Rule set learning has recently been frequently revisited because of its
interpretability. Existing methods have several shortcomings though. First,
most existing methods impose orders among rules, either explicitly or
implicitly, which makes the models less comprehensible. Second, due to the
difficulty of handling conflicts caused by overlaps (i.e., instances covered by
multiple rules), existing methods often do not consider probabilistic rules.
Third, learning classification rules for multi-class target is understudied, as
most existing methods focus on binary classification or multi-class
classification via the ``one-versus-rest" approach.
To address these shortcomings, we propose TURS, for Truly Unordered Rule
Sets. To resolve conflicts caused by overlapping rules, we propose a novel
model that exploits the probabilistic properties of our rule sets, with the
intuition of only allowing rules to overlap if they have similar probabilistic
outputs. We next formalize the problem of learning a TURS model based on the
MDL principle and develop a carefully designed heuristic algorithm. We
benchmark against a wide range of rule-based methods and demonstrate that our
method learns rule sets that have lower model complexity and highly competitive
predictive performance. In addition, we empirically show that rules in our
model are empirically ``independent" and hence truly unordered.

我们提出了 TURS，也就是真正无序规则集，来解决现有方法中的一些缺点，并展示了这种方法在规则集学习方面的竞争性预测性能和较低的模型复杂度。

概率无序规则集

Probabilistic Truly Unordered Rule Sets

Rule set learning has long been studied and has recently been frequently
revisited due to the need for interpretable models. Still, existing methods
have several shortcomings: 1) most recent methods require a binary feature
matrix as input, while learning rules directly from numeric variables is
understudied; 2) existing methods impose orders among rules, either explicitly
or implicitly, which harms interpretability; and 3) currently no method exists
for learning probabilistic rule sets for multi-class target variables (there is
only one for probabilistic rule lists).
We propose TURS, for Truly Unordered Rule Sets, which addresses these
shortcomings. We first formalize the problem of learning truly unordered rule
sets. To resolve conflicts caused by overlapping rules, i.e., instances covered
by multiple rules, we propose a novel approach that exploits the probabilistic
properties of our rule sets. We next develop a two-phase heuristic algorithm
that learns rule sets by carefully growing rules. An important innovation is
that we use a surrogate score to take the global potential of the rule set into
account when learning a local rule.
Finally, we empirically demonstrate that, compared to non-probabilistic and
(explicitly or implicitly) ordered state-of-the-art methods, our method learns
rule sets that not only have better interpretability but also better predictive
performance.

本研究提出了 TURS 作为解决现有方法缺陷的方法，TURS 通过利用规则集的概率特性和开发两阶段启发式算法来学习无序规则集，并在实验中证明 TURS 相对于现有方法在解释性和预测性能方面均具有优势。