In this paper, we focus on the prediction phase of a random forest and study the problem of representing a bag of decision trees using a smaller bag of decision trees, where we only consider binary decision problems on the binary domain and simple decision trees in which an internal node is limited to querying the Boolean value of a single variable. As a main result, we show that the majority function of $n$ variables can be represented by a bag of $T$ ($< n$) decision trees each with polynomial size if $n-T$ is a constant, where $n$ and $T$ must be odd (in order to avoid the tie break). We also show that a bag of $n$ decision trees can be represented by a bag of $T$ decision trees each with polynomial size if $n-T$ is a constant and a small classification error is allowed. A related result on the $k$-out-of-$n$ functions is presented too.

Despite their remarkable effectiveness and broad application, the drivers of success underlying ensembles of trees (especially random forests and gradient boosting) are still not fully understood. In this paper, we highlight how interpreting tree ensembles as adaptive and self-regularizing smoothers can provide new intuition and deeper insight to this topic. We use this perspective to show that, when studied as smoothers - whose predictions can be understood as simple weighted averages of the training labels - randomized tree ensembles not only make predictions that are quantifiably more smooth than the predictions of the individual trees they consist of, but also further regulate their smoothness at test-time based on the dissimilarity between testing and training inputs. First, we use this insight to revisit, refine and reconcile two recent explanations of forest success by providing a new way of quantifying the conjectured behaviors of tree ensembles objectively by measuring the effective degree of smoothing they imply. Then, we move beyond existing explanations for the mechanisms by which tree ensembles improve upon individual trees and challenge the popular wisdom that the superior performance of forests should be understood as a consequence of variance reduction alone. We argue that the current high-level dichotomy into bias-and variance-reduction prevalent in statistics is insufficient to understand tree ensembles - because the prevailing definition of bias does not capture differences in the expressivity of the hypothesis classes formed by trees and forests. Instead, we show that forests can improve upon trees by three distinct mechanisms that are usually implicitly entangled. In particular, we demonstrate that the smoothing effect of ensembling can reduce variance in predictions due to noise in outcome generation, reduce variability in the quality of the learned function given fixed input data and reduce potential bias in learnable functions by enriching the available hypothesis space.

Recent developments enable the quantification of causal control given a structural causal model (SCM). This has been accomplished by introducing quantities which encode changes in the entropy of one variable when intervening on another. These measures, named causal entropy and causal information gain, aim to address limitations in existing information theoretical approaches for machine learning tasks where causality plays a crucial role. They have not yet been properly mathematically studied. Our research contributes to the formal understanding of the notions of causal entropy and causal information gain by establishing and analyzing fundamental properties of these concepts, including bounds and chain rules. Furthermore, we elucidate the relationship between causal entropy and stochastic interventions. We also propose definitions for causal conditional entropy and causal conditional information gain. Overall, this exploration paves the way for enhancing causal machine learning tasks through the study of recently-proposed information theoretic quantities grounded in considerations about causality.

This study explores the usefulness of machine learning classifiers for modeling freight mode choice. We investigate eight commonly used machine learning classifiers, namely Naive Bayes, Support Vector Machine, Artificial Neural Network, K-Nearest Neighbors, Classification and Regression Tree, Random Forest, Boosting and Bagging, along with the classical Multinomial Logit model. US 2012 Commodity Flow Survey data are used as the primary data source; we augment it with spatial attributes from secondary data sources. The performance of the classifiers is compared based on prediction accuracy results. The current research also examines the role of sample size and training-testing data split ratios on the predictive ability of the various approaches. In addition, the importance of variables is estimated to determine how the variables influence freight mode choice. The results show that the tree-based ensemble classifiers perform the best. Specifically, Random Forest produces the most accurate predictions, closely followed by Boosting and Bagging. With regard to variable importance, shipment characteristics, such as shipment distance, industry classification of the shipper and shipment size, are the most significant factors for freight mode choice decisions.

We research into the clinical, biochemical and neuroimaging factors associated with the outcome of stroke patients to generate a predictive model using machine learning techniques for prediction of mortality and morbidity 3 months after admission. The dataset consisted of patients with ischemic stroke (IS) and non-traumatic intracerebral hemorrhage (ICH) admitted to Stroke Unit of a European Tertiary Hospital prospectively registered. We identified the main variables for machine learning Random Forest (RF), generating a predictive model that can estimate patient mortality/morbidity. In conclusion, machine learning algorithms RF can be effectively used in stroke patients for long-term outcome prediction of mortality and morbidity.

