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We develop Latent Exploration Score (LES) to mitigate over-exploration in Latent Space Op- timization (LSO), a popular method for solv- ing black-box discrete optimization problems. LSO utilizes continuous optimization within the latent space of a Variational Autoencoder (VAE) and is known to be susceptible to over- exploration, which manifests in unrealistic solu- tions that reduce its practicality. LES leverages the trained decoder’s approximation of the data distribution, and can be employed with any VAE decoder–including pretrained ones–without addi- tional training, architectural changes or access to the training data. Our evaluation across five LSO benchmark tasks and twenty-two VAE mod- els demonstrates that LES always enhances the quality of the solutions while maintaining high objective values, leading to improvements over ex- isting solutions in most cases. We believe that new avenues to LSO will be opened by LES’ ability to identify out of distribution areas, differentiability, and computational tractability. 

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 Classification and Regression Trees (CART) algorithm to simultaneously grow a flexible number of trees in summation. By combining logical rules with addition, FIGS adapts to additive structure while remaining highly interpretable. Experiments on real-world datasets show 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 decision-making. Specifically, we introduce a variant of FIGS known as Group Probability-Weighted Tree Sums (G-FIGS) that accounts for 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. Theoretically, we prove that FIGS learns components of additive models, a property we refer to as disentanglement. Further, we show (under oracle conditions) that tree-sum models leverage disentanglement to generalize more efficiently than single 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 performs competitively with random forests and XGBoost on real-world datasets. 

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. 

Tree-based models such as decision trees and random forests (RF) are a cornerstone of modern machine-learning practice. To mitigate overfitting, trees are typically regularized by a variety of techniques that modify their structure (e.g. pruning). We introduce Hierarchical Shrinkage (HS), a post-hoc algorithm that does not modify the tree structure, and instead regularizes the tree by shrinking the prediction over each node towards the sample means of its ancestors. The amount of shrinkage is controlled by a single regularization parameter and the number of data points in each ancestor. Since HS is a post-hoc method, it is extremely fast, compatible with any tree growing algorithm, and can be used synergistically with other regularization techniques. Extensive experiments over a wide variety of real world datasets show that HS substantially increases the predictive performance of decision trees, even when used in conjunction with other regularization techniques. Moreover, we find that applying HS to each tree in an RF often improves accuracy, as well as its interpretability by simplifying and stabilizing its decision boundaries and SHAP values. We further explain the success of HS in improving prediction performance by showing its equivalence to ridge regression on a (supervised) basis constructed of decision stumps associated with the internal nodes of a tree. All code and models are released in a full fledged package available on Github.