This paper introduces the centroid decision forest (CDF), a novel ensemble learning framework that redefines the splitting strategy and tree building in the ordinary decision trees for high-dimensional classification. The splitting approach in CDF differs from the traditional decision trees in theat the class separability score (CSS) determines the selection of the most discriminative features at each node to construct centroids of the partitions (daughter nodes). The splitting criterion uses the Euclidean distance measurements from each class centroid to achieve a splitting mechanism that is more flexible and robust. Centroids are constructed by computing the mean feature values of the selected features for each class, ensuring a class-representative division of the feature space. This centroid-driven approach enables CDF to capture complex class structures while maintaining interpretability and scalability. To evaluate CDF, 23 high-dimensional datasets are used to assess its performance against different state-of-the-art classifiers through classification accuracy and Cohen's kappa statistic. The experimental results show that CDF outperforms the conventional methods establishing its effectiveness and flexibility for high-dimensional classification problems.

There are many approaches for training decision trees. This work introduces a novel gradient-based method for constructing decision trees that optimize arbitrary differentiable loss functions, overcoming the limitations of heuristic splitting rules. Unlike traditional approaches that rely on heuristic splitting rules, the proposed method refines predictions using the first and second derivatives of the loss function, enabling the optimization of complex tasks such as classification, regression, and survival analysis. We demonstrate the method's applicability to classification, regression, and survival analysis tasks, including those with censored data. Numerical experiments on both real and synthetic datasets compare the proposed method with traditional decision tree algorithms, such as CART, Extremely Randomized Trees, and SurvTree. The implementation of the method is publicly available, providing a practical tool for researchers and practitioners. This work advances the field of decision tree-based modeling, offering a more flexible and accurate approach for handling structured data and complex tasks. By leveraging gradient-based optimization, the proposed method bridges the gap between traditional decision trees and modern machine learning techniques, paving the way for further innovations in interpretable and high-performing models.

Predicting microporosity and permeability in clastic reservoirs is a challenge in reservoir quality assessment, especially in formations where direct measurements are difficult or expensive. These reservoir properties are fundamental in determining a reser voir's capacity for fluid storage and transmission, yet conventional methods for evaluating them, such as Mercury Injection Capillary Pressure (MICP) and Scanning Electron Microscopy (SEM), are resource - intensive. The aim of this study is to develop a cost - effective machine learning model to predict complex reservoir properties using readily available field data and basic laboratory analyses. A Random Forest classifier was employed, utilizing key geological parameters such as porosity, grain size distri bution, and spectral gamma - ray (SGR) measurements. An uncertainty analysis was applied to account for natural variability, expanding the dataset, and enhancing the model's robustness. The model achieved a high level of accuracy in predicting microporosity (93%) and permeability levels (88%). By using easily obtainable data, this model reduces the reliance on expensive laboratory methods, making it a valuable tool for early - stage exploration, especially in remote or offshore environments. The integration of machine learning with uncertainty analysis provides a reliable and cost - effective approach for evaluating key reservoir properties in siliciclastic formations. This model offers a practical solution to improve reservoir quality assessments, enabling more i nformed decision - making and optimizing exploration efforts.

The range of potential applications of acoustic analysis is wide. Classification of sounds, in particular, is a typical machine learning task that received a lot of attention in recent years. The most common approaches to sound classification are sub-symbolic, typically based on neural networks, and result in black-box models with high performances but very low transparency. In this work, we consider several audio tasks, namely, age and gender recognition, emotion classification, and respiratory disease diagnosis, and we approach them with a symbolic technique, that is, (modal) decision tree learning. We prove that such tasks can be solved using the same symbolic pipeline, that allows to extract simple rules with very high accuracy and low complexity. In principle, all such tasks could be associated to an autonomous conversation system, which could be useful in different contexts, such as an automatic reservation agent for an hospital or a clinic.

Decision-making processes in healthcare can be highly complex and challenging. Machine Learning tools offer significant potential to assist in these processes. However, many current methodologies rely on complex models that are not easily interpretable by experts. This underscores the need to develop interpretable models that can provide meaningful support in clinical decision-making. When approaching such tasks, humans typically compare the situation at hand to a few key examples and representative cases imprinted in their memory. Using an approach which selects such exemplary cases and grounds its predictions on them could contribute to obtaining high-performing interpretable solutions to such problems. To this end, we evaluate PivotTree, an interpretable prototype selection model, on an oral lesion detection problem, specifically trying to detect the presence of neoplastic, aphthous and traumatic ulcerated lesions from oral cavity images. We demonstrate the efficacy of using such method in terms of performance and offer a qualitative and quantitative comparison between exemplary cases and ground-truth prototypes selected by experts.

Alzheimer's disease and related dementias (AD/ADRD) represent a growing healthcare crisis affecting over 6 million Americans. While genetic factors play a crucial role, emerging research reveals that social determinants of health (SDOH) significantly influence both the risk and progression of cognitive functioning, such as cognitive scores and cognitive decline. This report examines how these social, environmental, and structural factors impact cognitive health trajectories, with a particular focus on Hispanic populations, who face disproportionate risk for AD/ADRD. Using data from the Mexican Health and Aging Study (MHAS) and its cognitive assessment sub study (Mex-Cog), we employed ensemble of regression trees models to predict 4-year and 9-year cognitive scores and cognitive decline based on SDOH. This approach identified key predictive SDOH factors to inform potential multilevel interventions to address cognitive health disparities in this population. Introduction Alzheimer's disease and related dementias (AD/ADRD) pose an escalating medical and public health challenge, currently affecting over 6 million Americans.

