Interpretable Deep Gaussian Processes with Moments
Interpretable Deep Gaussian Processes with Moments
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发表时间：
2019-05
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通讯作者：
Chi-Ken Lu;Scott Cheng-Hsin Yang;Xiaoran Hao;Patrick Shafto
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作者：
Chi-Ken Lu;Scott Cheng-Hsin Yang;Xiaoran Hao;Patrick Shafto
深度高斯过程（DGP）联合收割机将深度神经网络（DNN）的表达能力与高斯过程（GP）的量化不确定性相结合。表达能力和难以处理的推理都来自于组合函数的非高斯分布。我们提出了可解释的DGP的基础上近似DGP作为一个GP通过计算精确的时刻，另外确定一些DGP分布的重尾性质。因此，我们的方法承认解释为指定的激活函数的神经网络和DGP的变分近似。我们确定了DGP的表达性参数，并从DGP组合中发现了非局部和非平稳的相关性。我们提供了一般配方推导出有效的内核DGP的两个，三个，或无限多层，由同质或异质内核。结果表明，我们的有效内核的表现力，通过样本的先验和推理的模拟和真实的数据，并展示了解释性的分析形式的优势，并绘制跨内核的关系和等价性。
Deep Gaussian Processes (DGPs) combine the expressiveness of Deep Neural Networks (DNNs) with quantified uncertainty of Gaussian Processes (GPs). Expressive power and intractable inference both result from the non-Gaussian distribution over composition functions. We propose interpretable DGP based on approximating DGP as a GP by calculating the exact moments, which additionally identify the heavy-tailed nature of some DGP distributions. Consequently, our approach admits interpretation as both NNs with specified activation functions and as a variational approximation to DGP. We identify the expressivity parameter of DGP and find non-local and non-stationary correlation from DGP composition. We provide general recipes for deriving the effective kernels for DGP of two, three, or infinitely many layers, composed of homogeneous or heterogeneous kernels. Results illustrate the expressiveness of our effective kernels through samples from the prior and inference on simulated and real data and demonstrate advantages of interpretability by analysis of analytic forms, and draw relations and equivalences across kernels.