Random forests for binary geospatial data
用于二元地理空间数据的随机森林AI 解读 ↓
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用于二元地理空间数据的随机森林
- 研究问题
- 面对存在空间或时间相关性的二元结局，如何让随机森林显式处理观测依赖，并估计非线性协变量效应及空间预测？
- 方法与思路
- 作者利用二元数据下基尼不纯度与最小二乘损失的等价性，引入广义最小二乘森林，再通过链接反演构建随机森林与高斯过程方法。
- 材料陈述的贡献
- 摘要称，所提方法具有均值函数和协变量效应估计的一致性，可处理一类平稳依赖过程，并在模拟与实证比较中表现较好。
- 阅读关注点
- 应核对损失等价关系、链接反演的条件、高斯过程与森林的衔接，以及一致性所需的平稳性和绝对正则性条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审与期刊接收均未核实；摘要未给出完整正则条件、比较设置与误差数值，优势不能推广至所有依赖数据。
原文摘要
The manuscript develops new method and theory for non-linear regression for binary dependent data using random forests. Existing implementations of random forests for binary data cannot explicitly account for data correlation common in geospatial and time-series settings. For continuous outcomes, recent work has extended random forests (RF) to RF-GLS that incorporate spatial covariance using the generalized least squares (GLS) loss. However, adoption of this idea for binary data is challenging due to the use of the Gini impurity measure in classification trees, which has no known extension to model dependence. We show that for binary data, the GLS loss is also an extension of the Gini impurity measure, as the latter is exactly equivalent to the ordinary least squares (OLS) loss. This justifies using RF-GLS for non-parametric mean function estimation for binary dependent data. We then consider the special case of generalized mixed effects models, the traditional statistical model for binary geospatial data, which models the spatial random effects as a Gaussian process (GP). We propose a novel link-inversion technique that embeds the RF-GLS estimate of the mean function from the first step within the generalized mixed effects model framework, enabling estimation of non-linear covariate effects and offering spatial predictions. We establish consistency of our method, RF-GP, for both mean function and covariate effect estimation. The theory holds for a general class of stationary absolutely regular dependent processes that includes common choices like Gaussian processes with Matérn or compactly supported covariances and autoregressive processes. The theory relaxes the common assumption of additive mean functions and accounts for the non-linear link. We demonstrate that RF-GP outperforms competing methods for estimation and prediction in both simulated and real-world data.