对定量与定性响应的联合建模的生成方法
A Generative Approach to Joint Modeling of Quantitative and Qualitative Responses
AI总结：
本文提出一种生成方法，联合建模定量和定性响应及预测变量，通过惩罚似然框架实现高效参数估计，并在材料科学和遗传学中通过模拟和实际案例验证其分类和预测的准确性。
摘要：
在许多科学领域，数据通常包含大量预测变量和定量与定性（QQ）响应。通过探索QQ响应之间的关联，现有方法通常在给定预测变量的情况下建立QQ响应的联合模型。然而，预测变量之间的依赖性也提供了对QQ响应建模的有用信息。本文提出了一种生成方法，用于建模QQ响应和预测变量的联合分布。所提出的生成模型在惩罚似然框架下实现了高效的参数估计。它能够实现对定性响应的准确分类和对定量响应的准确预测，并具有高效的计算能力。由于生成方法框架，所提出方法在某些正则条件下可以建立分类和预测的渐近最优性。通过模拟和材料科学和遗传学中的实际案例研究，评估了所提出方法的性能。
英文摘要：
In many scientific areas, data with quantitative and qualitative (QQ) responses are commonly encountered with a large number of predictors. By exploring the association between QQ responses, existing approaches often consider a joint model of QQ responses given the predictor variables. However, the dependency among predictive variables also provides useful information for modeling QQ responses. In this work, we propose a generative approach to model the joint distribution of the QQ responses and predictors. The proposed generative model provides efficient parameter estimation under a penalized likelihood framework. It achieves accurate classification for qualitative response and accurate prediction for quantitative response with efficient computation. Because of the generative approach framework, the asymptotic optimality of classification and prediction of the proposed method can be established under some regularity conditions. The performance of the proposed method is examined through simulations and real case studies in material science and genetics.
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