Likelihood approximations via Gaussian approximate inference

• URL: http://arxiv.org/abs/2410.20754v1
• Date: Mon, 28 Oct 2024 05:39:26 GMT
• Title: Likelihood approximations via Gaussian approximate inference
• Authors: Thang D. Bui,
• Abstract summary: We propose efficient schemes to approximate the effects of non-Gaussian likelihoods by Gaussian densities. Our results attain good approximation quality for binary and multiclass classification in large-scale point-estimate and distributional inferential settings. As a by-product, we show that the proposed approximate log-likelihoods are a superior alternative to least-squares on raw labels for neural network classification.
• Score: 3.4991031406102238
• License:
• Abstract: Non-Gaussian likelihoods are essential for modelling complex real-world observations but pose significant computational challenges in learning and inference. Even with Gaussian priors, non-Gaussian likelihoods often lead to analytically intractable posteriors, necessitating approximation methods. To this end, we propose efficient schemes to approximate the effects of non-Gaussian likelihoods by Gaussian densities based on variational inference and moment matching in transformed bases. These enable efficient inference strategies originally designed for models with a Gaussian likelihood to be deployed. Our empirical results demonstrate that the proposed matching strategies attain good approximation quality for binary and multiclass classification in large-scale point-estimate and distributional inferential settings. In challenging streaming problems, the proposed methods outperform all existing likelihood approximations and approximate inference methods in the exact models. As a by-product, we show that the proposed approximate log-likelihoods are a superior alternative to least-squares on raw labels for neural network classification.

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