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.

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 firstlayer 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.

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While neural networks have been achieving increasingly significant excitement in solving classification tasks such as natural language processing, their lack of interpretability becomes a great challenge for neural networks to be deployed in certain high-stakes human-centered applications. To address this issue, we propose a new approach for generating interpretable predictions by inferring a simple three-layer neural network with threshold activations, so that it can benefit from effective neural network training algorithms and at the same time, produce human-understandable explanations for the results. In particular, the hidden layer neurons in the proposed model are trained with floating point weights and binary output activations. The output neuron is also trainable as a threshold logic function that implements a disjunctive operation, forming the logical-OR of the first-level threshold logic functions. This neural network can be trained using state-of-the-art training methods to achieve high prediction accuracy. An important feature of the proposed architecture is that only a simple greedy algorithm is required to provide an explanation with the prediction that is human-understandable. In comparison with other explainable decision models, our proposed approach achieves more accurate predictions on a broad set of tabular data classification datasets.

This paper extends recent work on decision rule learning from neural networks for tabular data classification. We propose alternative formulations to trainable Boolean logic operators as neurons with continuous weights, including trainable NAND neurons. These alternative formulations provide uniform treatments to different trainable logic neurons so that they can be uniformly trained, which enables, for example, the direct application of existing sparsity-promoting neural net training techniques like reweighted L1 regularization to derive sparse networks that translate to simpler rules. In addition, we present an alternative network architecture based on trainable NAND neurons by applying De Morgan’s law to realize a NAND-NAND network instead of an AND-OR network, both of which can be readily mapped to decision rule sets. Our experimental results show that these alternative formulations can also generate accurate decision rule sets that achieve state-of-the-art performance in terms of accuracy in tabular learning applications.