论文标题
非缀合物高斯工艺模型的零件恒定近似
A piece-wise constant approximation for non-conjugate Gaussian Process models
论文作者
论文摘要
高斯工艺（GPS）是贝叶斯机器学习中一种多功能且流行的方法。常见的修改是稀疏的变异高斯过程（SVGP），非常适合处理大型数据集。尽管GP可以优雅地处理封闭形式的高斯分布的目标变量，但它们的适用性也可以扩展到非高斯数据。这些延伸通常无法以封闭形式处理，因此需要近似解决方案。本文提出了近似逆链接函数，这是通过零件恒定函数在非高斯可能性上工作时必不可少的。可以证明，这将产生相应的SVGP下限的封闭形式解决方案。此外，还证明了如何优化零件的常数函数本身，从而产生了逆链接函数，可以从手头的数据中学到。
Gaussian Processes (GPs) are a versatile and popular method in Bayesian Machine Learning. A common modification are Sparse Variational Gaussian Processes (SVGPs) which are well suited to deal with large datasets. While GPs allow to elegantly deal with Gaussian-distributed target variables in closed form, their applicability can be extended to non-Gaussian data as well. These extensions are usually impossible to treat in closed form and hence require approximate solutions. This paper proposes to approximate the inverse-link function, which is necessary when working with non-Gaussian likelihoods, by a piece-wise constant function. It will be shown that this yields a closed form solution for the corresponding SVGP lower bound. In addition, it is demonstrated how the piece-wise constant function itself can be optimized, resulting in an inverse-link function that can be learnt from the data at hand.
