Tree-Based Predictive Models for Noisy Input Data
面向含噪输入数据的树基预测模型AI 解读 ↓
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面向含噪输入数据的树基预测模型AI 解读 ↓
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Measurement error is prevalent across all domains of scientific research where only imprecise observations, rather than the true underlying values, can be obtained. For example, estimates of human microbiome diversity are based on small samples from a much larger, generally unobserved system and reflect both sampling error and technical variation. In high-noise settings like these, it becomes difficult to make accurate predictions and to summarize uncertainty. Methods have previously been proposed to accommodate measurement error in classic predictive models, such as linear regression. However, relatively little work has been done to address measurement error in more complex and flexible models. Bayesian additive regression trees (BART), a Bayesian nonparametric model that sums the output of many decision trees, offers robust predictions with built-in uncertainty quantification. In this work, we propose measurement error BART (meBART), a novel extension to the BART model that directly incorporates measurement error in the independent variable(s). Through simulation studies, we show that in the presence of measurement error, our model enables more accurate parameter estimation, more robust uncertainty quantification, and superior predictive performance. We illustrate the utility of our proposed approach through two biomedical applications where the predictors of interest are subject to measurement error.
RBF 核高斯过程最大似然估计的精确渐近理论
Gaussian processes (GPs) are widely used across machine learning, spatial statistics, time-series analysis, optimization, Bayesian statistics, and scientific applications. A central component of a GP model is its kernel, which is typically specified through a parametric family. Among the most widely used choices is the radial basis function (RBF), also known as the squared exponential or Gaussian kernel, owing to its simple form, smoothness, and flexibility. In practice, the…
图分割贝叶斯因果森林:空间异质性处理效应估计
In spatial observational studies, treatment assignment and outcomes often exhibit spatial dependence patterns, and treatment effects may vary across space and subpopulations due to both measured and unmeasured spatially structured confounders. Accounting for spatial dependence while estimating heterogeneous treatment effects (HTEs) is a central task in spatial causal inference. Causal Bayesian additive regression tree methods are popular nonparametric methods for modeling…
析因多变量贝叶斯因果森林:多处理的异质主效应与交互效应
Many studies expose units to several binary treatments at once and record several correlated outcomes, yet analysts usually estimate one treatment's average effect on one outcome at a time -- discarding how treatments interact and how their effects vary across units. We introduce the factorial multivariate Bayesian causal forest, a Bayesian nonparametric model that decomposes the factorial response surface over the treatment lattice into a prognostic sum-of-trees plus one…
贝叶斯加性回归树的稳健半参数推断
Bayesian additive regression trees (BART) provide a class of flexible nonparametric regressions in machine learning. Their rich tree-based structure can generate non-Donsker classes of regression functions. We study posterior inference for the population mean under missing at random. We derive a new Bernstein-von Mises (BvM) theorem showing that even a one-step posterior based on BART and Bayesian-bootstrap reweighting retains a non-negligible bias term in the non-Donsker…
动态空间贝叶斯机器学习:美国代际流动与地理收入不平等应用
We develop a Dynamic Spatial Panel Bayesian Additive Regression Trees model with Horseshoe shrinkage (DSP-BART-HS) for high-dimensional spatio-temporal panel data. We jointly evaluate the model against a comprehensive suite of structural spatial econometrics, non-parametric machine learning methods, and small-area estimators across nine data-generating scenarios spanning 200 replicates each, including irregular spatial topologies, dense policy effects, and non-linear…
见树亦见林:BART 的高斯过程极限
Bayesian Additive Regression Trees (BART) have shown state-of-the-art performance in both prediction and causal inference problems. Previous theoretical work has attempted to explain BART's superior performance by establishing posterior contraction rates for standard BART models, but these rates depend strongly on the number of covariates. Here, we take a different approach and study the behavior of BART as the number of trees grows towards infinity. We show that in this…