This manuscript proposes to extend the information set of time-series regression trees with latent stationary factors extracted via state-space methods. First, it allows to handle predictors that exhibit measurement error, non-stationary trends, seasonality and/or irregularities such as missing observations. Second, it gives a transparent way for using domain-specific theory to inform time-series regression trees. As a byproduct, this technique sets the foundations for structuring powerful ensembles. Their real-world applicability is studied under the lenses of empirical macro-finance. Keywords: Ensemble learning, Factor models, State-space models, Time series, Unobserved components.Introduction In time series, the simplicity of regression trees (Morgan and Sonquist, 1963; Breiman et al., 1984; Quinlan, 1986) comes at a cost: irregularities, complicated periodic patterns and non-stationary trends cannot be explicitly modelled, and this is unfortunate given that many real-world examples are subject to them. Following, in spirit, Harvey et al. (1998), this paper proposes to pre-process problematic predictors using state-space representations general enough to deal with all these complexities at once. This operation can be thought as an automated feature engineering process that extracts stationary patterns hidden across multiple predictors, while handling problematic data characteristics. Besides, when the state-space representation is compatible with domain-specific theory, this becomes a transparent way for extracting signals with structural interpretation. The resulting stationary common components, referred hereinbelow as stationary dynamic factors, are then employed as regular predictors for standard time-series regression trees. This manuscript calls them factor-augmented regression trees to stress their dependence on latent components. I thank Matteo Barigozzi and Kostas Kalogeropoulos for their valuable suggestions and supervision; Serena Lariccia and Qiwei Yao for their helpful comments on a preliminary draft of this article.

Comparing prediction methods to define which one should be used for the task at hand is a daily activity for most data scientists. Usually, one will have a pool of classification models and will validate them using cross-validation to define which one is best. Another goal, however, is not to compare classifiers, but the learning algorithms themselves. The idea is: given this task (data), which learning algorithm (KNN, SVM, Random Forests, etc) will generate more accurate classifiers on a dataset of size D? As we will see, every method presented here has some pros and cons. However, the first intuition of using a two proportions test can lead to some really bad results.

A major challenge in embedding or visualizing clinical patient data is the heterogeneity of variable types including continuous lab values, categorical diagnostic codes, as well as missing or incomplete data. In particular, in EHR data, some variables are {\em missing not at random (MNAR)} but deliberately not collected and thus are a source of information. For example, lab tests may be deemed necessary for some patients on the basis of suspected diagnosis, but not for others. Here we present the MURAL forest -- an unsupervised random forest for representing data with disparate variable types (e.g., categorical, continuous, MNAR). MURAL forests consist of a set of decision trees where node-splitting variables are chosen at random, such that the marginal entropy of all other variables is minimized by the split. This allows us to also split on MNAR variables and discrete variables in a way that is consistent with the continuous variables. The end goal is to learn the MURAL embedding of patients using average tree distances between those patients. These distances can be fed to nonlinear dimensionality reduction method like PHATE to derive visualizable embeddings. While such methods are ubiquitous in continuous-valued datasets (like single cell RNA-sequencing) they have not been used extensively in mixed variable data. We showcase the use of our method on one artificial and two clinical datasets. We show that using our approach, we can visualize and classify data more accurately than competing approaches. Finally, we show that MURAL can also be used to compare cohorts of patients via the recently proposed tree-sliced Wasserstein distances.

Cybersecurity has been a concern for quite a while now. In the latest years, cyberattacks have been increasing in size and complexity, fueled by significant advances in technology. Nowadays, there is an unavoidable necessity of protecting systems and data crucial for business continuity. Hence, many intrusion detection systems have been created in an attempt to mitigate these threats and contribute to a timelier detection. This work proposes an interpretable and explainable hybrid intrusion detection system, which makes use of artificial intelligence methods to achieve better and more long-lasting security. The system combines experts' written rules and dynamic knowledge continuously generated by a decision tree algorithm as new shreds of evidence emerge from network activity.

Individual Treatment Effect (ITE) prediction is an important area of research in machine learning which aims at explaining and estimating the causal impact of an action at the granular level. It represents a problem of growing interest in multiple sectors of application such as healthcare, online advertising or socioeconomics. To foster research on this topic we release a publicly available collection of 13.9 million samples collected from several randomized control trials, scaling up previously available datasets by a healthy 210x factor. We provide details on the data collection and perform sanity checks to validate the use of this data for causal inference tasks. First, we formalize the task of uplift modeling (UM) that can be performed with this data, along with the relevant evaluation metrics. Then, we propose synthetic response surfaces and heterogeneous treatment assignment providing a general set-up for ITE prediction. Finally, we report experiments to validate key characteristics of the dataset leveraging its size to evaluate and compare - with high statistical significance - a selection of baseline UM and ITE prediction methods.

