Machine learning provides powerful methods for inferential and predictive modeling of complicated multivariate relationships to support decision-making for spatial problems such as optimization of unconventional reservoir development. Current machine-learning methods have been widely used in exhaustive spatial data sets like satellite images. However, geological subsurface characterization is significantly different because it is conditioned by sparse, nonrepresentative sampling. These sparse spatial data sets are generally not sampled in a representative manner; therefore, they are biased. The critical questions are: first, does spatial bias in training data result in a bias for machine-learning-based predictive models; and if there is a bias, how can we mitigate the bias in these spatial machine-learning-based predictions?

The presence and mitigation of prediction with spatial sampling bias is demonstrated with tree-based machine learning due to its high degree of interpretability. In expectation, training data bias imposes bias in machine-learning predictions over a wide variety of spatial data configurations and degrees of bias, even when the model is applied to make predictions with unbiased testing and real-world data. We reduce the bias in prediction with a novel spatial weighted tree method over a variety of spatial data configurations and degrees of spatial sampling bias. The proposed method is able to improve the accuracy for reservoir evaluation. We recommend modeling checking and bias mitigation for all machine-learning prediction models with sparse, spatial data sets, because bias in, bias out.

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