While random forests are commonly used for regression problems, existing methods often lack adaptability in complex situations or lose optimality under simple, smooth scenarios. In this study, we introduce the adaptive split balancing forest (ASBF), capable of learning tree representations from data while simultaneously achieving minimax optimality under the Lipschitz class. To exploit higher-order smoothness levels, we further propose a localized version that attains the minimax rate under the H\"older class $\mathcal{H}^{q,\beta}$ for any $q\in\mathbb{N}$ and $\beta\in(0,1]$. Rather than relying on the widely-used random feature selection, we consider a balanced modification to existing approaches. Our results indicate that an over-reliance on auxiliary randomness may compromise the approximation power of tree models, leading to suboptimal results. Conversely, a less random, more balanced approach demonstrates optimality. Additionally, we establish uniform upper bounds and explore the application of random forests in average treatment effect estimation problems. Through simulation studies and real-data applications, we demonstrate the superior empirical performance of the proposed methods over existing random forests.

We propose a new nonparametric learning method based on multivariate dyadic regression trees (MDRTs). Unlike traditional dyadic decision trees (DDTs) or classification and regression trees (CARTs), MDRTs are constructed using penalized empirical risk minimization with a novel sparsity-inducing penalty. Theoretically, we show that MDRTs can simultaneously adapt to the unknown sparsity and smoothness of the true regression functions, and achieve the nearly optimal rates of convergence (in a minimax sense) for the class of (\alpha, C) -smooth functions. Empirically, MDRTs can simultaneously conduct function estimation and variable selection in high dimensions. To make MDRTs applicable for large-scale learning problems, we propose a greedy heuristics.

In many applications, it is of interest to model Y given another random vector X as input. We refer to the problem of estimating the graph G(x) of Y conditioned on X x as graph-valued regression''. In this paper, we propose a semiparametric method for estimating G(x) that builds a tree on the X space just as in CART (classification and regression trees), but at each leaf of the tree estimates a graph. We call the method Graph-optimized CART'', or Go-CART. We study the theoretical properties of Go-CART using dyadic partitioning trees, establishing oracle inequalities on risk minimization and tree partition consistency.

We combine random forest (RF) and conditional random field (CRF) into a new computational framework, called random forest random field (RF) 2. Inference of (RF) 2 uses the Swendsen-Wang cut algorithm, characterized by Metropolis-Hastings jumps. A jump from one state to another depends on the ratio of the proposal distributions, and on the ratio of the posterior distributions of the two states. Prior work typically resorts to a parametric estimation of these four distributions, and then computes their ratio. Our key idea is to instead directly estimate these ratios using RF. RF collects in leaf nodes of each decision tree the class histograms of training examples.

We present a novel approach to efficiently learn a label tree for large scale classification with many classes. The key contribution of the approach is a technique to simultaneously determine the structure of the tree and learn the classifiers for each node in the tree. This approach also allows fine grained control over the efficiency vs accuracy trade-off in designing a label tree, leading to more balanced trees. Experiments are performed on large scale image classification with 10184 classes and 9 million images. We demonstrate significant improvements in test accuracy and efficiency with less training time and more balanced trees compared to the previous state of the art by Bengio et al.

Decision trees built with data remain in widespread use for nonparametric prediction. Predicting probability distributions is preferred over point predictions when uncertainty plays a prominent role in analysis and decision-making. We study modifying a tree to produce nonparametric predictive distributions. We find the standard method for building trees may not result in good predictive distributions and propose changing the splitting criteria for trees to one based on proper scoring rules. Analysis of both simulated data and several real datasets demonstrates that using these new splitting criteria results in trees with improved predictive properties considering the entire predictive distribution.

Global ambient air pollution, a transboundary challenge, is typically addressed through interventions relying on data from spatially sparse and heterogeneously placed monitoring stations. These stations often encounter temporal data gaps due to issues such as power outages. In response, we have developed a scalable, data-driven, supervised machine learning framework. This model is designed to impute missing temporal and spatial measurements, thereby generating a comprehensive dataset for pollutants including NO$_2$, O$_3$, PM$_{10}$, PM$_{2.5}$, and SO$_2$. The dataset, with a fine granularity of 0.25$^{\circ}$ at hourly intervals and accompanied by prediction intervals for each estimate, caters to a wide range of stakeholders relying on outdoor air pollution data for downstream assessments. This enables more detailed studies. Additionally, the model's performance across various geographical locations is examined, providing insights and recommendations for strategic placement of future monitoring stations to further enhance the model's accuracy.

Gradient Boost Decision Trees (GBDT) is a powerful additive model based on tree ensembles. Its nature makes GBDT a black-box model even though there are multiple explainable artificial intelligence (XAI) models obtaining information by reinterpreting the model globally and locally. Each tree of the ensemble is a transparent model itself but the final outcome is the result of a sum of these trees and it is not easy to clarify. In this paper, a feature contribution method for GBDT is developed. The proposed method takes advantage of the GBDT architecture to calculate the contribution of each feature using the residue of each node. This algorithm allows to calculate the sequence of node decisions given a prediction. Theoretical proofs and multiple experiments have been carried out to demonstrate the performance of our method which is not only a local explicability model for the GBDT algorithm but also a unique option that reflects GBDTs internal behavior. The proposal is aligned to the contribution of characteristics having impact in some artificial intelligence problems such as ethical analysis of Artificial Intelligence (AI) and comply with the new European laws such as the General Data Protection Regulation (GDPR) about the right to explain and nondiscrimination.

This study is based on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset and aims to explore early detection and disease progression in Alzheimer's disease (AD). We employ innovative data preprocessing strategies, including the use of the random forest algorithm to fill missing data and the handling of outliers and invalid data, thereby fully mining and utilizing these limited data resources. Through Spearman correlation coefficient analysis, we identify some features strongly correlated with AD diagnosis. We build and test three machine learning models using these features: random forest, XGBoost, and support vector machine (SVM). Among them, the XGBoost model performs the best in terms of diagnostic performance, achieving an accuracy of 91%. Overall, this study successfully overcomes the challenge of missing data and provides valuable insights into early detection of Alzheimer's disease, demonstrating its unique research value and practical significance.

The use of machine-learning techniques has grown in numerous research areas. Currently, it is also widely used in statistics, including the official statistics for data collection (e.g. satellite imagery, web scraping and text mining, data cleaning, integration and imputation) but also for data analysis. However, the usage of these methods in survey sampling including small area estimation is still very limited. Therefore, we propose a predictor supported by these algorithms which can be used to predict any population or subpopulation characteristics based on cross-sectional and longitudinal data. Machine learning methods have already been shown to be very powerful in identifying and modelling complex and nonlinear relationships between the variables, which means that they have very good properties in case of strong departures from the classic assumptions. Therefore, we analyse the performance of our proposal under a different set-up, in our opinion of greater importance in real-life surveys. We study only small departures from the assumed model, to show that our proposal is a good alternative in this case as well, even in comparison with optimal methods under the model. What is more, we propose the method of the accuracy estimation of machine learning predictors, giving the possibility of the accuracy comparison with classic methods, where the accuracy is measured as in survey sampling practice. The solution of this problem is indicated in the literature as one of the key issues in integration of these approaches. The simulation studies are based on a real, longitudinal dataset, freely available from the Polish Local Data Bank, where the prediction problem of subpopulation characteristics in the last period, with "borrowing strength" from other subpopulations and time periods, is considered.