Decision trees are powerful machine learning algorithms, widely used in fields such as economics and medicine for their simplicity and interpretability. However, decision trees such as CART are prone to overfitting, especially when grown deep or the sample size is small. Conventional methods to reduce overfitting include pre-pruning and post-pruning, which constrain the growth of uninformative branches. In this paper, we propose a complementary approach by introducing a covariance-driven splitting criterion for regression trees (CovRT). This method is more robust to overfitting than the empirical risk minimization criterion used in CART, as it produces more balanced and stable splits and more effectively identifies covariates with true signals. We establish an oracle inequality of CovRT and prove that its predictive accuracy is comparable to that of CART in high-dimensional settings. We find that CovRT achieves superior prediction accuracy compared to CART in both simulations and real-world tasks.

We study U.S. Treasury yield curve forecasting under distributional uncertainty and recast forecasting as an operations research and managerial decision problem. Rather than minimizing average forecast error, the forecaster selects a decision rule that minimizes worst case expected loss over an ambiguity set of forecast error distributions. To this end, we propose a distributionally robust ensemble forecasting framework that integrates parametric factor models with high dimensional nonparametric machine learning models through adaptive forecast combinations. The framework consists of three machine learning components. First, a rolling window Factor Augmented Dynamic Nelson Siegel model captures level, slope, and curvature dynamics using principal components extracted from economic indicators. Second, Random Forest models capture nonlinear interactions among macro financial drivers and lagged Treasury yields. Third, distributionally robust forecast combination schemes aggregate heterogeneous forecasts under moment uncertainty, penalizing downside tail risk via expected shortfall and stabilizing second moment estimation through ridge regularized covariance matrices. The severity of the worst case criterion is adjustable, allowing the forecaster to regulate the trade off between robustness and statistical efficiency. Using monthly data, we evaluate out of sample forecasts across maturities and horizons from one to twelve months ahead. Adaptive combinations deliver superior performance at short horizons, while Random Forest forecasts dominate at longer horizons. Extensions to global sovereign bond yields confirm the stability and generalizability of the proposed framework.

AB S TRACT This study evaluates the performance of various classifiers in three distinct models: r esponse, r isk, and r esponse - r isk, concerning credit card mail campaigns and default prediction. In the r esponse model, the Extra Trees classifier demonstrates the highest recall level (79.1%), emphasizing its effectiveness in identifying potential responders to targeted credit card offers. Conversely, in the r isk model, the Random Forest classifier exhibits remarkable specificity of 84.1%, crucial for identifying customers least likely to default. Furthermore, in the multi - class r esponse - r isk model, the Random Forest classifier achieve s the highest accuracy (83.2%), indicating its efficacy in discerning both potential responders to credit card mail campaign and low - risk credit card users . In this study, we optimized various performance metrics to solve a specific credit risk and mail responsiveness business problem.

This paper develops a practical framework for using observational data to audit the consumer surplus effects of AI-driven decisions, specifically in targeted pricing and algorithmic lending. Traditional approaches first estimate demand functions and then integrate to compute consumer surplus, but these methods can be challenging to implement in practice due to model misspecification in parametric demand forms and the large data requirements and slow convergence of flexible nonparametric or machine learning approaches. Instead, we exploit the randomness inherent in modern algorithmic pricing, arising from the need to balance exploration and exploitation, and introduce an estimator that avoids explicit estimation and numerical integration of the demand function. Each observed purchase outcome at a randomized price is an unbiased estimate of demand and by carefully reweighting purchase outcomes using novel cumulative propensity weights (CPW), we are able to reconstruct the integral. Building on this idea, we introduce a doubly robust variant named the augmented cumulative propensity weighting (ACPW) estimator that only requires one of either the demand model or the historical pricing policy distribution to be correctly specified. Furthermore, this approach facilitates the use of flexible machine learning methods for estimating consumer surplus, since it achieves fast convergence rates by incorporating an estimate of demand, even when the machine learning estimate has slower convergence rates. Neither of these estimators is a standard application of off-policy evaluation techniques as the target estimand, consumer surplus, is unobserved. To address fairness, we extend this framework to an inequality-aware surplus measure, allowing regulators and firms to quantify the profit-equity trade-off. Finally, we validate our methods through comprehensive numerical studies.

This study proposes an end-to-end algorithm for policy learning in causal inference. We observe data consisting of covariates, treatment assignments, and outcomes, where only the outcome corresponding to the assigned treatment is observed. The goal of policy learning is to train a policy from the observed data, where a policy is a function that recommends an optimal treatment for each individual, to maximize the policy value. In this study, we first show that maximizing the policy value is equivalent to minimizing the mean squared error for the conditional average treatment effect (CATE) under $\{-1, 1\}$ restricted regression models. Based on this finding, we modify the causal forest, an end-to-end CATE estimation algorithm, for policy learning. We refer to our algorithm as the causal-policy forest. Our algorithm has three advantages. First, it is a simple modification of an existing, widely used CATE estimation method, therefore, it helps bridge the gap between policy learning and CATE estimation in practice. Second, while existing studies typically estimate nuisance parameters for policy learning as a separate task, our algorithm trains the policy in a more end-to-end manner. Third, as in standard decision trees and random forests, we train the models efficiently, avoiding computational intractability.

