Gradient Boosted Decision Tree (GBDT) is a widely-used machine learning algorithm that has been shown to achieve state-of-the-art results on many standard data science problems. We are interested in its application to multioutput problems when the output is highly multidimensional. Although there are highly effective GBDT implementations, their scalability to such problems is still unsatisfactory. In this paper, we propose novel methods aiming to accelerate the training process of GBDT in the multioutput scenario. The idea behind these methods lies in the approximate computation of a scoring function used to find the best split of decision trees.

The need to learn from positive and unlabeled data, or PU learning, arises in many applications and has attracted increasing interest. While random forests are known to perform well on many tasks with positive and negative data, recent PU algorithms are generally based on deep neural networks, and the potential of tree-based PU learning is under-explored. In this paper, we propose new random forest algorithms for PU-learning. Key to our approach is a new interpretation of decision tree algorithms for positive and negative data as \emph{recursive greedy risk minimization algorithms}. We extend this perspective to the PU setting to develop new decision tree learning algorithms that directly minimizes PU-data based estimators for the expected risk.

Numerous studies have compared machine learning (ML) and discrete choice models (DCMs) in predicting travel demand. However, these studies often lack generalizability as they compare models deterministically without considering contextual variations. To address this limitation, our study develops an empirical benchmark by designing a tournament model, thus efficiently summarizing a large number of experiments, quantifying the randomness in model comparisons, and using formal statistical tests to differentiate between the model and contextual effects. This benchmark study compares two large-scale data sources: a database compiled from literature review summarizing 136 experiments from 35 studies, and our own experiment data, encompassing a total of 6,970 experiments from 105 models and 12 model families. This benchmark study yields two key findings. Firstly, many ML models, particularly the ensemble methods and deep learning, statistically outperform the DCM family (i.e., multinomial, nested, and mixed logit models). However, this study also highlights the crucial role of the contextual factors (i.e., data sources, inputs and choice categories), which can explain models' predictive performance more effectively than the differences in model types alone. Model performance varies significantly with data sources, improving with larger sample sizes and lower dimensional alternative sets. After controlling all the model and contextual factors, significant randomness still remains, implying inherent uncertainty in such model comparisons. Overall, we suggest that future researchers shift more focus from context-specific model comparisons towards examining model transferability across contexts and characterizing the inherent uncertainty in ML, thus creating more robust and generalizable next-generation travel demand models.

Variable Importance (VI) has traditionally been cast as the process of estimating each variables contribution to a predictive model's overall performance. Recent research has sought to address this concern via analysis of Rashomon sets - sets of alternative model instances that exhibit equivalent predictive performance to some reference model, but which take different functional forms. Measures such as Model Class Reliance (MCR) have been proposed, that are computed against Rashomon sets, in order to ascertain how much a variable must be relied on to make robust predictions, or whether alternatives exist. If MCR range is tight, we have no choice but to use a variable; if range is high then there exists competing, perhaps fairer models, that provide alternative explanations of the phenomena being examined. Applications are wide, from enabling construction of fairer' models in areas such as recidivism, health analytics and ethical marketing.

Bayesian Additive Regression Trees [BART, Chipman et al., 2010] have gained significant popularity due to their remarkable predictive performance and ability to quantify uncertainty. However, standard decision tree models rely on recursive data splits at each decision node, using deterministic decision rules based on a single univariate feature. This approach limits their ability to effectively capture complex decision boundaries, particularly in scenarios involving multiple features, such as spatial domains, or when transitions are either sharp or smoothly varying. In this paper, we introduce a novel probabilistic additive decision tree model that employs a soft split rule. This method enables highly flexible splits that leverage both univariate and multivariate features, while also respecting the geometric properties of the feature domain. Notably, the probabilistic split rule adapts dynamically across decision nodes, allowing the model to account for varying levels of smoothness in the regression function. We demonstrate the utility of the proposed model through comparisons with existing tree-based models on synthetic datasets and a New York City education dataset.

