Title | ||
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Loss function based second-order Jensen inequality and its application to particle variational inference. |
Abstract | ||
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Bayesian model averaging, obtained as the expectation of a likelihood function by a posterior distribution, has been widely used for prediction, evaluation of uncertainty, and model selection. Various approaches have been developed to efficiently capture the information in the posterior distribution; one such approach is the optimization of a set of models simultaneously with interaction to ensure the diversity of the individual models in the same way as ensemble learning. A representative approach is particle variational inference (PVI), which uses an ensemble of models as an empirical approximation for the posterior distribution. PVI iteratively updates each model with a repulsion force to ensure the diversity of the optimized models. However, despite its promising performance, a theoretical understanding of this repulsion and its association with the generalization ability remains unclear. In this paper, we tackle this problem in light of PAC-Bayesian analysis. First, we provide a new second-order Jensen inequality, which has the repulsion term based on the loss function. Thanks to the repulsion term, it is tighter than the standard Jensen inequality. Then, we derive a novel generalization error bound and show that it can be reduced by enhancing the diversity of models. Finally, we derive a new PVI that optimizes the generalization error bound directly. Numerical experiments demonstrate that the performance of the proposed PVI compares favorably with existing methods in the experiment. |
Year | Venue | DocType |
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2021 | Annual Conference on Neural Information Processing Systems | Conference |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
5 |
Name | Order | Citations | PageRank |
---|---|---|---|
Futami, Futoshi | 1 | 0 | 2.03 |
Tomoharu Iwata | 2 | 0 | 1.01 |
Naonori Ueda | 3 | 0 | 0.68 |
Issei Sato | 4 | 331 | 41.59 |
Masashi Sugiyama | 5 | 0 | 3.04 |