A decision tree is one of the most popular approaches in machine learning fields. However, it suffers from the problem of overfitting caused by overly deepened trees. Then, a meta-tree is recently proposed. It solves the problem of overfitting caused by overly deepened trees. Moreover, the meta-tree guarantees statistical optimality based on Bayes decision theory. Therefore, the meta-tree is expected to perform better than the decision tree. In contrast to a single decision tree, it is known that ensembles of decision trees, which are typically constructed boosting algorithms, are more effective in improving predictive performance. Thus, it is expected that ensembles of meta-trees are more effective in improving predictive performance than a single meta-tree, and there are no previous studies that construct multiple meta-trees in boosting. Therefore, in this study, we propose a method to construct multiple meta-trees using a boosting approach. Through experiments with synthetic and benchmark datasets, we conduct a performance comparison between the proposed methods and the conventional methods using ensembles of decision trees. Furthermore, while ensembles of decision trees can cause overfitting as well as a single decision tree, experiments confirmed that ensembles of meta-trees can prevent overfitting due to the tree depth.

We develop optimal algorithms for learning undirected Gaussian trees and directed Gaussian polytrees from data. We consider both problems of distribution learning (i.e. in KL distance) and structure learning (i.e. exact recovery). The first approach is based on the Chow-Liu algorithm, and learns an optimal tree-structured distribution efficiently. The second approach is a modification of the PC algorithm for polytrees that uses partial correlation as a conditional independence tester for constraint-based structure learning. We derive explicit finite-sample guarantees for both approaches, and show that both approaches are optimal by deriving matching lower bounds. Additionally, we conduct numerical experiments to compare the performance of various algorithms, providing further insights and empirical evidence.

Artificial Intelligence (AI) shows promising applications for the perception and planning tasks in autonomous driving (AD) due to its superior performance compared to conventional methods. However, inscrutable AI systems exacerbate the existing challenge of safety assurance of AD. One way to mitigate this challenge is to utilize explainable AI (XAI) techniques. To this end, we present the first comprehensive systematic literature review of explainable methods for safe and trustworthy AD. We begin by analyzing the requirements for AI in the context of AD, focusing on three key aspects: data, model, and agency. We find that XAI is fundamental to meeting these requirements. Based on this, we explain the sources of explanations in AI and describe a taxonomy of XAI. We then identify five key contributions of XAI for safe and trustworthy AI in AD, which are interpretable design, interpretable surrogate models, interpretable monitoring, auxiliary explanations, and interpretable validation. Finally, we propose a modular framework called SafeX to integrate these contributions, enabling explanation delivery to users while simultaneously ensuring the safety of AI models.

Estimation of heterogeneous treatment effects from observational data has become an important problem. It plays a crucial role in determining the individualized causal effects of a treatment, which then leads to a personalized assignment of optimal treatment (Wendling et al., 2018; Rekkas et al., 2020). Estimation of such heterogeneity however requires reasonable representations from each treatment subgroup. With the increasing availability of large-scale health outcome data such as electronic health records (EHR) data in recent years, it has become possible to develop individualized treatment strategies efficiently. This led to the development of several novel statistical methods, primarily tailored for binary treatment scenarios (Wendling et al., 2018; Cheng et al., 2020), with some accommodating multiple treatment settings (Brown et al., 2020; Chalkou et al., 2021). Most of these approaches are specifically designed for estimating population average treatment effects (ATEs) (Van Der Laan and Rubin, 2006; Chernozhukov et al., 2018; McCaffrey et al., 2013) and more recently, methods are being developed to estimate conditional average treatment effects (CATEs) (Taddy et al., 2016; Wager and Athey, 2018; Künzel et al., 2019; Nie and Wager, 2021). Here, we tackle a generic problem of heterogeneous treatment effect or CATE estimation in a multi-treatment setting, where the treatment responses may share some commonalities.

In the general framework of Bayesian inference, the target distribution can only be evaluated up-to a constant of proportionality. Classical consistent Bayesian methods such as sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC) have unbounded time complexity requirements. We develop a fully parallel sequential Monte Carlo (pSMC) method which provably delivers parallel strong scaling, i.e. the time complexity (and per-node memory) remains bounded if the number of asynchronous processes is allowed to grow. More precisely, the pSMC has a theoretical convergence rate of MSE$ = O(1/NR)$, where $N$ denotes the number of communicating samples in each processor and $R$ denotes the number of processors. In particular, for suitably-large problem-dependent $N$, as $R \rightarrow \infty$ the method converges to infinitesimal accuracy MSE$=O(\varepsilon^2)$ with a fixed finite time-complexity Cost$=O(1)$ and with no efficiency leakage, i.e. computational complexity Cost$=O(\varepsilon^{-2})$. A number of Bayesian inference problems are taken into consideration to compare the pSMC and MCMC methods.

