Representation learning plays a crucial role in automated feature selection,
particularly in the context of high-dimensional data, where non-parametric
methods often struggle. In this study, we focus on supervised learning
scenarios where the pertinent information resides within a lower-dimensional
linear subspace of the data, namely the multi-index model. If this subspace
were known, it would greatly enhance prediction, computation, and
interpretation. To address this challenge, we propose a novel method for linear
feature learning with non-parametric prediction, which simultaneously estimates
the prediction function and the linear subspace. Our approach employs empirical
risk minimisation, augmented with a penalty on function derivatives, ensuring
versatility. Leveraging the orthogonality and rotation invariance properties of
Hermite polynomials, we introduce our estimator, named RegFeaL. By utilising
alternative minimisation, we iteratively rotate the data to improve alignment
with leading directions and accurately estimate the relevant dimension in
practical settings. We establish that our method yields a consistent estimator
of the prediction function with explicit rates. Additionally, we provide
empirical results demonstrating the performance of RegFeaL in various
experiments.

利用非参数预测的线性特征学习方法 RegFeaL，同时估计预测函数和线性子空间，经过实验证实其在不同实验中的表现。

非参数线性特征学习与回归正则化

Nonparametric Linear Feature Learning in Regression Through  Regularisation

We study the problem of balancing effectiveness and efficiency in automated
feature selection. After exploring many feature selection methods, we observe a
computational dilemma: 1) traditional feature selection is mostly efficient,
but difficult to identify the best subset; 2) the emerging reinforced feature
selection automatically navigates to the best subset, but is usually
inefficient. Can we bridge the gap between effectiveness and efficiency under
automation? Motivated by this dilemma, we aim to develop a novel feature space
navigation method. In our preliminary work, we leveraged interactive
reinforcement learning to accelerate feature selection by external
trainer-agent interaction. In this journal version, we propose a novel
interactive and closed-loop architecture to simultaneously model interactive
reinforcement learning (IRL) and decision tree feedback (DTF). Specifically,
IRL is to create an interactive feature selection loop and DTF is to feed
structured feature knowledge back to the loop. First, the tree-structured
feature hierarchy from decision tree is leveraged to improve state
representation. In particular, we represent the selected feature subset as an
undirected graph of feature-feature correlations and a directed tree of
decision features. We propose a new embedding method capable of empowering
graph convolutional network to jointly learn state representation from both the
graph and the tree. Second, the tree-structured feature hierarchy is exploited
to develop a new reward scheme. In particular, we personalize reward assignment
of agents based on decision tree feature importance. In addition, observing
agents' actions can be feedback, we devise another reward scheme, to weigh and
assign reward based on the feature selected frequency ratio in historical
action records. Finally, we present extensive experiments on real-world
datasets to show the improved performance.

我们提出了一种新的交互式和闭环架构，同时建模交互式强化学习（IRL）和决策树反馈（DTF），以在自动化过程中平衡有效性和效率的问题。通过实验，我们发现传统特征选择方法大多数是有效的，但难以识别最佳子集；而新兴的增强特征选择方法虽然可以自动导航到最佳子集，但通常效率较低。因此，我们的工作旨在开发一种新的特征空间导航方法。

循环决策树中的交互式强化学习特征选择

Interactive Reinforcement Learning for Feature Selection with Decision  Tree in the Loop

In this paper, we study the problem of balancing effectiveness and efficiency
in automated feature selection. Feature selection is a fundamental intelligence
for machine learning and predictive analysis. After exploring many feature
selection methods, we observe a computational dilemma: 1) traditional feature
selection methods (e.g., mRMR) are mostly efficient, but difficult to identify
the best subset; 2) the emerging reinforced feature selection methods
automatically navigate feature space to explore the best subset, but are
usually inefficient. Are automation and efficiency always apart from each
other? Can we bridge the gap between effectiveness and efficiency under
automation? Motivated by such a computational dilemma, this study is to develop
a novel feature space navigation method. To that end, we propose an Interactive
Reinforced Feature Selection (IRFS) framework that guides agents by not just
self-exploration experience, but also diverse external skilled trainers to
accelerate learning for feature exploration. Specifically, we formulate the
feature selection problem into an interactive reinforcement learning framework.
In this framework, we first model two trainers skilled at different searching
strategies: (1) KBest based trainer; (2) Decision Tree based trainer. We then
develop two strategies: (1) to identify assertive and hesitant agents to
diversify agent training, and (2) to enable the two trainers to take the
teaching role in different stages to fuse the experiences of the trainers and
diversify teaching process. Such a hybrid teaching strategy can help agents to
learn broader knowledge, and, thereafter, be more effective. Finally, we
present extensive experiments on real-world datasets to demonstrate the
improved performances of our method: more efficient than existing reinforced
selection and more effective than classic selection.

研究如何在自动化特征选择中平衡有效性和效率。通过提出一个新的交互式增强特征选择框架，将特征选择问题形式化为交互式强化学习框架，该框架通过自我探索经验及多元化外部技术指导训练器，从而加速学习。此外，该研究利用多种不同搜索策略进行训练，并提出了一种混合教学策略来帮助智能体学习更广泛的知识。最后，对真实世界数据集进行广泛实验以展示该方法的性能改进。