We propose a simple generalization of standard and empirically successful decision tree learning algorithms such as ID3, C4.5, and CART. These algorithms, which have been central to machine learning for decades, are greedy in nature: they grow a decision tree by iteratively splitting on the best attribute. Our algorithm, Top-$k$, considers the $k$ best attributes as possible splits instead of just the single best attribute. We demonstrate, theoretically and empirically, the power of this simple generalization. We first prove a greediness hierarchy theorem showing that for every $k\in \mathbb{N}$, Top-$(k+1)$ can be dramatically more powerful than Top-$k$: there are data distributions for which the former achieves accuracy $1-\epsilon$, whereas the latter only achieves accuracy $\frac{1}{2}+\epsilon$. We then show, through extensive experiments, that Top-$k$ outperforms the two main approaches to decision tree learning: classic greedy algorithms and more recent ``optimal decision tree'' algorithms. On one hand, Top-$k$ consistently enjoys significant accuracy gains over greedy algorithms across a wide range of benchmarks. On the other hand, Top-$k$ is markedly more scalable than optimal decision tree algorithms and is able to handle dataset and feature set sizes that remain far beyond the reach of these algorithms.

The Landsat program is the longest-running Earth observation program in history, with 50+ years of data acquisition by 8 satellites. The multispectral imagery captured by sensors onboard these satellites is critical for a wide range of scientific fields. Despite the increasing popularity of deep learning and remote sensing, the majority of researchers still use decision trees and random forests for Landsat image analysis due to the prevalence of small labeled datasets and lack of foundation models. In this paper, we introduce SSL4EO-L, the first ever dataset designed for Self-Supervised Learning for Earth Observation for the Landsat family of satellites (including 3 sensors and 2 product levels) and the largest Landsat dataset in history (5M image patches). Additionally, we modernize and re-release the L7 Irish and L8 Biome cloud detection datasets, and introduce the first ML benchmark datasets for Landsats 4-5 TM and Landsat 7 ETM+ SR. Finally, we pre-train the first foundation models for Landsat imagery using SSL4EO-L and evaluate their performance on multiple semantic segmentation tasks. All datasets and model weights are available via the TorchGeo library, making reproducibility and experimentation easy, and enabling scientific advancements in the burgeoning field of remote sensing for a multitude of downstream applications.

Decision trees are a well-established tool in machine learning for classification and regression tasks. In this paper, we introduce a novel non-parametric Bayesian model that uses variational inference to approximate a posterior distribution over the space of stochastic decision trees. We evaluate the model's performance on 18 datasets and demonstrate its competitiveness with other state-of-the-art methods in regression tasks. We also explore its application to causal inference problems. We provide a fully vectorized implementation of our algorithm in PyTorch.

We study the robustness verification problem of tree based models, including random forest (RF) and gradient boosted decision tree (GBDT). Formal robustness verification of decision tree ensembles involves finding the exact minimal adversarial perturbation or a guaranteed lower bound of it. Existing approaches cast this verification problem into a mixed integer linear programming (MILP) problem, which finds the minimal adversarial distortion in exponential time so is impractical for large ensembles. Although this verification problem is NP-complete in general, we give a more precise complexity characterization. We show that there is a simple linear time algorithm for verifying a single tree, and for tree ensembles the verification problem can be cast as a max-clique problem on a multi-partite boxicity graph. For low dimensional problems when boxicity can be viewed as constant, this reformulation leads to a polynomial time algorithm. For general problems, by exploiting the boxicity of the graph, we devise an efficient verification algorithm that can give tight lower bounds on robustness of decision tree ensembles, and allows iterative improvement and any-time termination. On RF/GBDT models trained on a variety of datasets, we significantly outperform the lower bounds obtained by relaxing the MILP formulation into a linear program (LP), and are hundreds times faster than solving MILPs to get the exact minimal adversarial distortion. Our proposed method is capable of giving tight robustness verification bounds on large GBDTs with hundreds of deep trees.

A fundamental task in active learning involves performing a sequence of tests to identify an unknown hypothesis that is drawn from a known distribution. This problem, known as optimal decision tree induction, has been widely studied for decades and the asymptotically best-possible approximation algorithm has been devised for it. We study a generalization where certain test outcomes are noisy, even in the more general case when the noise is persistent, i.e., repeating the test on the scenario gives the same noisy output, disallowing simple repetition as a way to gain confidence. We design new approximation algorithms for both the non-adaptive setting, where the test sequence must be fixed a-priori, and the adaptive setting where the test sequence depends on the outcomes of prior tests. Previous work in the area assumed at most a constant number of noisy outcomes per test and per scenario and provided approximation ratios that were problem dependent (such as the minimum probability of a hypothesis). Our new approximation algorithms provide guarantees that are nearly best-possible and work for the general case of a large number of noisy outcomes per test or per hypothesis where the performance degrades smoothly with this number. Our results adapt and generalize methods used for submodular ranking and stochastic set cover. We evaluate the performance of our algorithms on two natural applications with noise: toxic chemical identification and active learning of linear classifiers. Despite our logarithmic theoretical approximation guarantees, our methods give solutions with cost very close to the information theoretic minimum, demonstrating the effectiveness of our methods.