LLM data mixture optimization benchmark. Our code is available through the anonymous repo \href{https://anonymous.4open.science/r/diffsurr-icml2026-C4FD/}{here}.

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 · Structure Learning

Shengxian Ding, Haonan Gao, Pangpang Liu, Xinyuan Tian, Yize Zhao

Electronic health records (EHR) pose large-scale multi-disease modeling problems in which many outcomes are rare and strongly influenced by shared risk factors. While modern approaches achieve strong predictive performance, they often treat diseases independently or rely on black-box architectures, offering limited insight into how risk factors organize disease risk and little principled uncertainty quantification. We introduce a Bayesian hypergraph inference framework that reframes multi-disease modeling around **latent, risk-factor-modulated disease pathways**. Risk factors act on hyperedges, latent disease subsets with shared risk patterns, allowing diseases to participate in multiple distinct pathways and enabling interpretable, higher-order structure beyond pairwise associations. A repulsion prior encourages parsimonious and identifiable structure, while posterior inference provides calibrated uncertainty over both disease groupings and risk-factor influence. To enable scalable inference on large EHR datasets, we develop a structured variational inference algorithm that preserves logical dependencies among hyperedge existence, disease membership, and pathway-level effects. Experiments on simulated data and UK Biobank demonstrate stable and interpretable disease pathway structure, well-calibrated uncertainty, improved estimation for rare diseases, and competitive predictive performance.

Probabilistic Methods · Structure Learning

Shengxian Ding, Haonan Gao, Pangpang Liu, Xinyuan Tian, Yize Zhao

Electronic health records (EHR) pose large-scale multi-disease modeling problems in which many outcomes are rare and strongly influenced by shared risk factors. While modern approaches achieve strong predictive performance, they often treat diseases independently or rely on black-box architectures, offering limited insight into how risk factors organize disease risk and little principled uncertainty quantification. We introduce a Bayesian hypergraph inference framework that reframes multi-disease modeling around **latent, risk-factor-modulated disease pathways**. Risk factors act on hyperedges, latent disease subsets with shared risk patterns, allowing diseases to participate in multiple distinct pathways and enabling interpretable, higher-order structure beyond pairwise associations. A repulsion prior encourages parsimonious and identifiable structure, while posterior inference provides calibrated uncertainty over both disease groupings and risk-factor influence. To enable scalable inference on large EHR datasets, we develop a structured variational inference algorithm that preserves logical dependencies among hyperedge existence, disease membership, and pathway-level effects. Experiments on simulated data and UK Biobank demonstrate stable and interpretable disease pathway structure, well-calibrated uncertainty, improved estimation for rare diseases, and competitive predictive performance.

Probabilistic Methods · Bayesian Models and Methods

Sergio Calvo Ordoñez, Jonathan Plenk, Richard Bergna, Alvaro Cartea, Yarin Gal, Jose Miguel Hernandez-Lobato, Kamil Ciosek

Bayesian last layers (BLLs) provide a convenient and computationally efficient way to estimate uncertainty in neural networks. However, they underestimate epistemic uncertainty because they apply a Bayesian treatment only to the final layer, ignoring uncertainty induced by earlier layers. We propose a method that improves BLLs by leveraging a projection of Neural Tangent Kernel (NTK) features onto the space spanned by the last-layer features. This enables posterior inference that accounts for variability of the full network while retaining the low computational cost of a standard BLL. We show that our method yields posterior variances that are provably greater or equal to those of a standard BLL, correcting its tendency to underestimate epistemic uncertainty. To further reduce computational cost, we introduce a uniform subsampling scheme for estimating the projection matrix and for posterior inference. We derive approximation bounds for both types of sub-sampling. Empirical evaluations on UCI regression, contextual bandits, and out-of-distribution detection tasks in image and tabular datasets, demonstrate improved calibration and uncertainty estimates compared to standard BLLs and competitive baselines, while reducing computational cost.

