标题： 结构化径向基函数网络：用于多假设预测的建模多样性 显示英文标题

标题： Structured Radial Basis Function Network: Modelling Diversity for Multiple Hypotheses Prediction

摘要： 多模态问题可以使用多个假设框架有效解决，但将这些框架整合到学习模型中面临着重大挑战。 本文介绍了一种结构化径向基函数网络（s-RBFN），作为回归的多个假设预测器的集成。 在预测器的训练过程中，首先根据其损失和真实标签形成中心 Voronoi 网格，从几何上表示多个假设的集合。 然后，训练好的预测器用于计算包含基函数中心和尺度的结构化数据集。 随后，使用这个结构化数据集训练一个径向基函数网络，以进行多个假设的预测。 s-RBFN 设计为在控制集成学习中的多样性的同时高效训练。 用于训练结构化集成模型的最小二乘方法为多个假设和结构化预测提供了闭式解。 在结构化数据集的形成过程中，采用了一个参数通过控制网格形状来避免模式崩溃。 该参数为 s-RBFN 提供了平衡多样性和泛化性能的机制。 在两个多变量预测数据集——空气质量预测和能源电器预测上的实证验证表明，与其它模型及其单一假设对应模型相比，结构化集成模型具有更优的泛化性能和计算效率。 显示英文摘要

摘要： Multi-modal problems can be effectively addressed using multiple hypothesis frameworks, but integrating these frameworks into learning models poses significant challenges. This paper introduces a Structured Radial Basis Function Network (s-RBFN) as an ensemble of multiple hypothesis predictors for regression. During the training of the predictors, first the centroidal Voronoi tessellations are formed based on their losses and the true labels, representing geometrically the set of multiple hypotheses. Then, the trained predictors are used to compute a structured dataset with their predictions, including centers and scales for the basis functions. A radial basis function network, with each basis function focused on a particular hypothesis, is subsequently trained using this structured dataset for multiple hypotheses prediction. The s-RBFN is designed to train efficiently while controlling diversity in ensemble learning parametrically. The least-squares approach for training the structured ensemble model provides a closed-form solution for multiple hypotheses and structured predictions. During the formation of the structured dataset, a parameter is employed to avoid mode collapse by controlling tessellation shapes. This parameter provides a mechanism to balance diversity and generalization performance for the s-RBFN. The empirical validation on two multivariate prediction datasets-air quality and energy appliance predictions-demonstrates the superior generalization performance and computational efficiency of the structured ensemble model compared to other models and their single-hypothesis counterparts.