用高斯近似解决非高斯似然的计算难题，让旧方法能高效处理复杂数据。
Likelihood approximations via Gaussian approximate inference
- 通过变分推断和变换基下的矩匹配，将非高斯似然近似为高斯形式
- 在大规模分类任务中逼近效果良好，流数据场景下优于现有方法
- 可替代原始标签的最小二乘法，提升神经网络分类性能
非高斯似然对建模复杂真实观测至关重要，但会带来显著的计算挑战。即使使用高斯先验，非高斯似然也常导致后验分布解析不可解，需依赖近似方法。为此，我们提出基于变分推断和变换基下矩匹配的高效方案，将非高斯似然的影响近似为高斯密度，使原本仅适用于高斯似然模型的高效推断策略得以应用。实验表明，该匹配策略在大规模点估计与分布推断场景下对二分类和多分类任务均取得良好逼近效果。在具有挑战性的流式学习问题中，所提方法在精确模型下超越所有现有似然近似与近似推断方法。作为副产品，我们证明所提出的近似对数似然在神经网络分类中是原始标签最小二乘法的更优替代。
原文摘要 · Abstract (English)
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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