Polynomial regression is widely used and can help to express nonlinear
patterns. However, considering very high polynomial orders may lead to
overfitting and poor extrapolation ability for unseen data. The paper presents
a method for constructing a high-order polynomial regression based on the
Taylor map factorization. This method naturally implements multi-target
regression and can capture internal relationships between targets.
Additionally, we introduce an approach for model interpretation in the form of
systems of differential equations. By benchmarking on UCI open access datasets,
Feynman symbolic regression datasets, and Friedman-1 datasets, we demonstrate
that the proposed method performs comparable to the state-of-the-art regression
methods and outperforms them on specific tasks.

基于泰勒映射因式分解的高阶多项式回归方法实现了多目标回归，并能捕捉目标之间的内在关系。通过在 UCI 等开放数据集上进行基准测试，该方法表现与现有回归方法相当，并在特定任务上表现优异。

TMPNN：基于 Taylor 映射分解的高阶多项式回归

TMPNN: High-Order Polynomial Regression Based on Taylor Map  Factorization

Multi-target regression is useful in a plethora of applications. Although
random forest models perform well in these tasks, they are often difficult to
interpret. Interpretability is crucial in machine learning, especially when it
can directly impact human well-being. Although model-agnostic techniques exist
for multi-target regression, specific techniques tailored to random forest
models are not available. To address this issue, we propose a technique that
provides rule-based interpretations for instances made by a random forest model
for multi-target regression, influenced by a recent model-specific technique
for random forest interpretability. The proposed technique was evaluated
through extensive experiments and shown to offer competitive interpretations
compared to state-of-the-art techniques.

本文提出了针对随机森林模型的多目标回归问题的一种技术，通过基于规则的解释提供了一种解释能力，并与最先进的技术相比具有竞争力的解释能力。

随机森林多目标回归的局部可解释性

Local Interpretability of Random Forests for Multi-Target Regression

There are relatively few works dealing with conformal prediction for
multi-task learning issues, and this is particularly true for multi-target
regression. This paper focuses on the problem of providing valid (i.e.,
frequency calibrated) multi-variate predictions. To do so, we propose to use
copula functions applied to deep neural networks for inductive conformal
prediction. We show that the proposed method ensures efficiency and validity
for multi-target regression problems on various data sets.

本研究旨在解决多目标回归中的频率校准问题，通过对深度神经网络应用随机向量函数解决问题，结果表明该方法能有效保证各种数据集上的多目标回归问题的效率和准确性。

基于 Copula 的多目标回归符合预测

Copula-based conformal prediction for Multi-Target Regression

Multi-target regression is concerned with the simultaneous prediction of
multiple continuous target variables based on the same set of input variables.
It arises in several interesting industrial and environmental application
domains, such as ecological modelling and energy forecasting. This paper
presents an ensemble method for multi-target regression that constructs new
target variables via random linear combinations of existing targets. We discuss
the connection of our approach with multi-label classification algorithms, in
particular RA$k$EL, which originally inspired this work, and a family of recent
multi-label classification algorithms that involve output coding. Experimental
results on 12 multi-target datasets show that it performs significantly better
than a strong baseline that learns a single model for each target using
gradient boosting and compares favourably to multi-objective random forest
approach, which is a state-of-the-art approach. The experiments further show
that our approach improves more when stronger unconditional dependencies exist
among the targets.

本文介绍了一种用于多目标回归的集成方法，通过现有目标的随机线性组合构建新的目标变量，并与 RAkEL 和一系列最新的多标签分类算法进行比较。在 12 个多目标数据集上的实验证明，该方法表现显著优于单一模型方法和随机森林方法。