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DanWaxman committed Aug 16, 2024
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Expand Up @@ -6,7 +6,7 @@ @article{waxman2024obs
author = {Waxman, Daniel and Llorente, Fernando and Djurić, Petar {M.}},
title = {Online Bayesian Stacking is a Portfolio Selection Problem},
note = {Submitted.},
abstract = {We address the problem of simultaneously learning and combining several Bayesian models in an online, continuous learning setting. In particular, we propose an online Bayesian stacking (OBS), which combines Bayesian models by optimizing a log-score over predictive distributions. We make a novel connection by phrasing OBS as a portfolio selection problem, which unlocks a rich, well-studied theoretical framework with efficient algorithms and extensive regret analysis. This framework additionally elucidates a connection to online Bayesian model averaging (BMA), showing a similar algorithmic approach to different cost functions. Additional interpretation and analysis from the empirical Bayes perspective are provided, showing OBS optimizes the evidence of a mixture of estimators. Following the theoretical development of Bayesian stacking, we apply OBS to an illustrative toy problem. Finally, to show real-world effectiveness, we apply OBS to online basis expansions and Gaussian processes, replacing the online BMA approaches in the literature.}
abstract = {We address the problem of simultaneously learning and combining several Bayesian models in an online, continual learning setting. In particular, we propose online Bayesian stacking (OBS), which combines Bayesian models by optimizing a log-score over predictive distributions. We make a novel connection by phrasing OBS as a portfolio selection problem, which unlocks a rich, well-studied theoretical framework with efficient algorithms and extensive regret analysis. This framework additionally elucidates a connection to online Bayesian model averaging (BMA), showing a similar algorithmic approach to different cost functions. Additional interpretation and analysis from the empirical Bayes perspective are provided, showing OBS optimizes the evidence of a mixture of estimators. Following the theoretical development of Bayesian stacking, we apply OBS to an illustrative toy problem. Finally, to show real-world effectiveness, we apply OBS to online basis expansions and Gaussian processes, replacing the online BMA approaches in the literature.}
}

@article{butler2024tangent,
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