Function-Space Distributions over Kernels
Function-Space Distributions over Kernels
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发表时间：
2019-10
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通讯作者：
Gregory W. Benton;Wesley J. Maddox;Jayson Salkey;J. Albinati;A. Wilson
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作者：
Gregory W. Benton;Wesley J. Maddox;Jayson Salkey;J. Albinati;A. Wilson
高斯过程是灵活的函数逼近器，具有由协方差核控制的归纳偏差。核学习是表征学习和强预测性能的关键。在本文中，我们发展了功能核学习（FKL）来直接推断核上的功能后验。特别地，我们在谱密度上放置一个变换的高斯过程，以诱导核函数上的非参数分布。由此产生的方法可以学习丰富的表示，支持任何固定的核，核值的不确定性，以及直接在核上的可解释的先验规范，而不需要复杂的初始化或人工干预。我们通过椭圆切片采样进行推理，这特别适合于对具有强相关先验的后验进行边缘化，这是函数空间建模的典型特征。我们为非均匀、大规模、多任务和多维数据开发了我们的方法，并在广泛的设置中显示出有希望的性能，包括插值、外推和核恢复实验。
Gaussian processes are flexible function approximators, with inductive biases controlled by a covariance kernel. Learning the kernel is the key to representation learning and strong predictive performance. In this paper, we develop functional kernel learning (FKL) to directly infer functional posteriors over kernels. In particular, we place a transformed Gaussian process over a spectral density, to induce a non-parametric distribution over kernel functions. The resulting approach enables learning of rich representations, with support for any stationary kernel, uncertainty over the values of the kernel, and an interpretable specification of a prior directly over kernels, without requiring sophisticated initialization or manual intervention. We perform inference through elliptical slice sampling, which is especially well suited to marginalizing posteriors with the strongly correlated priors typical to function space modeling. We develop our approach for non-uniform, large-scale, multi-task, and multidimensional data, and show promising performance in a wide range of settings, including interpolation, extrapolation, and kernel recovery experiments.