Continual learning based on data stream mining deals with ubiquitous sources of Big Data arriving at high-velocity and in real-time. Adaptive Random Forest ({\em ARF}) is a popular ensemble method used for continual learning due to its simplicity in combining adaptive leveraging bagging with fast random Hoeffding trees. While the default ARF size provides competitive accuracy, it is usually over-provisioned resulting in the use of additional classifiers that only contribute to increasing CPU and memory consumption with marginal impact in the overall accuracy. This paper presents Elastic Swap Random Forest ({\em ESRF}), a method for reducing the number of trees in the ARF ensemble while providing similar accuracy. {\em ESRF} extends {\em ARF} with two orthogonal components: 1) a swap component that splits learners into two sets based on their accuracy (only classifiers with the highest accuracy are used to make predictions); and 2) an elastic component for dynamically increasing or decreasing the number of classifiers in the ensemble. The experimental evaluation of {\em ESRF} and comparison with the original {\em ARF} shows how the two new components contribute to reducing the number of classifiers up to one third while providing almost the same accuracy, resulting in speed-ups in terms of per-sample execution time close to 3x.

Tree-based machine learning models such as random forests, decision trees, and gradient boosted trees are the most popular non-linear predictive models used in practice today, yet comparatively little attention has been paid to explaining their predictions. Here we significantly improve the interpretability of tree-based models through three main contributions: 1) The first polynomial time algorithm to compute optimal explanations based on game theory. 2) A new type of explanation that directly measures local feature interaction effects. 3) A new set of tools for understanding global model structure based on combining many local explanations of each prediction. We apply these tools to three medical machine learning problems and show how combining many high-quality local explanations allows us to represent global structure while retaining local faithfulness to the original model. These tools enable us to i) identify high magnitude but low frequency non-linear mortality risk factors in the general US population, ii) highlight distinct population sub-groups with shared risk characteristics, iii) identify non-linear interaction effects among risk factors for chronic kidney disease, and iv) monitor a machine learning model deployed in a hospital by identifying which features are degrading the model's performance over time. Given the popularity of tree-based machine learning models, these improvements to their interpretability have implications across a broad set of domains.

Interpretable machine learning has become a strong competitor for traditional black-box models. However, the possible loss of the predictive performance for gaining interpretability is often inevitable, putting practitioners in a dilemma of choosing between high accuracy (black-box models) and interpretability (interpretable models). In this work, we propose a novel framework for building a Hybrid Predictive Model (HPM) that integrates an interpretable model with any black-box model to combine their strengths. The interpretable model substitutes the black-box model on a subset of data where the black-box is overkill or nearly overkill, gaining transparency at no or low cost of the predictive accuracy. We design a principled objective function that considers predictive accuracy, model interpretability, and model transparency (defined as the percentage of data processed by the interpretable substitute.) Under this framework, we propose two hybrid models, one substituting with association rules and the other with linear models, and we design customized training algorithms for both models. We test the hybrid models on structured data and text data where interpretable models collaborate with various state-of-the-art black-box models. Results show that hybrid models obtain an efficient trade-off between transparency and predictive performance, characterized by our proposed efficient frontiers.

Recent advances in machine learning and artificial intelligence are now being considered in safety-critical autonomous systems where software defects may cause severe harm to humans and the environment. Design organizations in these domains are currently unable to provide convincing arguments that their systems are safe to operate when machine learning algorithms are used to implement their software. In this paper, we present an efficient method to extract equivalence classes from decision trees and tree ensembles, and to formally verify that their input-output mappings comply with requirements. The idea is that, given that safety requirements can be traced to desirable properties on system input-output patterns, we can use positive verification outcomes in safety arguments. This paper presents the implementation of the method in the tool VoTE (Verifier of Tree Ensembles), and evaluates its scalability on two case studies presented in current literature. We demonstrate that our method is practical for tree ensembles trained on low-dimensional data with up to 25 decision trees and tree depths of up to 20. Our work also studies the limitations of the method with high-dimensional data and preliminarily investigates the trade-off between large number of trees and time taken for verification.

We propose a novel method designed for large-scale regression problems, namely the two-stage best-scored random forest (TBRF). "Best-scored" means to select one regression tree with the best empirical performance out of a certain number of purely random regression tree candidates, and "two-stage" means to divide the original random tree splitting procedure into two: In stage one, the feature space is partitioned into non-overlapping cells; in stage two, child trees grow separately on these cells. The strengths of this algorithm can be summarized as follows: First of all, the pure randomness in TBRF leads to the almost optimal learning rates, and also makes ensemble learning possible, which resolves the boundary discontinuities long plaguing the existing algorithms. Secondly, the two-stage procedure paves the way for parallel computing, leading to computational efficiency. Last but not least, TBRF can serve as an inclusive framework where different mainstream regression strategies such as linear predictor and least squares support vector machines (LS-SVMs) can also be incorporated as value assignment approaches on leaves of the child trees, depending on the characteristics of the underlying data sets. Numerical assessments on comparisons with other state-of-the-art methods on several large-scale real data sets validate the promising prediction accuracy and high computational efficiency of our algorithm.