Probabilistic Methods · Bayesian Models and Methods

Giovanni Charles, Cosmo Santoni, Seth Flaxman, Elizaveta Semenova

The cost of simulator evaluations is a key practical bottleneck for Simulation Based Inference (SBI). In hierarchical settings with shared global parameters and exchangeable site-level parameters and observations, this structure can be exploited to improve simulation efficiency. Existing hierarchical SBI approaches factorise the posterior yet still simulate across multiple sites per training sample; We instead explore likelihood factorisation (LF) to train from single-site simulations. In LF sampling we learn a per-site (factorised) likelihood and then assemble synthetic multi-site observations to amortise inference for the full hierarchical posterior. Building on this, we propose Tokenised Flow Matching for Posterior Estimation (TFMPE), a tokenised flow matching approach that supports function-valued observations through likelihood factorisation. To enable systematic evaluation, we introduce a benchmark for hierarchical SBI. We validate TFMPE on this benchmark and on realistic infectious disease and computational fluid dynamics models, finding well-calibrated posteriors while reducing computational cost.

Probabilistic Methods · Bayesian Models and Methods

Rik Knowles, Tom Rainforth

We investigate which models admit a collapse of the expected information gain (EIG) and its derivative from a doubly intractable to a singly intractable expression. We prove that a sufficient condition is that the posterior distribution belongs to an exponential family (EF) that depends on the experimental design and data only through its natural parameters, and derive corresponding singly intractable and unbiased estimators for the $\operatorname{EIG}$ and its (reparameterised) gradient. We further derive necessary conditions on the likelihood to obtain an EF posterior of the required form, showing that this does not necessarily require the prior to be conjugate. This is complemented by a theoretical analysis of certain degenerate behaviors that may arise when optimizing the $\operatorname{EIG}$ for EF-modeled experiments. Finally, we empirically demonstrate the benefits of our singly intractable estimators, showing substantial performance gains over standard nested estimators.

Probabilistic Methods · Bayesian Models and Methods

Lifu Wei, Yinuo Ren, Naichen Shi, Yiping Lu

Data assimilation (DA) addresses the problem of sequentially estimating the state of a dynamical system from noisy and incomplete observations. In this work, we employ a diffusion model as a world model to simulate and predict the system’s dynamics. Recently, score-based diffusion models have learned global diffusion priors that effectively model (stochastic) dynamics, revealing strong potential for data assimilation. In this paper, we investigate how information from noisy observations can be incorporated to enable continuous correction and refinement of the predicted system state when using a diffusion prior. Motivated by particle filtering methods, we represent the posterior distribution using a set of particles. After receiving noisy observations, the diffusion model is guided using the observation likelihood to steer the generation process toward observation-consistent states. Nevertheless, such guidance does not guarantee sampling from the true posterior. We therefore employ a Sequential Monte Carlo approach over the diffusion trajectory, viewed as a path measure, to reweight and resample particles, thereby correcting the generation process and ensuring convergence toward the desired posterior distribution. This leads to an unbiased particle filtering method that rigorously fuses observational data with diffusion model simulations.

Probabilistic Methods · Bayesian Models and Methods

Shaorong Zhang, Rob Brekelmans, Greg Ver Steeg

Diffusion Posterior Sampling (DPS) provides a principled Bayesian approach to inverse problems by sampling from $p(x_0 \mid y)$. While posterior sampling is valuable for capturing uncertainty and multi-modality, many classical and practical inverse problem settings ultimately prioritize accurate point estimation—most notably the MAP estimator, which has long served as a standard reconstruction objective in imaging and scientific applications. We introduce Local MAP Sampling (LMAPS), a new inference framework that iteratively solving local MAP subproblems along the diffusion trajectory. This perspective clarifies their connection to global MAP and DPS, offering a unified probabilistic interpretation for optimization-based methods. Building on this foundation, we develop practical algorithms with a covariance approximation motivated by Gaussian prior assumption, a reformulated objective for stability and interpretability. Across a broad set of image restoration and scientific tasks, LMAPS achieves state-of-the-art performance.

