Tempering the Bayes Filter towards Improved Model-Based Estimation

• URL: http://arxiv.org/abs/2512.02823v1
• Date: Tue, 02 Dec 2025 14:31:10 GMT
• Title: Tempering the Bayes Filter towards Improved Model-Based Estimation
• Abstract summary: We develop the tempered Bayes filter, improving estimation performance.<n>A region of the tempering space can be understood as interpolating between the Bayes- and MAP filters.<n>Specializing the results to the linear Gaussian case, we obtain the tempered Kalman filter.
• Score: 0.5599792629509229
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Model-based filtering is often carried out while subject to an imperfect model, as learning partially-observable stochastic systems remains a challenge. Recent work on Bayesian inference found that tempering the likelihood or full posterior of an imperfect model can improve predictive accuracy, as measured by expected negative log likelihood. In this paper, we develop the tempered Bayes filter, improving estimation performance through both of the aforementioned, and one newly introduced, modalities. The result admits a recursive implementation with a computational complexity no higher than that of the original Bayes filter. Our analysis reveals that -- besides the well-known fact in the field of Bayesian inference that likelihood tempering affects the balance between prior and likelihood -- full-posterior tempering tunes the level of entropy in the final belief distribution. We further find that a region of the tempering space can be understood as interpolating between the Bayes- and MAP filters, recovering these as special cases. Analytical results further establish conditions under which a tempered Bayes filter achieves improved predictive performance. Specializing the results to the linear Gaussian case, we obtain the tempered Kalman filter. In this context, we interpret how the parameters affect the Kalman state estimate and covariance propagation. Empirical results confirm that our method consistently improves predictive accuracy over the Bayes filter baseline.

