Adaptive learning is necessary for non-stationary environments where the learning machine needs to forget past data distribution. Efficient algorithms require a compact model update to not grow in computational burden with the incoming data and with the lowest possible computational cost for online parameter updating. Existing solutions only partially cover these needs. Here, we propose the first adaptive sparse Gaussian Process (GP) able to address all these issues. We first reformulate a variational sparse GP algorithm to make it adaptive through a forgetting factor. Next, to make the model inference as simple as possible, we propose updating a single inducing point of the sparse GP model together with the remaining model parameters every time a new sample arrives. As a result, the algorithm presents a fast convergence of the inference process, which allows an efficient model update (with a single inference iteration) even in highly non-stationary environments. Experimental results demonstrate the capabilities of the proposed algorithm and its good performance in modeling the predictive posterior in mean and confidence interval estimation compared to state-of-the-art approaches.

翻译：自适应学习对于非平稳环境是必要的，在这种环境中学习机器需要遗忘过去的数据分布。高效算法需要紧凑的模型更新，以避免随着新数据的到来而增加计算负担，并且在线参数更新的计算成本应尽可能低。现有解决方案仅部分满足这些需求。本文提出了首个能够解决所有上述问题的自适应稀疏高斯过程（GP）。我们首先重新推导了变分稀疏GP算法，通过引入遗忘因子使其具备自适应性。其次，为尽可能简化模型推理，我们提出在新样本到达时，每次仅更新稀疏GP模型中的一个诱导点以及其余模型参数。由此，该算法实现了推理过程的快速收敛，使得即使在高度非平稳环境中也能高效进行模型更新（仅需单次推理迭代）。实验结果表明，与现有最先进方法相比，所提算法在预测后验均值与置信区间估计方面具有优越性能。