Probabilistic Methods · Bayesian Models and Methods

John-Joseph Brady, Nikolas Nüsken, Yunpeng Li

Latent state space systems are ubiquitous in statistical modelling, arising naturally when a time-series is observed through a noisy measurement function, however training deep state space models (DSSM) at scale remains difficult. Two largely distinct strategies and literatures have developed around the training of DSSMs. Firstly, auto-encoding DSSMs train generative DSSMs by optimising a variational lower bound. Secondly, DSSMs trained by back-propagating the outputs of a classical sequential Monte Carlo algorithm (SMC). Such approaches can train DSSMs for discriminative as well as generative tasks, however, due to the sequentiality of their forward pass, scale poorly on modern hardware. We propose a new training method _Parallel Variational Monte Carlo_ (PVMC) that bridges the gap between the paradigms, and can be used robustly to train DSSMs for both discriminative and generative tasks. Our method achieves state-of-the-art or better results on a set of baseline experiments and trains $10\times$ faster than the fastest competing SMC approach.

Reinforcement Learning · Batch/Offline

Hongqiang Lin, Pengfei Wang, Nenggan Zheng

Offline reinforcement learning (RL) aims to optimize policies from pre-collected datasets. A bottleneck of this paradigm is managing epistemic uncertainty, which arises from limited data coverage (sample-level) and the ambiguity in identifying transition dynamics from finite data (model-level). To provide a unified quantification of these uncertainties, Bayesian RL has been proposed by treating the dynamics model as a random variable and maintaining a corresponding belief. Despite its theoretical appeal, policy optimization in Bayesian RL remains computationally challenging as it requires solving composite objectives with expectations. Prior methods either employ search-based techniques with poor computational scalability or impose restrictive posterior assumptions that sacrifice the adaptability of Bayesian RL. To address these limitations, we propose Posterior Hybrid Bayesian Belief (PhyB), which reformulates the expectation as a convex combination over a subset of dynamics models. Theoretical analysis demonstrates that the objective discrepancy induced by this approximation remains bounded. Based on PhyB, we develop an iterative regularized policy optimization algorithm that provides metric-agnostic guarantees for monotonic improvement until convergence. Empirical results demonstrate that PhyB achieves state-of-the-art performance on various benchmarks.

Applications · Computer Vision

Ke Wang, Yuanyuan Liu, Kejun Liu, Yuyang Xia, Chang Tang, Yibing Zhan, Zhe Chen

Dynamic Facial Expression Recognition (DFER) models the temporal evolution of facial expressions in videos. In real-world deployments, changing scenarios distort expression trajectories over time, making it difficult for existing methods to maintain performance. While most current approaches address this issue through passive feature alignment across scenarios or domain-incremental learning techniques that preserve previously learned representations, they do not explicitly model scenario evolution over time, limiting their ability to robustly capture expression dynamics under scenario-incremental changes. To end this, we propose **EmWorld**, an emotion world model for DFER that explicitly models latent emotion state evolution under scenario variations. Specifically, **EmWorld** formulates scenario-incremental DFER as a progressive Bayesian inference problem over latent world states with dual temporal scales. Slow-timescale component (**STS**) models scenario evolution using stochastic evolutionary priors, capturing long-term scenario effects and providing proactive guidance in new scenarios. Fast-timescale component (**FTS**) models frame-level expression dynamics with temporally consistent latent transitions, effectively decoupling expression dynamics from scenario influences. By jointly inferring latent states at both timescales, **EmWorld**, shifts DFER from a passive feature discrimination process to a active probabilistic state inference under evolving scenarios. Experiments on FERV39k, DFEW, and MAFW demonstrate that **EmWorld**, consistently outperforms state-of-the-art methods, achieving up to 3.84\% improvement while exhibiting strong cross-scenario stability and long-term robustness.

General Machine Learning · Evaluation

Till Aczel, Lucas Theis, Roger Wattenhofer

Evaluating generative models is challenging because standard metrics often fail to reflect human preferences. Human evaluations are more reliable but costly and noisy, as participants vary in expertise, attention, and diligence. Pairwise comparisons improve consistency, yet aggregating them into overall quality scores requires careful modeling. Bradley-Terry-based methods update item scores from comparisons, but existing approaches either ignore rater variability or lack convergence guarantees, limiting robustness and interpretability. We introduce BBQ, a Bayesian Bradley-Terry variant that explicitly models rater quality, downweighting or removing unreliable participants, and provides guaranteed monotonic likelihood convergence through an Expectation-Maximization algorithm. Empirical results show that BBQ achieves faster convergence, well-calibrated uncertainty estimates, and more robust, interpretable rankings compared to baseline Bradley-Terry models, even with noisy or crowdsourced raters. This framework enables more reliable and cost-effective human evaluation of generative models.

