aiqbench analysis
This research introduces a framework for adaptive Bayesian online learning by aggregating multiple update rules as experts to achieve robust performance without needing prior oracle selection. The approach is validated through applications in conformal inference and Gaussian process regression, offering improved uncertainty quantification on data streams with varying smoothness properties.
Adaptive Bayesian Online Learning via Expert Aggregation
arXiv:2607.20239v1 Announce Type: cross Abstract: Bayesian online learning promises uncertainty-aware prediction on data streams, but its performance hinges on inferential choices, including learning rates, prior distributions and variational families, which are usually fixed before seeing the stream. We address this by treating Bayesian update rules as experts and aggregating the Bayesian experts according to sequential predictive losses. We prove that the resulting aggregate competes with the best expert in hindsight at an aggregation cost determined by how each expert's per-round performance is evaluated. We instantiate the framework in online conformal inference and Gaussian process regression. The conformal inference application yields a smoothed Bayesian counterpart of adaptive conformal inference with long-run randomized coverage, while the Gaussian process application gives an oracle inequality in cumulative predictive Kullback-Leibler risk and adaptation to unknown H\"older smoothness up to logarithmic factors. Experiments show that the aggregate tracks strong experts without oracle expert selection.
Abstract:Bayesian online learning promises uncertainty-aware prediction on data streams, but its performance hinges on inferential choices, including learning rates, prior distributions and variational families, which are usually fixed before seeing the stream. We address this by treating Bayesian update rules as experts and aggregating the Bayesian experts according to sequential predictive losses. We prove that the resulting aggregate competes with the best expert in hindsight at an aggregation cost determined by how each expert's per-round performance is evaluated. We instantiate the framework in online conformal inference and Gaussian process regression. The conformal inference application yields a smoothed Bayesian counterpart of adaptive conformal inference with long-run randomized coverage, while the Gaussian process application gives an oracle inequality in cumulative predictive Kullback-Leibler risk and adaptation to unknown Hölder smoothness up to logarithmic factors. Experiments show that the aggregate tracks strong experts without oracle expert selection.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2607.20239 [stat.ML]
(or arXiv:2607.20239v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2607.20239 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 240 words
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