Abstract: Background: Understanding cardiovascular artery disease risk factors, the leading global cause of mortality, is crucial for influencing its etiology, prevalence, and treatment. This study aims to evaluate prognostic markers for coronary artery disease in Mashhad using Naive Bayes, REP Tree, J48, CART, and CHAID algorithms. Methods: Using data from the 2009 MASHAD STUDY, prognostic factors for coronary artery disease were determined with Naive Bayes, REP Tree, J48, CART, CHAID, and Random Forest algorithms using R 3.5.3 and WEKA 3.9.4. Model efficiency was compared by sensitivity, specificity, and accuracy. Cases were patients with coronary artery disease; each had three controls (totally 940). Results: Prognostic factors for coronary artery disease in Mashhad residents varied by algorithm. CHAID identified age, myocardial infarction history, and hypertension. CART included depression score and physical activity. REP added education level and anxiety score. NB included diabetes and family history. J48 highlighted father's heart disease and weight loss. CHAID had the highest accuracy (0.80). Conclusion: Key prognostic factors for coronary artery disease in CART and CHAID models include age, myocardial infarction history, hypertension, depression score, physical activity, and BMI. NB, REP Tree, and J48 identified numerous factors. CHAID had the highest accuracy, sensitivity, and specificity. CART offers simpler interpretation, aiding physician and paramedic model selection based on specific. Keywords: RF, Na\"ive Bayes, REP, J48 algorithms, Coronary Artery Disease (CAD).

Nowadays, more and more images are available. Annotation and retrieval of the images pose classification problems, where each class is defined as the group of database images labelled with a common semantic label. Various systems have been proposed for content-based retrieval, as well as for image classification and indexing. In this paper, a hierarchical classification framework has been proposed for bridging the semantic gap effectively and achieving multi-category image classification. A well known pre-processing and post-processing method was used and applied to three problems; image segmentation, object identification and image classification. The method was applied to classify single object images from Amazon and Google datasets. The classification was tested for four different classifiers; BayesNetwork (BN), Random Forest (RF), Bagging and Vote. The estimated classification accuracies ranged from 20% to 99% (using 10-fold cross validation). The Bagging classifier presents the best performance, followed by the Random Forest classifier.

Computing an optimal classification tree that provably maximizes training performance within a given size limit, is NP-hard, and in practice, most state-of-the-art methods do not scale beyond computing optimal trees of depth three. Therefore, most methods rely on a coarse binarization of continuous features to maintain scalability. We propose a novel algorithm that optimizes trees directly on the continuous feature data using dynamic programming with branch-and-bound. We develop new pruning techniques that eliminate many sub-optimal splits in the search when similar to previously computed splits and we provide an efficient subroutine for computing optimal depth-two trees. Our experiments demonstrate that these techniques improve runtime by one or more orders of magnitude over state-of-the-art optimal methods and improve test accuracy by 5% over greedy heuristics.

This paper introduces a novel tree-based model, Learning Hyperplane Tree (LHT), which outperforms state-of-the-art (SOTA) tree models for classification tasks on several public datasets. The structure of LHT is simple and efficient: it partitions the data using several hyperplanes to progressively distinguish between target and non-target class samples. Although the separation is not perfect at each stage, LHT effectively improves the distinction through successive partitions. During testing, a sample is classified by evaluating the hyperplanes defined in the branching blocks and traversing down the tree until it reaches the corresponding leaf block. The class of the test sample is then determined using the piecewise linear membership function defined in the leaf blocks, which is derived through least-squares fitting and fuzzy logic. LHT is highly transparent and interpretable--at each branching block, the contribution of each feature to the classification can be clearly observed.

This paper presents a framework for privacy-preserving verification of machine learning models, focusing on models trained on sensitive data. Integrating Local Differential Privacy (LDP) with model explanations from LIME and SHAP, our framework enables robust verification without compromising individual privacy. It addresses two key tasks: binary classification, to verify if a target model was trained correctly by applying the appropriate preprocessing steps, and multi-class classification, to identify specific preprocessing errors. Evaluations on three real-world datasets-Diabetes, Adult, and Student Record-demonstrate that while the ML-based approach is particularly effective in binary tasks, the threshold-based method performs comparably in multi-class tasks. Results indicate that although verification accuracy varies across datasets and noise levels, the framework provides effective detection of preprocessing errors, strong privacy guarantees, and practical applicability for safeguarding sensitive data.