Decision trees have been widely used as classifiers in many machine learning applications thanks to their lightweight and interpretable decision process. This paper introduces Tree in Tree decision graph (TnT), a framework that extends the conventional decision tree to a more generic and powerful directed acyclic graph. The time complexity of TnT is linear to the number of nodes in the graph, therefore it can construct decision graphs on large datasets. Compared to decision trees, we show that TnT achieves better classification performance with reduced model size, both as a stand-alone classifier and as a base-estimator in bagging/AdaBoost ensembles. Our proposed model is a novel, more efficient and accurate alternative to the widely-used decision trees.

If causal relationships are linear and acyclic and noise terms are independent and Gaussian, causal orientation is not identified from observational data --- even if faithfulness is satisfied (Spirtes et al., 2002). Shimizu et al. (2006) showed that acyclic, linear, {\bf non}-Gaussian (LiNGAM) causal models {\em are} identified from observational data, so long as no latent confounders are present. That holds even when faithfulness fails. Genin and Mayo-Wilson (2020) refine that result: not only are causal relationships identified, but causal orientation is {\em statistically decidable}. That means that for every \epsilon 0, there is a method that converges in probability to the correct orientation and, at every sample size, outputs an incorrect orientation with probability less than \epsilon.

Decision trees are widely used in many settings where interpretable models are preferred or required. There is indeed a vast literature on the design and analysis of decision tree algorithms that aim at optimizing these parameters.This paper contributes to this important line of research: we propose as a novel criterion of measuring the interpretability of a decision tree, the sparsity of the set of attributes that are (on average) required to explain the classification of the examples. We give a tight characterization of the best possible guarantees achievable by a decision tree built to optimize both our newmeasure (which we call the {\em explanation size}) and the more classical measures of worst-case and average depth. In particular, we give an algorithm that guarantees O(\ln n) -approximation (hence optimal if P eq NP) for the minimization of both the average/worst-case explanation size and the average/worst-case depth. In addition to our theoretical contributions, experiments with 20 real datasets show that our algorithm has accuracy competitive with CART while producing trees that allow for much simpler explanations.

Medical diagnosis is a crucial task in the medical field, in terms of providing accurate classification and respective treatments. Having near-precise decisions based on correct diagnosis can affect a patient's life itself, and may extremely result in a catastrophe if not classified correctly. Several traditional machine learning (ML), such as support vector machines (SVMs) and logistic regression, and state-of-the-art tabular deep learning (DL) methods, including TabNet and TabTransformer, have been proposed and used over tabular medical datasets. Additionally, due to the superior performances, lower computational costs, and easier optimization over different tasks, ensemble methods have been used in the field more recently. They offer a powerful alternative in terms of providing successful medical decision-making processes in several diagnosis tasks. In this study, we investigated the benefits of ensemble methods, especially the Gradient Boosting Decision Tree (GBDT) algorithms in medical classification tasks over tabular data, focusing on XGBoost, CatBoost, and LightGBM. The experiments demonstrate that GBDT methods outperform traditional ML and deep neural network architectures and have the highest average rank over several benchmark tabular medical diagnosis datasets. Furthermore, they require much less computational power compared to DL models, creating the optimal methodology in terms of high performance and lower complexity.

Decision trees have gained popularity as interpretable surrogate models for learning-based control policies. However, providing safety guarantees for systems controlled by decision trees is an open challenge. We show that the problem is undecidable even for systems with the simplest dynamics, and PSPACE-complete for finite-horizon properties. The latter can be verified for discrete-time systems via bounded model checking. However, for continuous-time systems, such an approach requires discretization, thereby weakening the guarantees for the original system. This paper presents the first algorithm to directly verify decision-tree controlled system in continuous time.

Decision tree algorithms have been among the most popular algorithms for interpretable (transparent) machine learning since the early 1980's. The problem that has plagued decision tree algorithms since their inception is their lack of optimality, or lack of guarantees of closeness to optimality: decision tree algorithms are often greedy or myopic, and sometimes produce unquestionably suboptimal models. Hardness of decision tree optimization is both a theoretical and practical obstacle, and even careful mathematical programming approaches have not been able to solve these problems efficiently. This work introduces the first practical algorithm for optimal decision trees for binary variables. The algorithm is a co-design of analytical bounds that reduce the search space and modern systems techniques, including data structures and a custom bit-vector library.

Causal inference is central to many areas of artificial intelligence, including complex reasoning, planning, knowledge-base construction, robotics, explanation, and fairness. An active community of researchers develops and enhances algorithms that learn causal models from data, and this work has produced a series of impressive technical advances. However, evaluation techniques for causal modeling algorithms have remained somewhat primitive, limiting what we can learn from experimental studies of algorithm performance, constraining the types of algorithms and model representations that researchers consider, and creating a gap between theory and practice. We argue for more frequent use of evaluation techniques that examine interventional measures rather than structural or observational measures, and that evaluate those measures on empirical data rather than synthetic data. We survey the current practice in evaluation and show that the techniques we recommend are rarely used in practice. We show that such techniques are feasible and that data sets are available to conduct such evaluations.

The training of optimal decision tree via mixed-integer programming (MIP) has attracted much attention in recent literature. However, for large datasets, state-of-the-art approaches struggle to solve the optimal decision tree training problems to a provable global optimal solution within a reasonable time. In this paper, we reformulate the optimal decision tree training problem as a two-stage optimization problem and propose a tailored reduced-space branch and bound algorithm to train optimal decision tree for the classification tasks with continuous features. The computation of bounds can be decomposed into the solution of many small-scale subproblems and can be naturally parallelized. With these bounding methods, we prove that our algorithm can converge by branching only on variables representing the optimal decision tree structure, which is invariant to the size of datasets. Moreover, we propose a novel sample reduction method that can predetermine the cost of part of samples at each BB node.

A fundamental task in active learning involves performing a sequence of tests to identify an unknown hypothesis that is drawn from a known distribution. This problem, known as optimal decision tree induction, has been widely studied for decades and the asymptotically best-possible approximation algorithm has been devised for it. We study a generalization where certain test outcomes are noisy, even in the more general case when the noise is persistent, i.e., repeating the test on the scenario gives the same noisy output, disallowing simple repetition as a way to gain confidence. We design new approximation algorithms for both the non-adaptive setting, where the test sequence must be fixed a-priori, and the adaptive setting where the test sequence depends on the outcomes of prior tests. Previous work in the area assumed at most a constant number of noisy outcomes per test and per scenario and provided approximation ratios that were problem dependent (such as the minimum probability of a hypothesis).

Out-of-distribution (OOD) detection has recently gained substantial attention due to the importance of identifying out-of-domain samples in reliability and safety. Although OOD detection methods have advanced by a great deal, they are still susceptible to adversarial examples, which is a violation of their purpose. To mitigate this issue, several defenses have recently been proposed. Nevertheless, these efforts remained ineffective, as their evaluations are based on either small perturbation sizes, or weak attacks. In this work, we re-examine these defenses against an end-to-end PGD attack on in/out data with larger perturbation sizes, e.g. up to commonly used \epsilon 8/255 for the CIFAR-10 dataset.