This paper explores a modern predictive uncertainty estimation approach, called evidential deep learning (EDL), in which a single neural network model is trained to learn a meta distribution over the predictive distribution by minimizing a specific objective function. Despite their strong empirical performance, recent studies by Bengs et al. identify a fundamental pitfall of the existing methods: the learned epistemic uncertainty may not vanish even in the infinite-sample limit. We corroborate the observation by providing a unifying view of a class of widely used objectives from the literature. Our analysis reveals that the EDL methods essentially train a meta distribution by minimizing a certain divergence measure between the distribution and a sample-size-independent target distribution, resulting in spurious epistemic uncertainty. Grounded in theoretical principles, we propose learning a consistent target distribution by modeling it with a mixture of Dirichlet distributions and learning via variational inference. Afterward, a final meta distribution model distills the learned uncertainty from the target model. Experimental results across various uncertainty-based downstream tasks demonstrate the superiority of our proposed method, and illustrate the practical implications arising from the consistency and inconsistency of learned epistemic uncertainty.

Affordances are fundamental descriptors of relationships between actions, objects and effects. They provide the means whereby a robot can predict effects, recognize actions, select objects and plan its behavior according to desired goals. This paper approaches the problem of an embodied agent exploring the world and learning these affordances autonomously from its sensory experiences. Models exist for learning the structure and the parameters of a Bayesian Network encoding this knowledge. Although Bayesian Networks are capable of dealing with uncertainty and redundancy, previous work considered complete observability of the discrete sensory data, which may lead to hard errors in the presence of noise. In this paper we consider a probabilistic representation of the sensors by Gaussian Mixture Models (GMMs) and explicitly taking into account the probability distribution contained in each discrete affordance concept, which can lead to a more correct learning.

Best arm identification (BAI) addresses the challenge of finding the optimal arm in a bandit environment (Lattimore and Szepesvári, 2020), with wide-ranging applications in online advertising, drug discovery or hyperparameter tuning. BAI is commonly approached through two primary paradigms: fixed-confidence and fixed-budget. In the fixed-confidence setting (Even-Dar et al., 2006; Kaufmann et al., 2016), the objective is to find the optimal arm with a pre-specified confidence level. Conversely, fixed-budget BAI (Audibert et al., 2010; Karnin et al., 2013; Carpentier and Locatelli, 2016) involves identifying the optimal arm within a fixed number of observations. Within this fixed-budget context, two main metrics are used: the probability of error (PoE) (Audibert et al., 2010; Karnin et al., 2013; Carpentier and Locatelli, 2016)--the likelihood of incorrectly identifying the optimal arm--and the simple regret (Bubeck et al., 2009; Russo, 2016; Komiyama et al., 2023)--the expected performance disparity between the chosen and the optimal arm.

Explainability and human interpretability are becoming an increasingly important part of research on machine learning. In addition to the immediate benefits of explanations and interpretability in scientific contexts, the capacity to provide explanations behind automated decisions has already been widely addressed also on the level of legislation. For example, the European General Data Protection Regulation [8] and California Consumer Privacy Act [4] both refer to the right of individuals to get explanations of automated decisions concerning them. This article investigates interpretability in the framework of tabular data. Tabular data is highly important for numerous scientific and real-life contexts, often even regarded as the most important form of data: see, e.g., [22, 2]. The aim of the current article is to introduce an efficient method for extracting highly interpretable binary classifiers from tabular data. While explainable AI (or XAI) methods custom-made for pictures and text cannot be readily used in the setting of tabular data [16], numerous succesful XAI methods for tabular data exist. See the survey [20] for an overview of XAI in relation to tabular data. The authors are given in the alphabetical order.

Cardiovascular diseases state as one of the greatest risks of death for the general population. Late detection in heart diseases highly conditions the chances of survival for patients. Age, sex, cholesterol level, sugar level, heart rate, among other factors, are known to have an influence on life-threatening heart problems, but, due to the high amount of variables, it is often difficult for an expert to evaluate each patient taking this information into account. In this manuscript, the authors propose using deep learning methods, combined with feature augmentation techniques for evaluating whether patients are at risk of suffering cardiovascular disease. The results of the proposed methods outperform other state of the art methods by 4.4%, leading to a precision of a 90%, which presents a significant improvement, even more so when it comes to an affliction that affects a large population.