This paper presents a brand new nonparametric density estimation strategy named the best-scored random forest density estimation whose effectiveness is supported by both solid theoretical analysis and significant experimental performance. The terminology best-scored stands for selecting one density tree with the best estimation performance out of a certain number of purely random density tree candidates and we then name the selected one the best-scored random density tree. In this manner, the ensemble of these selected trees that is the best-scored random density forest can achieve even better estimation results than simply integrating trees without selection. From the theoretical perspective, by decomposing the error term into two, we are able to carry out the following analysis: First of all, we establish the consistency of the best-scored random density trees under $L_1$-norm. Secondly, we provide the convergence rates of them under $L_1$-norm concerning with three different tail assumptions, respectively. Thirdly, the convergence rates under $L_{\infty}$-norm is presented. Last but not least, we also achieve the above convergence rates analysis for the best-scored random density forest. When conducting comparative experiments with other state-of-the-art density estimation approaches on both synthetic and real data sets, it turns out that our algorithm has not only significant advantages in terms of estimation accuracy over other methods, but also stronger resistance to the curse of dimensionality.

We provide a machine learning solution that replaces the traditional methods for deciding the pesticide application time of Sunn Pest. We correlate climate data with phases of Sunn Pest in its life-cycle and decide whether the fields should be sprayed. Our solution includes two groups of prediction models. The first group contains decision trees that predict migration time of Sunn Pest from winter quarters to wheat fields. The second group contains random forest models that predict the nymphal stage percentages of Sunn Pest which is a criterion for pesticide application. We trained our models on four years of climate data which was collected from Kir\c{s}ehir and Aksaray. The experiments show that our promised solution make correct predictions with high accuracies.

Models often need to be constrained to a certain size for them to be considered interpretable, for e.g., a decision tree of depth 5 is much easier to make sense of than one of depth 30. This suggests a trade-off between interpretability and accuracy. Our work tries to minimize this trade-off by suggesting the optimal distribution of the data to learn from, that surprisingly, may be different from the original distribution. We use an Infinite Beta Mixture Model (IBMM) to represent a specific set of sampling schemes. The parameters of the IBMM are learned using a Bayesian Optimizer (BO). While even under simplistic assumptions a distribution in the original $d$-dimensional space would need to optimize for $O(d)$ variables - cumbersome for most real-world data - our technique lowers this number significantly to a fixed set of 8 variables at the cost of some additional preprocessing. The proposed technique is \emph{model-agnostic}; it can be applied to any classifier. It also admits a general notion of model size. We demonstrate its effectiveness using multiple real-world datasets to construct decision trees, linear probability models and gradient boosted models.

Scientific Computing relies on executing computer algorithms coded in some programming languages. Given a particular available hardware, algorithms speed is a crucial factor. There are many scientific computing environments used to code such algorithms. Matlab is one of the most tremendously successful and widespread scientific computing environments that is rich of toolboxes, libraries, and data visualization tools. OpenCV is a (C++)-based library written primarily for Computer Vision and its related areas. This paper presents a comparative study using 20 different real datasets to compare the speed of Matlab and OpenCV for some Machine Learning algorithms. Although Matlab is more convenient in developing and data presentation, OpenCV is much faster in execution, where the speed ratio reaches more than 80 in some cases. The best of two worlds can be achieved by exploring using Matlab or similar environments to select the most successful algorithm; then, implementing the selected algorithm using OpenCV or similar environments to gain a speed factor.

Interpretable classifiers have recently witnessed an increase in attention from the data mining community because they are inherently easier to understand and explain than their more complex counterparts. Examples of interpretable classification models include decision trees, rule sets, and rule lists. Learning such models often involves optimizing hyperparameters, which typically requires substantial amounts of data and may result in relatively large models. In this paper, we consider the problem of learning compact yet accurate probabilistic rule lists for multiclass classification. Specifically, we propose a novel formalization based on probabilistic rule lists and the minimum description length (MDL) principle. This results in virtually parameter-free model selection that naturally allows to trade-off model complexity with goodness of fit, by which overfitting and the need for hyperparameter tuning are effectively avoided. Finally, we introduce the Classy algorithm, which greedily finds rule lists according to the proposed criterion. We empirically demonstrate that Classy selects small probabilistic rule lists that outperform state-of-the-art classifiers when it comes to the combination of predictive performance and interpretability. We show that Classy is insensitive to its only parameter, i.e., the candidate set, and that compression on the training set correlates with classification performance, validating our MDL-based selection criterion.