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1. Connecting Interpretability and Robustness in Decision Trees through Separation

   Moshkovitz, Michal; Yang, Yao-Yuan; Chaudhuri, Kamalika (July 2021, Proceedings of Machine Learning Research)

   null (Ed.)

   Recent research has recognized interpretability and robustness as essential properties of trustworthy classification. Curiously, a connection between robustness and interpretability was empirically observed, but the theoretical reasoning behind it remained elusive. In this paper, we rigorously investigate this connection. Specifically, we focus on interpretation using decision trees and robustness to l1-perturbation. Previous works defined the notion of r-separation as a sufficient condition for robustness. We prove upper and lower bounds on the tree size in case the data is r-separated. We then show that a tighter bound on the size is possible when the data is linearly separated. We provide the first algorithm with provable guarantees both on robustness, interpretability, and accuracy in the context of decision trees. Experiments confirm that our algorithm yields classifiers that are both interpretable and robust and have high accuracy. 

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2. Explainable models via compression of tree ensembles

   https://doi.org/10.1007/s10994-023-06463-1  

   Yan, Siwen; Natarajan, Sriraam; Joshi, Saket; Khardon, Roni; Tadepalli, Prasad (March 2024, Machine Learning)

   Ensemble models (bagging and gradient-boosting) of relational decision trees have proved to be some of the most effective learning methods in the area of probabilistic logic models (PLMs). While effective, they lose one of the most important benefits of PLMs—interpretability. In this paper we consider the problem of compressing a large set of learned trees into a single explainable model. To this effect, we propose CoTE—Compression of Tree Ensembles—that produces a single small decision list as a compressed representation. CoTE first converts the trees to decision lists and then performs the combination and compression with the aid of the original training set. An experimental evaluation demonstrates the effectiveness of CoTE in several benchmark relational data sets. 

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3. Tree Space Prototypes: Another Look at Making Tree Ensembles Interpretable

   https://doi.org/3412815.3416893  

   Tan, Sarah; Soloviev, Matvey; Hooker, Giles; Wells, Martin (October 2020, Foundations of data science)

   null (Ed.)

   Ensembles of decision trees perform well on many problems, but are not interpretable. In contrast to existing approaches in interpretability that focus on explaining relationships between features and predictions, we propose an alternative approach to interpret tree ensemble classifiers by surfacing representative points for each class -- prototypes. We introduce a new distance for Gradient Boosted Tree models, and propose new, adaptive prototype selection methods with theoretical guarantees, with the flexibility to choose a different number of prototypes in each class. We demonstrate our methods on random forests and gradient boosted trees, showing that the prototypes can perform as well as or even better than the original tree ensemble when used as a nearest-prototype classifier. In a user study, humans were better at predicting the output of a tree ensemble classifier when using prototypes than when using Shapley values, a popular feature attribution method. Hence, prototypes present a viable alternative to feature-based explanations for tree ensembles. 

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4. Bolt: Fast Inference for Random Forests

   https://doi.org/10.1145/3528535.3531519  

   Romero, Eduardo; Stewart, Christopher; Li, Angela; Hale, Kyle; Morris, Nathaniel (October 2022, Proceedings of the 23rd ACM/IFIP International Middleware Conference)

   Random forests use ensembles of decision trees to boost accuracy for machine learning tasks. However, large ensembles slow down inference on platforms that process each tree in an ensemble individually. We present Bolt, a platform that restructures whole random forests, not just individual trees, to speed up inference. Conceptually, Bolt maps every path in each tree to a lookup table which, if cache were large enough, would allow inference with just one memory access. When the size of the lookup table exceeds cache capacity, Bolt employs a novel combination of lossless compression, parameter selection, and bloom filters to shrink the table while preserving fast inference. We compared inference speed in Bolt to three state-of-the-art platforms: Python Scikit-Learn, Ranger, and Forest Packing. We evaluated these platforms using datasets with vision, natural language processing and categorical applications. We observed that on ensembles of shallow decision trees Bolt can run 2-14X faster than competing platforms and that Bolt's speedups persist as the number of decision trees in an ensemble increases. 

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5. Decision tree heuristics can fail, even in the smoothed setting

   Blanc, G.; Lange, J.; Qiao, M.; Tan, L. (January 2021, APPROX/RANDOM 2021)

   Greedy decision tree learning heuristics are mainstays of machine learning practice, but theoretical justification for their empirical success remains elusive. In fact, it has long been known that there are simple target functions for which they fail badly (Kearns and Mansour, STOC 1996). Recent work of Brutzkus, Daniely, and Malach (COLT 2020) considered the smoothed analysis model as a possible avenue towards resolving this disconnect. Within the smoothed setting and for targets f that are k-juntas, they showed that these heuristics successfully learn f with depth-k decision tree hypotheses. They conjectured that the same guarantee holds more generally for targets that are depth-k decision trees. We provide a counterexample to this conjecture: we construct targets that are depth-k decision trees and show that even in the smoothed setting, these heuristics build trees of depth 2^{Ω(k)} before achieving high accuracy. We also show that the guarantees of Brutzkus et al. cannot extend to the agnostic setting: there are targets that are very close to k-juntas, for which these heuristics build trees of depth 2^{Ω(k)} before achieving high accuracy. 

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