Collaborative robots and machine learning-based virtual agents are increasingly entering the human workspace with the aim of increasing productivity and enhancing safety.

We study the robustness verification problem of tree based models, including random forest (RF) and gradient boosted decision tree (GBDT). Formal robustness verification of decision tree ensembles involves finding the exact minimal adversarial perturbation or a guaranteed lower bound of it. Existing approaches cast this verification problem into a mixed integer linear programming (MILP) problem, which finds the minimal adversarial distortion in exponential time so is impractical for large ensembles. Although this verification problem is NP-complete in general, we give a more precise complexity characterization. We show that there is a simple linear time algorithm for verifying a single tree, and for tree ensembles the verification problem can be cast as a max-clique problem on a multi-partite boxicity graph. For low dimensional problems when boxicity can be viewed as constant, this reformulation leads to a polynomial time algorithm. For general problems, by exploiting the boxicity of the graph, we devise an efficient verification algorithm that can give tight lower bounds on robustness of decision tree ensembles, and allows iterative improvement and any-time termination. On RF/GBDT models trained on a variety of datasets, we significantly outperform the lower bounds obtained by relaxing the MILP formulation into a linear program (LP), and are hundreds times faster than solving MILPs to get the exact minimal adversarial distortion. Our proposed method is capable of giving tight robustness verification bounds on large GBDTs with hundreds of deep trees.

In spite of several claims stating that some models are more interpretable than others --e.g., linear models are more interpretable than deep neural networks-- we still lack a principled notion of interpretability that allows us to formally compare among different classes of models. We make a step towards such a theory by studying whether folklore interpretability claims have a correlate in terms of computational complexity theory. We focus on post-hoc explainability queries that, intuitively, attempt to answer why individual inputs are classified in a certain way by a given model. In a nutshell, we say that a class C1 of models is more interpretable than another class C2, if the computational complexity of answering post-hoc queries for models in C2 is higher than for C1. We prove that this notion provides a good theoretical counterpart to current beliefs on the interpretability of models; in particular, we show that under our definition and assuming standard complexity-theoretical assumptions (such as P!=NP), both linear and tree-based models are strictly more interpretable than neural networks. Our complexity analysis, however, does not provide a clear-cut difference between linear and tree-based models, as we obtain different results depending on the particular {post-hoc explanations} considered. Finally, by applying a finer complexity analysis based on parameterized complexity, we are able to prove a theoretical result suggesting that shallow neural networks are more interpretable than deeper ones.

Researchers have proposed many methods for fair and robust machine learning, but comprehensive empirical evaluation of their subgroup robustness is lacking. In this work, we address this gap in the context of tabular data, where sensitive subgroups are clearly-defined, real-world fairness problems abound, and prior works often do not compare to state-of-the-art tree-based models as baselines. We conduct an empirical comparison of several previously-proposed methods for fair and robust learning alongside state-of-the-art tree-based methods and other baselines. Via experiments with more than $340{,}000$ model configurations on eight datasets, we show that tree-based methods have strong subgroup robustness, even when compared to robustness-and fairness-enhancing methods. Moreover, the best tree-based models tend to show good performance over a range of metrics, while robust or group-fair models can show brittleness, with significant performance differences across different metrics for a fixed model. We also demonstrate that tree-based models show less sensitivity to hyperparameter configurations, and are less costly to train. Our work suggests that tree-based ensemble models make an effective baseline for tabular data, and are a sensible default when subgroup robustness is desired.

Bayesian quadrature (BQ) is a method for solving numerical integration problems in a Bayesian manner, which allows users to quantify their uncertainty about the solution. The standard approach to BQ is based on a Gaussian process (GP) approximation of the integrand. As a result, BQ is inherently limited to cases where GP approximations can be done in an efficient manner, thus often prohibiting very high-dimensional or non-smooth target functions. This paper proposes to tackle this issue with a new Bayesian numerical integration algorithm based on Bayesian Additive Regression Trees (BART) priors, which we call BART-Int. BART priors are easy to tune and well-suited for discontinuous functions. We demonstrate that they also lend themselves naturally to a sequential design setting and that explicit convergence rates can be obtained in a variety of settings. The advantages and disadvantages of this new methodology are highlighted on a set of benchmark tests including the Genz functions, on a rare-event simulation problem and on a Bayesian survey design problem.

Modern astronomy has generated an extensive taxonomy of celestial objects based on their physical characteristics and predicted future state. As theories of the development, expansion, history, and predicted future state of the universe rely on identifying and observing celestial bodies, it is essential to have quick and accurate classification of newly observed objects. Historically, classification was performed manually, but the rapid expansion of modern catalogues of celestial objects - such as the Sloan Digital Sky Survey, which grows at a rate of thousands of entries daily [1] - makes this manual classification impractical. Supervised and semi-supervised machine learning represent the most promising candidates for the desired computational classification. Until recently, the data, hardware, and software required for large-scale training and deployment of these methods were unavailable to the general research community. However, improvements to parallel processing hardware have driven increased success and adoption, resulting in the invention of models capable of equaling or surpassing human-level intelligence in tasks formerly considered intractable to computers. Such improvements have been recognized in facial recognition [2] and combinatorial game theory [3], but despite their meteoric rise in popularity, there is a significant gap in astronomical literature on applying machine learning models to the problem of celestial object classification. In an effort to improve this state, we explore a number of machine learning based models for a simplified celestial object classification problem to assess the performance and potential of these models in the field of astronomy.

Collaborative robots and machine learning-based virtual agents are increasingly entering the human workspace with the aim of increasing productivity and enhancing safety.

Deep Neural Networks (DNNs) have revolutionized artificial intelligence, achieving impressive results on diverse data types, including images, videos, and texts.