This paper presents robust weighted variants of batch and online standard Gaussian processes (GPs) to effectively reduce the negative impact of outliers in the corresponding GP models. This is done by introducing robust data weighers that rely on robust and quasi-robust weight functions that come from robust M-estimators. Our robust GPs are compared to various GP models on four datasets. It is shown that our batch and online robust weighted GPs are indeed robust to outliers, significantly outperforming the corresponding standard GPs and the recently proposed heteroscedastic GP method GPz. Our experiments also show that our methods are comparable to and sometimes better than a state-of-the-art robust GP that uses a Student-t likelihood.

本文介绍了批处理和在线标准高斯过程（GP）的鲁棒加权变量，可有效减少相应GP模型中异常值的负面影响。这是通过引入鲁棒的数据加权器来完成的，这些加权器依赖于鲁棒的M估计器的鲁棒和准鲁棒加权函数。我们将强大的GP与四个数据集上的各种GP模型进行了比较。结果表明，我们的批处理和在线鲁棒加权GP确实对异常值具有鲁棒性，明显优于相应的标准GP和最近提出的异方差GP方法GPz。我们的实验还表明，我们的方法与使用Student- t可能性的最新健壮GP相当，有时甚至更好。