Optimal decision tree (\odt) is a fundamental problem arising in applications such as active learning, entity identification, and medical diagnosis. An instance of \odt is given by $m$ hypotheses, out of which an unknown ``true'' hypothesis is drawn according to some probability distribution. An algorithm needs to identify the true hypothesis by making queries: each query incurs a cost and has a known response for each hypothesis. The goal is to minimize the expected query cost to identify the true hypothesis. We consider the most general setting with arbitrary costs, probabilities and responses. \odt is NP-hard to approximate better than $\ln m$ and there are $O(\ln m)$ approximation algorithms known for it. However, these algorithms and/or their analyses are quite complex. Moreover, the leading constant factors are large. We provide a simple algorithm and analysis for \odt, proving an approximation ratio of $8 \ln m$.

Integer quantization has emerged as a critical technique to facilitate deployment on resource-constrained devices. Although they do reduce the complexity of the learning models, their inference performance is often prone to quantization-induced errors. To this end, we introduce InTreeger: an end-to-end framework that takes a training dataset as input, and outputs an architecture-agnostic integer-only C implementation of tree-based machine learning model, without loss of precision. This framework enables anyone, even those without prior experience in machine learning, to generate a highly optimized integer-only classification model that can run on any hardware simply by providing an input dataset and target variable. We evaluated our generated implementations across three different architectures (ARM, x86, and RISC-V), resulting in significant improvements in inference latency. In addition, we show the energy efficiency compared to typical decision tree implementations that rely on floating-point arithmetic. The results underscore the advantages of integer-only inference, making it particularly suitable for energy- and area-constrained devices such as embedded systems and edge computing platforms, while also enabling the execution of decision trees on existing ultra-low power devices.

Machine Learning produces efficient decision and prediction models based on input-output data only. Such models have the form of decision trees or neural nets and are far from transparent analytical models, based on mathematical formulas. Analytical model discovery requires additional knowledge and may be performed with Grammatical Evolution. Such models are transparent, concise, and have readable components and structure. This paper reports on a non-trivial experiment with generating such models.

This paper introduces a novel nonparametric method for estimating high-dimensional dynamic covariance matrices with multiple conditioning covariates, leveraging random forests and supported by robust theoretical guarantees. Unlike traditional static methods, our dynamic nonparametric covariance models effectively capture distributional heterogeneity. Furthermore, unlike kernel-smoothing methods, which are restricted to a single conditioning covariate, our approach accommodates multiple covariates in a fully nonparametric framework. To the best of our knowledge, this is the first method to use random forests for estimating high-dimensional dynamic covariance matrices. In high-dimensional settings, we establish uniform consistency theory, providing nonasymptotic error rates and model selection properties, even when the response dimension grows sub-exponentially with the sample size. These results hold uniformly across a range of conditioning variables. The method's effectiveness is demonstrated through simulations and a stock dataset analysis, highlighting its ability to model complex dynamics in high-dimensional scenarios.

Measuring social influence is difficult due to the lack of counter-factuals and comparisons. By combining machine learning-based modeling and network science, we present general properties of social value, a recent measure for social influence using synthetic control applicable to political behavior. Social value diverges from centrality measures on in that it relies on an external regressor to predict an output variable of interest, generates a synthetic measure of influence, then distributes individual contribution based on a social network. Through theoretical derivations, we show the properties of SV under linear regression with and without interaction, across lattice networks, power-law networks, and random graphs. A reduction in computation can be achieved for any ensemble model. Through simulation, we find that the generalized friendship paradox holds -- that in certain situations, your friends have on average more influence than you do.

This work studies one of the parallel decision tree learning algorithms, pdsCART, designed for scalable and efficient data analysis. The method incorporates three core capabilities. First, it supports real-time learning from data streams, allowing trees to be constructed incrementally. Second, it enables parallel processing of high-volume streaming data, making it well-suited for large-scale applications. Third, the algorithm integrates seamlessly into the MapReduce framework, ensuring compatibility with distributed computing environments. In what follows, we present the algorithm's key components along with results highlighting its performance and scalability.

Given a classification model and a prediction for some input, there are heuristic strategies for ranking features according to their importance in regard to the prediction. One common approach to this task is rooted in propositional logic and the notion of \textit{sufficient reason}. Through this concept, the categories of relevant and necessary features were proposed in order to identify the crucial aspects of the input. This paper improves the existing techniques and algorithms for deciding which are the relevant and/or necessary features, showing in particular that necessity can be detected efficiently in complex models such as neural networks. We also generalize the notion of relevancy and study associated problems. Moreover, we present a new global notion (i.e. that intends to explain whether a feature is important for the behavior of the model in general, not depending on a particular input) of \textit{usefulness} and prove that it is related to relevancy and necessity. Furthermore, we develop efficient algorithms for detecting it in decision trees and other more complex models, and experiment on three datasets to analyze its practical utility.

Interpretable policy representations like Behavior Trees (BTs) and Dynamic Motion Primitives (DMPs) enable robot skill transfer from human demonstrations, but each faces limitations: BTs require expert-crafted low-level actions, while DMPs lack high-level task logic. We address these limitations by integrating DMP controllers into a BT framework, jointly learning the BT structure and DMP actions from single demonstrations, thereby removing the need for predefined actions. Additionally, by combining BT decision logic with DMP motion generation, our method enhances policy interpretability, modularity, and adaptability for autonomous systems. Our approach readily affords both learning to replicate low-level motions and combining partial demonstrations into a coherent and easy-to-modify overall policy.

Gaussian process regression is a popular model in the small data regime due to its sound uncertainty quantification and the exploitation of the smoothness of the regression function that is encountered in a wide range of practical problems. However, Gaussian processes perform sub-optimally when the degree of smoothness is non-homogeneous across the input domain. Random forest regression partially addresses this issue by providing local basis functions of variable support set sizes that are chosen in a data-driven way. However, they do so at the expense of forgoing any degree of smoothness, which often results in poor performance in the small data regime. Here, we aim to combine the advantages of both models by applying a kernel-based smoothing mechanism to a learned random forest or any other piecewise constant prediction function. As we demonstrate empirically, the resulting model consistently improves the predictive performance of the underlying random forests and, in almost all test cases, also improves the log loss of the usual uncertainty quantification based on inter-tree variance. The latter advantage can be attributed to the ability of the smoothing model to take into account the uncertainty over the exact tree-splitting locations.

Oblique decision trees have attracted attention due to their potential for improved classification performance over traditional axis-aligned decision trees. However, methods that rely on exhaustive search to find oblique splits face computational challenges. As a result, they have not been widely explored. We introduce a novel algorithm, Classification and Regression Tree - Exhaustive Linear Combinations (CART-ELC), for inducing oblique decision trees that performs an exhaustive search on a restricted set of hyperplanes. We then investigate the algorithm's computational complexity and its predictive capabilities. Our results demonstrate that CART-ELC consistently achieves competitive performance on small datasets, often yielding statistically significant improvements in classification accuracy relative to existing decision tree induction algorithms, while frequently producing shallower, simpler, and thus more interpretable trees.