Related papers

• Learning Probabilistic Filters with Strictly Proper Scoring Rules [8.61813579171868]
  We introduce the proper scoring ensemble filter (PSEF), an ensemble data assimilation method based on training an analysis map to approximate the filtering distribution.<n>We prove that, under a realizability assumption, the population objective is minimized by the true Bayesian filtering distribution.<n> Numerical experiments show that the learned filter accurately approximates challenging filtering distributions, including nonlinear, non-Gaussian, and multi-modal posteriors.
  arXiv  Detail & Related papers  (2026-06-25T01:04:21Z)
• Global Convergence of Gradient Descent for Score Matching in Gaussian Mixtures via Reverse Fisher Divergence [67.12978375116599]
  We study an alternative objective: the reverse Fisher divergence, where the expectation is taken with respect to the student distribution.<n>We prove global convergence guarantees under a $widetilde(1)$-separation assumption on the target means.<n>Our rely on a new Lyapunov-based analysis of the gradient descent dynamics, showing that the reverse Fisher divergence has a much more favorable optimization landscape than the forward Fisher divergence.
  arXiv  Detail & Related papers  (2026-06-18T07:34:33Z)
• Ensemble Score Filtering for Real-Data Energy Consumption Forecast Correction [11.027420128235903]
  We study a high-dimensional data assimilation problem for real energy-consumption data.<n>We employ the Ensemble Score Filter (EnSF) to assimilate partial and noisy observations and correct the forecast trajectory over time.
  arXiv  Detail & Related papers  (2026-05-27T20:27:38Z)
• Rethinking Forward Processes for Score-Based Data Assimilation in High Dimensions [2.3550058325130974]
  We propose a measurement-aware score-based filter (MASF) that defines a measurement-aware forward process directly from the measurement equation.<n>For linear measurements, we derive the exact likelihood score and combine it with a learned prior score to obtain the posterior score.<n> Numerical experiments covering a range of settings, including high-dimensional datasets, demonstrate improved accuracy and stability over existing score-based filters.
  arXiv  Detail & Related papers  (2026-04-03T08:55:38Z)
• Bregman geometry-aware split Gibbs sampling for Bayesian Poisson inverse problems [8.115032818930457]
  We propose a novel framework for solving inverse problems by a Monte Carlo sampling algorithm.<n>We show that the method achieves competitive performance in terms of reconstruction quality.
  arXiv  Detail & Related papers  (2025-11-15T15:27:31Z)
• Recursive KalmanNet: Deep Learning-Augmented Kalman Filtering for State Estimation with Consistent Uncertainty Quantification [0.0]
  This paper introduces Recursive KalmanNet, a Kalman-filter-informed recurrent neural network designed for accurate state estimation.<n> Experiments with non-Gaussian measurement white noise demonstrate that our model outperforms both the conventional Kalman filter and an existing state-of-the-art deep learning based estimator.
  arXiv  Detail & Related papers  (2025-06-13T10:11:32Z)
• Outlier-robust Kalman Filtering through Generalised Bayes [45.51425214486509]
  We derive a novel, provably robust, and closed-form Bayesian update rule for online filtering in state-space models. Our method matches or outperforms other robust filtering methods at a much lower computational cost.
  arXiv  Detail & Related papers  (2024-05-09T09:40:56Z)
• Closed-form Filtering for Non-linear Systems [83.91296397912218]
  We propose a new class of filters based on Gaussian PSD Models, which offer several advantages in terms of density approximation and computational efficiency. We show that filtering can be efficiently performed in closed form when transitions and observations are Gaussian PSD Models. Our proposed estimator enjoys strong theoretical guarantees, with estimation error that depends on the quality of the approximation and is adaptive to the regularity of the transition probabilities.
  arXiv  Detail & Related papers  (2024-02-15T08:51:49Z)
• An adaptive ensemble filter for heavy-tailed distributions: tuning-free inflation and localization [0.3749861135832072]
  Heavy tails is a common feature of filtering distributions that results from the nonlinear dynamical and observation processes. We propose an algorithm to estimate the prior-to-posterior update from samples of joint forecast distribution of the states and observations. We demonstrate the benefits of this new ensemble filter on challenging filtering problems.
  arXiv  Detail & Related papers  (2023-10-12T21:56:14Z)
• Sampling from Gaussian Process Posteriors using Stochastic Gradient Descent [43.097493761380186]
  gradient algorithms are an efficient method of approximately solving linear systems. We show that gradient descent produces accurate predictions, even in cases where it does not converge quickly to the optimum. Experimentally, gradient descent achieves state-of-the-art performance on sufficiently large-scale or ill-conditioned regression tasks.
  arXiv  Detail & Related papers  (2023-06-20T15:07:37Z)
• Double Robust Bayesian Inference on Average Treatment Effects [2.458652618559425]
  We propose a double robust Bayesian inference procedure on the average treatment effect (ATE) under unconfoundedness.<n>For our new Bayesian approach, we first adjust the prior distributions of the conditional mean functions, and then correct the posterior distribution of the resulting ATE.
  arXiv  Detail & Related papers  (2022-11-29T15:32:25Z)
• Distributional Gradient Boosting Machines [77.34726150561087]
  Our framework is based on XGBoost and LightGBM. We show that our framework achieves state-of-the-art forecast accuracy.
  arXiv  Detail & Related papers  (2022-04-02T06:32:19Z)
• Efficient CDF Approximations for Normalizing Flows [64.60846767084877]
  We build upon the diffeomorphic properties of normalizing flows to estimate the cumulative distribution function (CDF) over a closed region. Our experiments on popular flow architectures and UCI datasets show a marked improvement in sample efficiency as compared to traditional estimators.
  arXiv  Detail & Related papers  (2022-02-23T06:11:49Z)
• Posterior temperature optimized Bayesian models for inverse problems in medical imaging [59.82184400837329]
  We present an unsupervised Bayesian approach to inverse problems in medical imaging using mean-field variational inference with a fully tempered posterior. We show that an optimized posterior temperature leads to improved accuracy and uncertainty estimation. Our source code is publicly available at calibrated.com/Cardio-AI/mfvi-dip-mia.
  arXiv  Detail & Related papers  (2022-02-02T12:16:33Z)
• Evaluating State-of-the-Art Classification Models Against Bayes Optimality [106.50867011164584]
  We show that we can compute the exact Bayes error of generative models learned using normalizing flows. We use our approach to conduct a thorough investigation of state-of-the-art classification models.
  arXiv  Detail & Related papers  (2021-06-07T06:21:20Z)
• Bayesian Deep Learning and a Probabilistic Perspective of Generalization [56.69671152009899]
  We show that deep ensembles provide an effective mechanism for approximate Bayesian marginalization. We also propose a related approach that further improves the predictive distribution by marginalizing within basins of attraction.
  arXiv  Detail & Related papers  (2020-02-20T15:13:27Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.