Regression with Linear Factored Functions
Regression with Linear Factored Functions
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DOI：
10.1007/978-3-319-23528-8_8
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发表时间：
2014-12
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通讯作者：
Wendelin Böhmer;K. Obermayer
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作者：
Wendelin Böhmer;K. Obermayer
许多使用经验估计函数的应用程序面临着维数的问题，因为大多数函数类上的积分必须通过采样来近似。本文介绍了一种新的学习线性因子函数（LFF）的回归算法。这类函数的结构特性允许解析求解某些积分和计算逐点乘积。像信念传播和恢复学习这样的应用可以利用这些特性来打破诅咒并加快计算速度。我们推导出一个正则化的贪婪优化方案，在训练过程中学习因子化的基函数。新的回归算法在基准任务上表现出与高斯过程的竞争力，并且学习的LFF函数平均具有4-9个因子基函数，非常紧凑。
Many applications that use empirically estimated functions face acurse of dimensionality, because integrals over most function classes must be approximated by sampling. This paper introduces a novelregression-algorithm that learnslinear factored functions(LFF). This class of functions has structural properties that allow to analytically solve certain integrals and to calculate point-wise products. Applications likebelief propagationandreinforcement learningcan exploit these properties to break the curse and speed up computation. We derive a regularized greedy optimization scheme, that learns factored basis functions during training. The novel regression algorithm performs competitively toGaussian processeson benchmark tasks, and the learned LFF functions are with 4-9 factored basis functions on average very compact.