Fast Interpretable Greedy-Tree Sums (2201.11931v3)

Abstract: Modern machine learning has achieved impressive prediction performance, but often sacrifices interpretability, a critical consideration in high-stakes domains such as medicine. In such settings, practitioners often use highly interpretable decision tree models, but these suffer from inductive bias against additive structure. To overcome this bias, we propose Fast Interpretable Greedy-Tree Sums (FIGS), which generalizes the CART algorithm to simultaneously grow a flexible number of trees in summation. By combining logical rules with addition, FIGS is able to adapt to additive structure while remaining highly interpretable. Extensive experiments on real-world datasets show that FIGS achieves state-of-the-art prediction performance. To demonstrate the usefulness of FIGS in high-stakes domains, we adapt FIGS to learn clinical decision instruments (CDIs), which are tools for guiding clinical decision-making. Specifically, we introduce a variant of FIGS known as G-FIGS that accounts for the heterogeneity in medical data. G-FIGS derives CDIs that reflect domain knowledge and enjoy improved specificity (by up to 20% over CART) without sacrificing sensitivity or interpretability. To provide further insight into FIGS, we prove that FIGS learns components of additive models, a property we refer to as disentanglement. Further, we show (under oracle conditions) that unconstrained tree-sum models leverage disentanglement to generalize more efficiently than single decision tree models when fitted to additive regression functions. Finally, to avoid overfitting with an unconstrained number of splits, we develop Bagging-FIGS, an ensemble version of FIGS that borrows the variance reduction techniques of random forests. Bagging-FIGS enjoys competitive performance with random forests and XGBoost on real-world datasets.

• The paper introduces FIGS, which extends traditional decision trees by summing multiple trees to mitigate bias against additive structures.
• It employs an iterative split-selection process that maximizes impurity reduction while preserving model transparency.
• Empirical results reveal that FIGS can enhance specificity by up to 20% over CART, showing promise for clinical decision-making.

Fast Interpretable Greedy-Tree Sums

The paper presents Fast Interpretable Greedy-Tree Sums (FIGS), an innovative approach that extends decision tree methodologies by addressing the intrinsic inductive bias against additive structures found in traditional models such as CART. This bias often limits the predictive accuracy of decision trees, notably in settings where interpretability and transparency are crucial, such as medical applications.

Methodology

FIGS builds on the decision tree framework by enabling the simultaneous growth of multiple trees, which are then summed together. This flexibility allows the model to capture additive relationships within data while maintaining high interpretability. The algorithm iteratively selects splits that maximize impurity reduction, considering potential splits across all existing trees and introducing new trees as needed.

The paper also introduces a variant called Group Probability-Weighted Tree Sums (G-FIGS), which adapts FIGS for datasets characterized by heterogeneity, such as medical records from diverse patient groups. G-FIGS incorporates domain-specific knowledge through learned decision rules, resulting in better specificity without compromising sensitivity.

Experimental Results

Empirical evaluation across various real-world datasets demonstrates that FIGS achieves state-of-the-art prediction performance compared to existing interpretable models. Notably, in the context of clinical decision instruments (CDIs), FIGS enhances specificity by up to 20% over CART, leveraging its ability to represent additive structures more efficiently.

Theoretical Insights

The authors provide theoretical validation of FIGS's ability to disentangle additive components in generative models, underpinning its robustness in capturing the inherent structure without the redundancy of multiple trees repeating similar splits. This disentanglement allows FIGS to achieve more efficient generalization, evidenced by the theoretical bounds presented which show improved rates compared to single-tree models.

Andrological and Practical Implications

The practical implications for FIGS are significant, particularly in high-stakes areas such as healthcare, where decision-making transparency is essential. The algorithm's interpretability and ease of use facilitate its integration into clinical workflows, providing actionable insights and assisting healthcare professionals in patient assessments.

Moreover, the introduction of Bagging-FIGS, an ensemble version of FIGS, aligns its predictive capability with advanced models like random forests or XGBoost, indicating its applicability in a broader range of machine learning tasks beyond those necessitating pure interpretability.

Future Directions

Future research may explore extending FIGS through global optimization techniques or regularization strategies to refine model selection and prevent overfitting in highly complex datasets. Additionally, expanded applications in domains requiring interpretable yet high-performing models, such as finance and legal systems, present further avenues for exploration.

Overall, the paper offers a compelling contribution to the development of interpretable machine learning models, emphasizing the balance between transparent decision making and robust predictive performance.