Decision trees are a crucial class of models offering robust predictive performance and inherent interpretability across various domains, including healthcare, finance, and logistics. However, current tree induction methods often face limitations such as suboptimal solutions from greedy methods or prohibitive computational costs and limited applicability of exact optimization approaches. To address these challenges, we propose an evolutionary optimization method for decision tree induction based on genetic programming (GP). Our key innovation is the integration of semantic priors and domain-specific knowledge about the search space into the optimization algorithm. To this end, we introduce $\texttt{LLEGO}$, a framework that incorporates semantic priors into genetic search operators through the use of Large Language Models (LLMs), thereby enhancing search efficiency and targeting regions of the search space that yield decision trees with superior generalization performance. This is operationalized through novel genetic operators that work with structured natural language prompts, effectively utilizing LLMs as conditional generative models and sources of semantic knowledge. Specifically, we introduce $\textit{fitness-guided}$ crossover to exploit high-performing regions, and $\textit{diversity-guided}$ mutation for efficient global exploration of the search space. These operators are controlled by corresponding hyperparameters that enable a more nuanced balance between exploration and exploitation across the search space. Empirically, we demonstrate across various benchmarks that $\texttt{LLEGO}$ evolves superior-performing trees compared to existing tree induction methods, and exhibits significantly more efficient search performance compared to conventional GP approaches.

Orthogonal-split trees perform well, but evidence suggests oblique splits can enhance their performance. This paper explores optimizing high-dimensional $s$-sparse oblique splits from $\{(\vec{w}, \vec{w}^{\top}\boldsymbol{X}_{i}) : i\in \{1,\dots, n\}, \vec{w} \in \mathbb{R}^p, \| \vec{w} \|_{2} = 1, \| \vec{w} \|_{0} \leq s \}$ for growing oblique trees, where $ s $ is a user-defined sparsity parameter. We establish a connection between SID convergence and $s_0$-sparse oblique splits with $s_0\ge 1$, showing that the SID function class expands as $s_0$ increases, enabling the capture of more complex data-generating functions such as the $s_0$-dimensional XOR function. Thus, $s_0$ represents the unknown potential complexity of the underlying data-generating function. Learning these complex functions requires an $s$-sparse oblique tree with $s \geq s_0$ and greater computational resources. This highlights a trade-off between statistical accuracy, governed by the SID function class size depending on $s_0$, and computational cost. In contrast, previous studies have explored the problem of SID convergence using orthogonal splits with $ s_0 = s = 1 $, where runtime was less critical. Additionally, we introduce a practical framework for oblique trees that integrates optimized oblique splits alongside orthogonal splits into random forests. The proposed approach is assessed through simulations and real-data experiments, comparing its performance against various oblique tree models.

Model trees provide an appealing way to perform interpretable machine learning for both classification and regression problems. In contrast to ``classic'' decision trees with constant values in their leaves, model trees can use linear combinations of predictor variables in their leaf nodes to form predictions, which can help achieve higher accuracy and smaller trees. Typical algorithms for learning model trees from training data work in a greedy fashion, growing the tree in a top-down manner by recursively splitting the data into smaller and smaller subsets. Crucially, the selected splits are only locally optimal, potentially rendering the tree overly complex and less accurate than a tree whose structure is globally optimal for the training data. In this paper, we empirically investigate the effect of constructing globally optimal model trees for classification and regression with linear support vector machines at the leaf nodes. To this end, we present mixed-integer linear programming formulations to learn optimal trees, compute such trees for a large collection of benchmark data sets, and compare their performance against greedily grown model trees in terms of interpretability and accuracy. We also compare to classic optimal and greedily grown decision trees, random forests, and support vector machines. Our results show that optimal model trees can achieve competitive accuracy with very small trees. We also investigate the effect on the accuracy of replacing axis-parallel splits with multivariate ones, foregoing interpretability while potentially obtaining greater accuracy.

We develop Clustered Random Forests, a random forests algorithm for clustered data, arising from independent groups that exhibit within-cluster dependence. The leaf-wise predictions for each decision tree making up clustered random forests takes the form of a weighted least squares estimator, which leverage correlations between observations for improved prediction accuracy. Clustered random forests are shown for certain tree splitting criteria to be minimax rate optimal for pointwise conditional mean estimation, while being computationally competitive with standard random forests. Further, we observe that the optimality of a clustered random forest, with regards to how (population level) optimal weights are chosen within this framework i.e. those that minimise mean squared prediction error, vary under covariate distribution shift. In light of this, we advocate weight estimation to be determined by a user-chosen covariate distribution with respect to which optimal prediction or inference is desired. This highlights a key difference in behaviour, between correlated and independent data, with regards to nonparametric conditional mean estimation under covariate shift. We demonstrate our theoretical findings numerically in a number of simulated and real-world settings.