使用 Transformers 进行多元系统中的单变量骨架预测
Univariate Skeleton Prediction in Multivariate Systems Using Transformers
AI总结：
针对多元系统符号回归难以识别单变量函数形式的问题，提出一种基于预训练 Multi-Set Transformer 的可解释神经符号回归方法，通过生成单变量符号骨架解释变量影响，其性能优于多种基线方法。
摘要：
符号回归（SR）方法试图学习逼近所观察系统行为的数学表达式。然而，在处理多元系统时，它们通常无法识别解释每个变量与系统响应之间关系的函数形式。为了着手解决这一问题，我们提出了一种可解释的神经 SR 方法，该方法生成单变量符号骨架，旨在解释每个变量如何影响系统响应。通过分析人工生成的多组数据（其中一组输入变量变化而其他变量固定），对每个输入变量的关系进行单独建模。此类人工数据集的响应使用回归神经网络（NN）进行估计。最后，多组输入-响应对由预训练的 Multi-Set Transformer 处理，该模型解决了我们称之为 Multi-Set Skeleton Prediction 的问题，并输出单变量符号骨架。因此，此类骨架表示对回归 NN 所逼近函数的解释。实验结果表明，该方法学习到的骨架表达式与底层函数相匹配，并优于两种基于 GP 的方法和两种神经 SR 方法。
英文摘要：
Symbolic regression (SR) methods attempt to learn mathematical expressions that approximate the behavior of an observed system. However, when dealing with multivariate systems, they often fail to identify the functional form that explains the relationship between each variable and the system's response. To begin to address this, we propose an explainable neural SR method that generates univariate symbolic skeletons that aim to explain how each variable influences the system's response. By analyzing multiple sets of data generated artificially, where one input variable varies while others are fixed, relationships are modeled separately for each input variable. The response of such artificial data sets is estimated using a regression neural network (NN). Finally, the multiple sets of input-response pairs are processed by a pre-trained Multi-Set Transformer that solves a problem we termed Multi-Set Skeleton Prediction and outputs a univariate symbolic skeleton. Thus, such skeletons represent explanations of the function approximated by the regression NN. Experimental results demonstrate that this method learns skeleton expressions matching the underlying functions and outperforms two GP-based and two neural SR methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
