In this paper, we introduce Partial Information Decomposition of Features
(PIDF), a new paradigm for simultaneous data interpretability and feature
selection. Contrary to traditional methods that assign a single importance
value, our approach is based on three metrics per feature: the mutual
information shared with the target variable, the feature's contribution to
synergistic information, and the amount of this information that is redundant.
In particular, we develop a novel procedure based on these three metrics, which
reveals not only how features are correlated with the target but also the
additional and overlapping information provided by considering them in
combination with other features. We extensively evaluate PIDF using both
synthetic and real-world data, demonstrating its potential applications and
effectiveness, by considering case studies from genetics and neuroscience.

本文介绍了 Partial Information Decomposition of Features（PIDF），一种同时实现数据可解释性和特征选择的新范式。相较于传统方法，我们的方法基于每个特征的三个度量值：与目标变量的相互信息、特征对协同信息的贡献以及冗余信息的数量。我们根据这三个度量值开发了一种新的程序，不仅揭示了特征与目标的相关性，还考虑了特征与其他特征的组合所提供的额外和重叠信息。我们广泛评估了 PIDF，使用了合成和真实数据，并通过遗传学和神经科学领域的案例研究展示了其潜在应用和有效性。

数据解释性和特征选择的部分信息分解

Partial Information Decomposition for Data Interpretability and Feature  Selection

Asking questions is a pervasive human activity, but little is understood
about what makes them difficult to answer. An analysis of a pair of large
databases, of New York Times crosswords and questions from the quiz-show
Jeopardy, establishes two orthogonal dimensions of question difficulty:
obscurity (the rarity of the answer) and opacity (the indirectness of question
cues, operationalized with word2vec). The importance of opacity, and the role
of synergistic information in resolving it, suggests that accounts of
difficulty in terms of prior expectations captures only a part of the
question-asking process. A further regression analysis shows the presence of
additional dimensions to question-asking: question complexity, the answer's
local network density, cue intersection, and the presence of signal words. Our
work shows how question-askers can help their interlocutors by using contextual
cues, or, conversely, how a particular kind of unfamiliarity with the domain in
question can make it harder for individuals to learn from others. Taken
together, these results suggest how Bayesian models of question difficulty can
be supplemented by process models and accounts of the heuristics individuals
use to navigate conceptual spaces.

本文研究问题的难度，并指出模糊性与稀有性两个维度影响问题回答的难度，同时发现问题复杂度、答案网络密度、线索交叉性及信号词的存在也会影响问题的难度。同时，通过本文的研究成果，指导个体在提问和学习过程中跨越领域困难，增强理解。

透明度、隐晦性和问题提出的几何学

Opacity, Obscurity, and the Geometry of Question-Asking

We propose new measures of shared information, unique information and
synergistic information that can be used to decompose the multi-information of
a pair of random variables $(Y,Z)$ with a third random variable $X$. Our
measures are motivated by an operational idea of unique information which
suggests that shared information and unique information should depend only on
the pair marginal distributions of $(X,Y)$ and $(X,Z)$. Although this
invariance property has not been studied before, it is satisfied by other
proposed measures of shared information. The invariance property does not
uniquely determine our new measures, but it implies that the functions that we
define are bounds to any other measures satisfying the same invariance
property. We study properties of our measures and compare them to other
candidate measures.

本文提出了新的测量共享信息，独特信息和协同信息的方法，用于分解与第三个随机变量 X 一起的一对随机变量 $（Y，Z）$ 的多信息。我们的措施受到独特信息的操作思想的启发，建议共享信息和独特信息应该仅依赖于 $（X，Y）$ 和 $（X，Z）$ 的对偶边际分布。虽然此不变性属性以前尚未研究，但其他所提出的共享信息措施满足此不变性属性。这种不变性属性并不能唯一地确定我们的新措施，但它意味着我们定义的函数是符合相同不变性属性的任何其他措施的范围。我们研究了我们的措施的性质并将它们与其他候选措施进行了比较。