Probabilistic Methods · Bayesian Models and Methods

Mikołaj Słupiński, Piotr Lipinski

The Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) is a Bayesian nonparametric extension of the classical Hidden Markov Model, well-suited for learning from (spatio-)temporal data. To relax the restrictive geometric assumption on state durations, the HDP Hidden Semi-Markov Model was introduced. However, both models assume stationary state durations, which limits their expressive power. In this work, we extend the HDP-HMM framework by incorporating recurrent explicit duration modeling, resulting in a more general and flexible model: the Recurrent Explicit Duration HDP-HMM (RED-HDP-HMM). We propose a Gibbs sampling method for efficient inference in this model. Empirical results on both synthetic and real-world segmentation tasks demonstrate that RED-HDP-HMM consistently outperforms the disentangled sticky HDP-HMM and the standard sticky HDP-HMM. We provide theoretical results on truncation error, expressiveness relative to HDP-HSMM. Empirically, RED-HDP-HMM yields consistent gains: a 2.6 percentage point accuracy increase on honey bee waggle dance data (89.9\% vs.~87.3\%) and 4–10 percentage point improvements on neural segmentation tasks over sticky and disentangled sticky HDP-HMM baselines.

Manuel Glöckler, Jose Pedro JP Manzano-Patron, Stamatios Sotiropoulos, Cornelius Schröder, Jakob Macke

Simulation plays a central role in scientific discovery. In many applications, the bottleneck is no longer running a simulator—it is choosing among large families of plausible simulators, each corresponding to different forward models/hypotheses consistent with observations. Over large model families, classical Bayesian workflows for model selection are impractical. Furthermore, amortized model-selection methods typically hard-code a fixed model prior—or complexity penalty—at training time, requiring users to commit to a particular parsimony assumption before seeing the data. We introduce PRISM, a simulation-based encoder-decoder that infers a joint posterior over both discrete model structures and associated continuous parameters, while enabling test-time control of model complexity via a tunable model prior that the network is conditioned on. We show that PRISM scales to families with combinatorially many (up to billions) of model instantiations on a synthetic symbolic regression task. As a scientific application, we evaluate PRISM on biophysical modeling for diffusion MRI data, showing the ability to perform model selection across several multi-compartment models, on both synthetic and in-vivo neuroimaging data.

Wenhao Li, Yue Lin, Yun Hua, Xiangfeng Wang, Bo Jin, Hongyuan Zha, Baoxiang Wang

Information design (ID) explores how a sender influence the optimal behavior of receivers to achieve specific objectives. While ID originates from everyday human communication, existing game-theoretic and learning methods often model information structures as numbers, which limits many applications to toy games. This work leverages LLMs and proposes a verbalized framework in Bayesian persuasion (BP), which extends classic BP to real-world games involving human dialogues for the first time. We map the BP to a verbalized mediator-augmented game, where LLMs instantiate the sender and receiver. To efficiently solve the verbalized game, we propose a generalized equilibrium-finding algorithm combining LLM and game solver. The algorithm is reinforced with techniques including verbalized commitment assumptions, verbalized obedience constraints, and information obfuscation. Experiments in dialogue scenarios, such as recommendation letters, law enforcement, diplomacy with press, validate that our framework can reproduce theoretical results in classic BP and discover effective persuasion strategies in more complex natural language and multi-stage scenarios.

