perform online updates

Traditional Bayesian calibration struggles in dynamic systems to disentangle model parameters from discrepancy terms and is ill-equipped to handle both gradual drifts and abrupt shifts, often being confined to offline settings. This work proposes the Bayesian Recursive Projection Calibration (BRPC) framework, which extends projection-based calibration to online scenarios for the first time. BRPC ensures identifiability and tracks gradual changes by decoupling parameter updates from discrepancy modeling via Gaussian processes, while incorporating a theoretically grounded restart mechanism coupled with online change detection to respond to sudden shifts. Experimental results on synthetic data and industrial process simulations demonstrate that BRPC significantly outperforms sliding-window Bayesian calibration and data assimilation baselines, achieving higher accuracy under gradual drift and maintaining robustness during abrupt changes.

This work addresses the issue of overconfident filtering in nonlinear state-space models caused by misspecification in either the dynamics or observation model. To mitigate this, the authors propose a Prediction-oriented (PrO) online filtering approach that does not strictly rely on Bayes’ theorem but instead learns only when the overall model is correctly specified. By integrating a linear-Gaussian approximation, the method establishes an efficient iterative update mechanism, yielding a variant of the extended Kalman filter termed EKF-PrO. This framework requires no hyperparameters, is computationally efficient, and automatically adapts to model misspecification. Experimental results demonstrate that, across various scenarios involving both linear and nonlinear model misspecifications, EKF-PrO achieves substantially improved inference robustness while maintaining computational costs comparable to existing methods.

This work addresses the inefficiency, high latency, and unbounded memory consumption associated with likelihood computation in Bayesian state estimation by introducing a novel Bayesian filtering approach grounded in native processor operations. For the first time, it integrates native uncertainty tracking into Bayesian inference and combines it with deterministic stratified importance resampling, enabling online inference for arbitrary procedural dynamic models. The proposed method achieves root mean square error (RMSE) accuracy comparable to particle filters while delivering up to an 805× average speedup over Monte Carlo methods. It further guarantees deterministic latency, bounded memory usage, and attains Pareto optimality in the trade-off between accuracy and latency.

This work addresses the challenges of particle degeneracy in traditional particle filters and the lack of rigorous Bayesian updating in existing generative approaches when assimilating high-dimensional, nonlinear, non-Gaussian data. To overcome these limitations, the authors propose the Flow-based Proposal Particle Filter (FPPF), which, for the first time, integrates a conditional generative model with computable likelihood into the particle filtering framework. By learning an approximation to the optimal proposal distribution that minimizes variance, FPPF steers particles toward high-likelihood regions and enables exact importance weighting for principled Bayesian updating. A localization strategy is further incorporated to ensure scalability in high-dimensional settings. Experimental results demonstrate that FPPF significantly outperforms both conventional and generative baselines across diverse complex dynamical systems, effectively mitigating particle degeneracy and yielding more accurate and stable posterior estimates.

Traditional Kalman filtering is constrained by linear Gaussian assumptions, leading to suboptimal performance in nonlinear sensing scenarios such as Doppler radar and LiDAR, where mere parameter tuning cannot overcome inherent structural limitations. This work proposes the Kalman Evolve framework, which for the first time introduces algorithmic structure discovery into state estimation by jointly optimizing noise parameters and update structures. Leveraging large language models as structured priors over program space, the method employs program synthesis to generate interpretable, non-affine filtering algorithms that retain recursive form while adapting effectively to nonlinear dynamics. Experiments across diverse real-world and synthetic tracking tasks demonstrate up to a 12% reduction in root mean square error (RMSE), significantly outperforming strong existing baselines.

This work addresses the sensitivity of conventional Kalman filters to model mismatch and inaccurate noise covariance specifications, as well as the limitations of existing learning-based approaches that require extensive labeled data and struggle to deliver consistent uncertainty estimates. The authors propose a self-supervised hybrid adaptive Kalman filter that leverages only observational data to online-learn structured corrections to both system dynamics and process noise covariances, while preserving the probabilistic framework of the filter to enable joint state estimation and model classification. This approach is the first to achieve adaptive Kalman filtering with statistically consistent uncertainty quantification without requiring labeled data, and it employs generalized Bayesian inference for data-efficient classification. Experiments demonstrate substantial improvements in estimation accuracy on both real-world and simulated datasets, along with robust classification performance across both small-sample and large-data regimes.

This work addresses the long-standing bottleneck of the $O(T^{2/3})$ lower bound on calibration error in online binary sequence calibration. The authors propose an efficient randomized predictor that integrates the SPR-Calibration procedure with an outer Blackwell-style correction mechanism, supported by a novel analytical framework based on proxy sequences and residual decomposition. By leveraging quadratic potential function analysis and exploiting sparsity structures, the method achieves—while maintaining computational efficiency—the first improvement over the classical bound, reducing the expected calibration error to $O(T^{2/3-\varepsilon})$ for some $\varepsilon > 0$, thereby significantly outperforming the previous best-known results.

In Bayesian sequential inference, the marginal likelihood is often treated as a static constant, overlooking its role in modulating the pace of belief updates. This work reveals that the marginal likelihood not only governs the magnitude of individual updates but also encodes frequency patterns embedded in historical data, which the authors reformulate as a dynamic regularizer. By introducing three diagnostic metrics to control online estimation gain and integrating prior and posterior distributions into a hybrid probabilistic mechanism, the proposed approach adaptively adjusts to distributional drift. The resulting framework unifies Bayesian updating with frequentist characteristics within a two-layer probabilistic architecture, substantially enhancing the robustness of sequential estimation and offering a novel paradigm for online risk quantification.

This work addresses the performance degradation in online forecasting of irregular multivariate time series caused by dynamically shifting data distributions. To tackle this challenge, the authors propose Under-Cali, a lightweight and model-agnostic online calibration framework that operates without updating the frozen source model. Under-Cali leverages uncertainty estimation as a core control signal and employs a dual-expert calibration mechanism coupled with an adaptive routing strategy to differentially process and jointly update samples with high versus low uncertainty. Evaluated across multiple benchmark datasets, the framework consistently achieves stable performance improvements while maintaining low computational overhead.