Local Kernel Ridge Regression for Scalable, Interpolating, Continuous Regression
Local Kernel Ridge Regression for Scalable, Interpolating, Continuous Regression
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发表时间：
2022
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通讯作者：
Mingxuan Han;Chenglong Ye;J. M. Phillips
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作者：
Mingxuan Han;Chenglong Ye;J. M. Phillips
我们研究了一种局部化版本的核岭回归，它可以连续、平滑地对与观测数据点具有高度非线性的潜在函数值进行内插。这种新方法可以处理(A)局部密度高度不均匀和(B)在某些小而未知的区域内函数值变化剧烈的数据。通过引入一种新的基于秩次的内插方法，它可以被解释为可变带宽的Nadaraya-Watson核回归，由我们的局部方法提供的内插值可以被证明是随着查询点的连续变化的。与传统的核岭回归方法相比，该方法避免了全矩阵求逆，具有良好的可扩展性。
We study a localized version of kernel ridge regression that can continuously, smoothly interpolate the underlying function values which are highly non-linear with observed data points. This new method can deal with the data of which (a) local density is highly uneven and (b) the function values change dramatically in certain small but unknown regions. By introducing a new rank-based interpolation scheme, which can be interpreted as a variable bandwidth Nadaraya-Watson Kernel Regression, the interpolated values provided by our local method can be proven to continuously vary with query points. Our method is scalable by avoiding the full matrix inverse, compared with traditional kernel ridge regression.