General Machine Learning · Transfer, Multitask and Meta-learning

Qingyang Zhu, Eric Oermann, Kyunghyun Cho

Bayesian predictive inference provides a principled framework for uncertainty quantification, data efficiency, and robust generalization. However, exact inference is often intractable, and scalable approximations may remain computationally expensive or require restrictive modeling assumptions that degrade predictive performance. Prior-Data Fitted and in-context learning networks have recently emerged as an amortized alternative by learning to map datasets directly to predictive distributions, but existing approaches are tightly coupled to the support of the training prior and lack explicit mechanisms for adapting to new priors at test time, resulting in limited robustness under distribution shift. We introduce a multi-task in-context learning framework for amortized hierarchical Bayesian predictive inference that explicitly represents prior information as a prefix of in-context datasets. A transformer trained on sequences of prior and target tasks learns to adapt its predictions across families of priors. On a suite of evaluations with increasing difficulty, including out-of-meta-distribution heavy-tailed priors and priors with high-dimensional latent structures, our method matches oracle Bayesian predictors while being orders of magnitude faster.

Applications · Computer Vision

Jingwen Ma, Xinpeng Zhang, Fan Shi, Xu Cheng, Shengyong Chen

Multi-frame infrared small target detection suffers from extreme semantic paucity of targets and representation collapse due to overwhelming class imbalance, resulting in the persistent inability to accurately distinguish point-like targets from dynamic background clutter. To address these issues, we propose CodeMamba, a collaborative dual-stream framework that reframes this task as the complementary mechanisms of background manifold modeling and motion singularity capturing. The implicit stream emphasizes background regularity and anomaly localization, while the explicit stream focuses on motion consistency and spatiotemporal singularity. Finally, we design a Bayesian uncertainty-weighted fusion module that estimates the reliability of each stream by quantifying its observation noise. Extensive experiments on the IRDST and DAUB benchmarks demonstrate that CodeMamba not only outperforms existing methods but also achieves enhanced sensitivity to point-like targets.

Probabilistic Methods · Bayesian Models and Methods

Ju Chen, Jun Feng, Shenyu Zhang

Truth inference is a critical technique for aggregating noisy and biased multi-class classification annotations. State-of-the-art approaches model each annotator using an individual confusion matrix. While well-grounded, they suffer from two fundamental bottlenecks: 1) confusion matrices are underfit when annotators label only a small subset of tasks or when classes are imbalanced, and 2) a single confusion matrix per annotator is inadequate for capturing complex annotator behaviors, leading to class-level collapse when tasks are extremely difficult. Simultaneously addressing these challenges is non-trivial, as it demands both robustness to data sparsity and sufficient expressiveness for complex annotator patterns. In this paper, we propose **CPBCC** (**C**lass-specific **P**rototype-driven **B**ayesian **C**lassifier **C**ombination), which creatively models annotators through a dual-pathway architecture: (i) learning class-specific prototype annotation patterns across all annotators, and (ii) learning annotator-specific weights over prototypes. This framework addresses the bottlenecks and achieves a robust yet rich annotator characterization. Experiments across 10 real-world datasets spanning five domains demonstrate that CPBCC yields a 26\% accuracy improvement in the best case, and boosts average accuracy from 68.73% to 74.11%.

General Machine Learning · Causality

Kenneth Lee, Zihan Zhou, Murat Kocaoglu

Modern cloud systems rely on architectures with many interconnected microservices, which enable scalability and flexibility but make troubleshooting failures difficult. Identifying the root cause requires navigating complex dependencies, often beyond the capacity of domain experts. Causal models offer a principled approach to root cause analysis (RCA), but prior methods are typically sample inefficient, as they assume access to the full causal graph or require large numbers of post-failure interventions. We introduce Bayesian Root Cause Discovery (BRCD), which leverages a partial causal structure (a CPDAG learned during the pre-failure period) and performs Bayesian inference without enumerating all DAGs from each interventional Markov equivalence class ($\mathcal{I}$-MEC) for each root cause candidate. Using a recent uniform DAG sampling framework (Wienöbst et al., 2023), BRCD provides the first statistical consistency guarantees for nonparametric RCA, with both identifiability and finite-sample posterior bounds under $\varepsilon$-vanishing approximation. Empirically, across synthetic benchmarks and three microservice systems (Online Boutique, Sockshop, Petshop), BRCD achieves state-of-the-art top-$l$ accuracy while remaining effective in low-failure-sample regimes and scaling to large graphs.