Interpretability is a pressing issue for decision systems. Many post hoc methods have been proposed to explain the predictions of any machine learning model. However, business processes and decision systems are rarely centered around a single, standalone model. These systems combine multiple models that produce key predictions, and then apply decision rules to generate the final decision. To explain such decision, we present SMACE, Semi-Model-Agnostic Contextual Explainer, a novel interpretability method that combines a geometric approach for decision rules with existing post hoc solutions for machine learning models to generate an intuitive feature ranking tailored to the end user. We show that established model-agnostic approaches produce poor results in this framework.

There are other two linear models that you should know: Lasso and Ridge. Sometimes we have too many features, and we suspect that many of them are not useful in predicting the label. So what we want to do is keep most of the weights to values near zero. Lasso and Ridge models do just that. The difference is just the method that they use.

Random Forests (RFs) are among the state-of-the-art in machine learning and offer excellent performance with nearly zero parameter tuning. Remarkably, RFs seem to be impervious to overfitting even though their basic building blocks are well-known to overfit. Recently, a broadly received study argued that a RF exhibits a so-called double-descent curve: First, the model overfits the data in a u-shaped curve and then, once a certain model complexity is reached, it suddenly improves its performance again. In this paper, we challenge the notion that model capacity is the correct tool to explain the success of RF and argue that the algorithm which trains the model plays a more important role than previously thought. We show that a RF does not exhibit a double-descent curve but rather has a single descent. Hence, it does not overfit in the classic sense. We further present a RF variation that also does not overfit although its decision boundary approximates that of an overfitted DT. Similar, we show that a DT which approximates the decision boundary of a RF will still overfit. Last, we study the diversity of an ensemble as a tool the estimate its performance. To do so, we introduce Negative Correlation Forest (NCForest) which allows for precise control over the diversity in the ensemble. We show, that the diversity and the bias indeed have a crucial impact on the performance of the RF. Having too low diversity collapses the performance of the RF into a a single tree, whereas having too much diversity means that most trees do not produce correct outputs anymore. However, in-between these two extremes we find a large range of different trade-offs with all roughly equal performance. Hence, the specific trade-off between bias and diversity does not matter as long as the algorithm reaches this good trade-off regime.

An ensemble of decision trees is known as Random Forest. As suggested by Breiman, the strength of unstable learners and the diversity among them are the ensemble models' core strength. In this paper, we propose two approaches known as oblique and rotation double random forests. In the first approach, we propose a rotation based double random forest. In rotation based double random forests, transformation or rotation of the feature space is generated at each node. At each node different random feature subspace is chosen for evaluation, hence the transformation at each node is different. Different transformations result in better diversity among the base learners and hence, better generalization performance. With the double random forest as base learner, the data at each node is transformed via two different transformations namely, principal component analysis and linear discriminant analysis. In the second approach, we propose oblique double random forest. Decision trees in random forest and double random forest are univariate, and this results in the generation of axis parallel split which fails to capture the geometric structure of the data. Also, the standard random forest may not grow sufficiently large decision trees resulting in suboptimal performance. To capture the geometric properties and to grow the decision trees of sufficient depth, we propose oblique double random forest. The oblique double random forest models are multivariate decision trees. At each non-leaf node, multisurface proximal support vector machine generates the optimal plane for better generalization performance. Also, different regularization techniques (Tikhonov regularisation and axis-parallel split regularisation) are employed for tackling the small sample size problems in the decision trees of oblique double random forest.

Internet companies are increasingly using machine learning models to create personalized policies which assign, for each individual, the best predicted treatment for that individual. They are frequently derived from black-box heterogeneous treatment effect (HTE) models that predict individual-level treatment effects. In this paper, we focus on (1) learning explanations for HTE models; (2) learning interpretable policies that prescribe treatment assignments. We also propose guidance trees, an approach to ensemble multiple interpretable policies without the loss of interpretability. These rule-based interpretable policies are easy to deploy and avoid the need to maintain a HTE model in a production environment.