Neural Information Processing Systems http://nips.cc/

Machine learning models deployed in sensitive areas such as healthcare must be interpretable to ensure accountability and fairness. However, learning such rule lists presents significant challenges. Existing methods based on combinatorial optimization require feature pre-discretization and impose restrictions on rule size. Neuro-symbolic methods use more scalable continuous optimization yet place similar pre-discretization constraints and suffer from unstable optimization. We formulate a continuous relaxation of the rule list learning problem that converges to a strict rule list through temperature annealing. Machine learning models are increasingly used in high-stakes applications such as healthcare (Deo, 2015), credit risk evaluation (Bhatore et al., 2020), and criminal justice (Lakkaraju & Rudin, 2017), where it is vital that each decision is fair and reasonable. Proxy measures such as Shapley values can give the illusion of interpretability, but are highly problematic as they can not faithfully represent a non-additive models decision process (Gosiewska & Biecek, 2019). Instead, Rudin (2019) argues that it is crucial to use inherently interpretable models, to create systems with human supervision in the loop (Kleinberg et al., 2018). For particularly sensitive domains such as stroke prediction or recidivism, so called Rule Lists are a popular choice (Letham et al., 2015) due to their fully transparent decision making. A rule list predicts based on nested "if-then-else" statements and naturally aligns with the human-decision making process. Each rule is active if its conditions are met, e.g. " if Thalassemia = normal Resting bps < 151 ", and carries a respective prediction, i.e. " then P ( Disease) = 10% ".

Tree ensemble methods represent a popular machine learning model, known for their effectiveness in supervised classification and regression tasks. Their performance derives from aggregating predictions of multiple decision trees, which are renowned for their interpretability properties. However, tree ensemble methods do not reliably exhibit interpretable output. Our work aims to extract an optimized list of rules from a trained tree ensemble, providing the user with a condensed, interpretable model that retains most of the predictive power of the full model. Our approach consists of solving a clean and neat set partitioning problem formulated through Integer Programming. The proposed method works with either tabular or time series data, for both classification and regression tasks, and does not require parameter tuning under the most common setting. Through rigorous computational experiments, we offer statistically significant evidence that our method is competitive with other rule extraction methods and effectively handles time series.

Learning interpretable models has become a major focus of machine learning research, given the increasing prominence of machine learning in socially important decision-making. Among interpretable models, rule lists are among the best-known and easily interpretable ones. However, finding optimal rule lists is computationally challenging, and current approaches are impractical for large datasets. We present a novel and scalable approach to learn nearly optimal rule lists from large datasets. Our algorithm uses sampling to efficiently obtain an approximation of the optimal rule list with rigorous guarantees on the quality of the approximation. In particular, our algorithm guarantees to find a rule list with accuracy very close to the optimal rule list when a rule list with high accuracy exists. Our algorithm builds on the VC-dimension of rule lists, for which we prove novel upper and lower bounds. Our experimental evaluation on large datasets shows that our algorithm identifies nearly optimal rule lists with a speed-up up to two orders of magnitude over state-of-the-art exact approaches. Moreover, our algorithm is as fast as, and sometimes faster than, recent heuristic approaches, while reporting higher quality rule lists. In addition, the rules reported by our algorithm are more similar to the rules in the optimal rule list than the rules from heuristic approaches.

Interpretability is often pointed out as a key requirement for trustworthy machine learning. However, learning and releasing models that are inherently interpretable leaks information regarding the underlying training data. As such disclosure may directly conflict with privacy, a precise quantification of the privacy impact of such breach is a fundamental problem. For instance, previous work have shown that the structure of a decision tree can be leveraged to build a probabilistic reconstruction of its training dataset, with the uncertainty of the reconstruction being a relevant metric for the information leak. In this paper, we propose of a novel framework generalizing these probabilistic reconstructions in the sense that it can handle other forms of interpretable models and more generic types of knowledge. In addition, we demonstrate that under realistic assumptions regarding the interpretable models' structure, the uncertainty of the reconstruction can be computed efficiently. Finally, we illustrate the applicability of our approach on both decision trees and rule lists, by comparing the theoretical information leak associated to either exact or heuristic learning algorithms. Our results suggest that optimal interpretable models are often more compact and leak less information regarding their training data than greedily-built ones, for a given accuracy level.

Differentially-private (DP) mechanisms can be embedded into the design of a machine learningalgorithm to protect the resulting model against privacy leakage, although this often comes with asignificant loss of accuracy. In this paper, we aim at improving this trade-off for rule lists modelsby establishing the smooth sensitivity of the Gini impurity and leveraging it to propose a DP greedyrule list algorithm. In particular, our theoretical analysis and experimental results demonstrate thatthe DP rule lists models integrating smooth sensitivity have higher accuracy that those using otherDP frameworks based on global sensitivity.

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.

We present sparse tree-based and list-based density estimation methods for binary/categorical data. Our density estimation models are higher dimensional analogies to variable bin width histograms. In each leaf of the tree (or list), the density is constant, similar to the flat density within the bin of a histogram. Histograms, however, cannot easily be visualized in more than two dimensions, whereas our models can. The accuracy of histograms fades as dimensions increase, whereas our models have priors that help with generalization. Our models are sparse, unlike high-dimensional fixed-bin histograms. We present three generative modeling methods, where the first one allows the user to specify the preferred number of leaves in the tree within a Bayesian prior. The second method allows the user to specify the preferred number of branches within the prior. The third method returns density lists (rather than trees) and allows the user to specify the preferred number of rules and the length of rules within the prior. The new approaches often yield a better balance between sparsity and accuracy of density estimates than other methods for this task. We present an application to crime analysis, where we estimate how unusual each type of modus operandi is for a house break-in.

Tree Ensemble (TE) models (like Gradient Boosted Trees) often provide higher prediction performance compared to single decision trees. However, TE models generally lack transparency and interpretability, as humans have difficulty understanding their decision logic. This paper presents a novel approach to convert a TE trained for a binary classification task, to a rule list (RL) that closely approximates the TE and is interpretable for a human. This RL can effectively explain the model even on the minority class predicted by the model. Experiments on benchmark datasets demonstrate that, (i) predictions from the RL generated by TE2Rules have higher fidelity (with respect to the original TE) compared to state-of-the-art methods, (ii) the run-time of TE2Rules is comparable to that of some other similar baselines and (iii) the run-time of TE2Rules algorithm can be traded off at the cost of a slightly lower fidelity.

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.