In supervised machine learning, feature selection plays a very important role by potentially enhancing explainability and performance as measured by computing time and accuracy-related metrics. In this paper, we investigate a method for feature selection based on the well-known L1 and L2 regularization strategies associated with logistic regression (LR). It is well known that the learned coefficients, which serve as weights, can be used to rank the features. Our approach is to synthesize the findings of L1 and L2 regularization. For our experiment, we chose the CIC-IDS2018 dataset owing partly to its size and also to the existence of two problematic classes that are hard to separate. We report first with the exclusion of one of them and then with its inclusion. We ranked features first with L1 and then with L2, and then compared logistic regression with L1 (LR+L1) against that with L2 (LR+L2) by varying the sizes of the feature sets for each of the two rankings. We found no significant difference in accuracy between the two methods once the feature set is selected. We chose a synthesis, i.e., only those features that were present in both the sets obtained from L1 and that from L2, and experimented with it on more complex models like Decision Tree and Random Forest and observed that the accuracy was very close in spite of the small size of the feature set. Additionally, we also report on the standard metrics: accuracy, precision, recall, and f1-score.

Interpretability and transparency are essential for incorporating causal effect models from observational data into policy decision-making. They can provide trust for the model in the absence of ground truth labels to evaluate the accuracy of such models. To date, attempts at transparent causal effect estimation consist of applying post hoc explanation methods to black-box models, which are not interpretable. Here, we present BICauseTree: an interpretable balancing method that identifies clusters where natural experiments occur locally. Our approach builds on decision trees with a customized objective function to improve balancing and reduce treatment allocation bias. Consequently, it can additionally detect subgroups presenting positivity violations, exclude them, and provide a covariate-based definition of the target population we can infer from and generalize to. We evaluate the method's performance using synthetic and realistic datasets, explore its bias-interpretability tradeoff, and show that it is comparable with existing approaches.

The growing popularity of Android requires malware detection systems that can keep up with the pace of new software being released. According to a recent study, a new piece of malware appears online every 12 seconds. To address this, we treat Android malware detection as a streaming data problem and explore the use of active online learning as a means of mitigating the problem of labelling applications in a timely and cost-effective manner. Our resulting framework achieves accuracies of up to 96\%, requires as little of 24\% of the training data to be labelled, and compensates for concept drift that occurs between the release and labelling of an application. We also consider the broader practicalities of online learning within Android malware detection, and systematically explore the trade-offs between using different static, dynamic and hybrid feature sets to classify malware.

The global optimization of classification trees has demonstrated considerable promise, notably in enhancing accuracy, optimizing size, and thereby improving human comprehensibility. While existing optimal classification trees substantially enhance accuracy over greedy-based tree models like CART, they still fall short when compared to the more complex black-box models, such as random forests. To bridge this gap, we introduce a new mixed-integer programming (MIP) formulation, grounded in multivariate Boolean rules, to derive the optimal classification tree. Our methodology integrates both linear metrics, including accuracy, balanced accuracy, and cost-sensitive cost, as well as nonlinear metrics such as the F1-score. The approach is implemented in an open-source Python package named BooleanOCT. We comprehensively benchmark these methods on the 36 datasets from the UCI machine learning repository. The proposed models demonstrate practical solvability on real-world datasets, effectively handling sizes in the tens of thousands. Aiming to maximize accuracy, this model achieves an average absolute improvement of 3.1\% and 1.5\% over random forests in small-scale and medium-sized datasets, respectively. Experiments targeting various objectives, including balanced accuracy, cost-sensitive cost, and F1-score, demonstrate the framework's wide applicability and its superiority over contemporary state-of-the-art optimal classification tree methods in small to medium-scale datasets.

In the realm of precision medicine, effective patient stratification and disease subtyping demand innovative methodologies tailored for multi-omics data. Clustering techniques applied to multi-omics data have become instrumental in identifying distinct subgroups of patients, enabling a finer-grained understanding of disease variability. This work establishes a powerful framework for advancing precision medicine through unsupervised random-forest-based clustering and federated computing. We introduce a novel multi-omics clustering approach utilizing unsupervised random-forests. The unsupervised nature of the random forest enables the determination of cluster-specific feature importance, unraveling key molecular contributors to distinct patient groups. Moreover, our methodology is designed for federated execution, a crucial aspect in the medical domain where privacy concerns are paramount. We have validated our approach on machine learning benchmark data sets as well as on cancer data from The Cancer Genome Atlas (TCGA). Our method is competitive with the state-of-the-art in terms of disease subtyping, but at the same time substantially improves the cluster interpretability. Experiments indicate that local clustering performance can be improved through federated computing.