Learning Accurate and Interpretable Decision Rule Sets from Neural Networks

Abstract

This paper proposes a new paradigm for learning a set of independent logical rules in disjunctive normal form as an interpretable model for classification. We consider the problem of learning an interpretable decision rule set as training a neural network in a specific, yet very simple two-layer architecture. Each neuron in the first layer directly maps to an interpretable if-then rule after training, and the output neuron in the second layer directly maps to a disjunction of the first layer rules to form the decision rule set. Our representation of neurons in this first rules layer enables us to encode both the positive and the negative association of features in a decision rule. State-of-the-art neural net training approaches can be leveraged for learning highly accurate classification models. Moreover, we propose a sparsity-based regularization approach to balance between classification accuracy and the simplicity of the derived rules. Our experimental results show that our method can generate more accurate decision rule sets than other state-of-the-art rule-learning algorithms with better accuracy-simplicity trade-offs. Further, when compared with uninterpretable black-box machine learning approaches such as random forests and full-precision deep neural networks, our approach can easily find interpretable decision rule sets that have comparable predictive performance.

Explaining with Greater Support: Weighted Column Sampling Optimization for q-Consistent Summary-Explanations

“…where 𝜎 (•) denotes the Softmax function, 𝑠 denotes the SIS vector (17), 𝑠 ′ is the normalized and scaled SIS with factor 𝑎, and 𝑠 ′ 𝑝 is the 𝑝th element of 𝑠 ′ for feature variable 𝑏 𝑝 . In this step, 𝑚 WCS IPs are created, each by sampling |P ′𝑒 𝑖 | = 𝜌 |P 𝑒 | (rounded, 0 < 𝜌 < 1) feature variables according to the probability Prob 𝑝 (18), and |N 𝑖 | = 𝑛 wcs observations uniformly from the observations set N .…”

“…Note that these varying implementations of branch-and-bound solution procedure only affect the time efficiencies in solving the models, and do not change the solution values. The proposed SIS-based WCS optimization method samples feature variables according to their SIS values' associated Softmax probabilities (18). As an alternative for comparison, the SIS-based feature sampling approach in WCS can be replaced with a uniform sampling approach, called random column sampling (RCS), which associates equal sampling probabilities for each feature variable.…”

“…To achieve better transparency, traditionally, global explanation techniques have been used to extract approximate interpretable models from black-box ML models to mimic their decision logic. For example, classification rules can be extracted from neural networks [1,18], and decision trees can be extracted from tree ensembles [11,16]. However, each of these traditional global explanation methods is usually dedicated to a certain type of models, such as neural networks and tree ensembles, and thus they are not model-agnostic.…”

Horn rule discovery with batched caching and rule identifier for proficient compressor of knowledge data

“…The optimization techniques in AMIE speed up the rule mining procedure by one order but heavily sacrifice the expressiveness of Horn rules. Neural networks are also adopted for learning logic rules in some recent work 34 …”

“…Neural networks are also adopted for learning logic rules in some recent work. 34 Association patterns are less expressive compared to Horn rules. For example, the patterns induced from LLC can be expressed as the following Horn rules:…”