A sparse expansion for deep Gaussian processes
提出一种基于张量马尔可夫高斯过程（TMGP）的深度高斯过程（DGP）模型，通过层次展开实现稀疏激活，将计算复杂度降至O(polylog(M))，在合成和真实数据上验证了高效性。
In this work, we use Deep Gaussian Processes (DGPs) as statistical surrogates for stochastic processes with complex distributions. Conventional inferential methods for DGP models can suffer from high computational complexity, as they require large-scale operations with kernel matrices for training and inference. In this work, we propose an efficient scheme for accurate inference and efficient training based on a range of Gaussian Processes, called the Tensor Markov Gaussian Processes (TMGP). We construct an induced approximation of TMGP referred to as the hierarchical expansion. Next, we develop a deep TMGP (DTMGP) model as the composition of multiple hierarchical expansion of TMGPs. The proposed DTMGP model has the following properties: (i) the outputs of each activation function are deterministic while the weights are chosen independently from standard Gaussian distribution; (ii) in training or prediction, only O(polylog(M)) (out of M) activation functions have non-zero outputs, which significantly boosts the computational efficiency. Our numerical experiments on synthetic models and real datasets show the superior computational efficiency of DTMGP over existing DGP models.