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。高效的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，并尽可能降低在线参数更新的计算成本。现有解决方案仅部分满足了这些需求。本文提出了首个自适应稀疏高斯过程（GP），能够解决上述所有问题。我们首先重新表述了变分稀疏GP算法，通过引入遗忘因子使其具备自适应性。其次，为使模型推理尽可能简单，我们建议在新样本到达时，每次仅更新稀疏GP模型的一个诱导点以及其余模型参数。因此，该算法在推理过程中具有快速收敛性，即使在高度非平稳的环境中也能实现高效的模型更新（只需单次推理迭代）。实验结果表明，与现有方法相比，所提算法在预测后验的均值和置信区间估计方面表现出良好的性能。