Explaining the decision process of machine learning algorithms is nowadays
crucial for both model's performance enhancement and human comprehension. This
can be achieved by assessing the variable importance of single variables, even
for high-capacity non-linear methods, e.g. Deep Neural Networks (DNNs). While
only removal-based approaches, such as Permutation Importance (PI), can bring
statistical validity, they return misleading results when variables are
correlated. Conditional Permutation Importance (CPI) bypasses PI's limitations
in such cases. However, in high-dimensional settings, where high correlations
between the variables cancel their conditional importance, the use of CPI as
well as other methods leads to unreliable results, besides prohibitive
computation costs. Grouping variables statistically via clustering or some
prior knowledge gains some power back and leads to better interpretations. In
this work, we introduce BCPI (Block-Based Conditional Permutation Importance),
a new generic framework for variable importance computation with statistical
guarantees handling both single and group cases. Furthermore, as handling
groups with high cardinality (such as a set of observations of a given
modality) are both time-consuming and resource-intensive, we also introduce a
new stacking approach extending the DNN architecture with sub-linear layers
adapted to the group structure. We show that the ensuing approach extended with
stacking controls the type-I error even with highly-correlated groups and shows
top accuracy across benchmarks. Furthermore, we perform a real-world data
analysis in a large-scale medical dataset where we aim to show the consistency
between our results and the literature for a biomarker prediction.

解释机器学习算法的决策过程对模型性能提升和人类理解至关重要，通过评估单个变量的重要性来实现，甚至对于高容量的非线性方法，如深度神经网络（DNNs）。在高维设置中，引入了 BCPI（基于块的条件排列重要性）作为一种新的通用框架来计算变量的重要性，具备统计保证并处理单个和群组情况。此外，通过将 DNN 架构扩展为适用于群组结构的次线性层，我们还引入了一种新的堆叠方法，以处理高基数群组，该方法在高度相关的群组中控制了一类错误，并在基准测试中展现了顶级准确性。此外，我们对大规模医学数据集进行了实际数据分析，旨在展示生物标志物预测方面的研究结果与文献的一致性。

高维情况下的变量重要性需要分组

Variable Importance in High-Dimensional Settings Requires Grouping

Variable importance assessment has become a crucial step in machine-learning
applications when using complex learners, such as deep neural networks, on
large-scale data. Removal-based importance assessment is currently the
reference approach, particularly when statistical guarantees are sought to
justify variable inclusion. It is often implemented with variable permutation
schemes. On the flip side, these approaches risk misidentifying unimportant
variables as important in the presence of correlations among covariates. Here
we develop a systematic approach for studying Conditional Permutation
Importance (CPI) that is model agnostic and computationally lean, as well as
reusable benchmarks of state-of-the-art variable importance estimators. We show
theoretically and empirically that $\textit{CPI}$ overcomes the limitations of
standard permutation importance by providing accurate type-I error control.
When used with a deep neural network, $\textit{CPI}$ consistently showed top
accuracy across benchmarks. An empirical benchmark on real-world data analysis
in a large-scale medical dataset showed that $\textit{CPI}$ provides a more
parsimonious selection of statistically significant variables. Our results
suggest that $\textit{CPI}$ can be readily used as drop-in replacement for
permutation-based methods.

我们提出了条件置换重要性（CPI）的系统方法，通过为复杂机器学习应用中的变量重要性评估提供精确的类型 - I 错误控制，并在大规模数据集和深度神经网络中的实证研究中表现出最高准确性。