We study a time series model that can be viewed as a decision tree with Markov temporal structure. The model is intractable for exact calculations, thus we utilize variational approximations. We consider three different distributions for the approximation: one in which the Markov calculations are performed exactly and the layers of the decision tree are decoupled, one in which the decision tree calculations are performed exactly and the time steps of the Markov chain are decoupled, and one in which a Viterbi-like assumption is made to pick out a single most likely state sequence.

An adaptive on-line algorithm is proposed to estimate hierarchical data structures for non-stationary data sources. The approach is based on the principle of minimum cross entropy to derive a decision tree for data clustering and it employs a metalearning idea (learning to learn) to adapt to changes in data characteristics. Its efficiency is demonstrated by grouping non-stationary artifical data and by hierarchical segmentation of LANDSAT images.

Recent theoretical results for pattern classification with thresh(cid:173) olded real-valued functions (such as support vector machines, sig(cid:173) moid networks, and boosting) give bounds on misclassification probability that do not depend on the size of the classifier, and hence can be considerably smaller than the bounds that follow from the VC theory. In this paper, we show that these techniques can be more widely applied, by representing other boolean functions as two-layer neural networks (thresholded convex combinations of boolean functions). For example, we show that with high probabil(cid:173) ity any decision tree of depth no more than d that is consistent with m training examples has misclassification probability no more than o ( ( (Neff VCdim(U) log2 m log d)) 1/2), where U is the class of node decision functions, and Neff::; N can be thought of as the effective number of leaves (it becomes small as the distribution on the leaves induced by the training data gets far from uniform). This bound is qualitatively different from the VC bound and can be considerably smaller. We use the same technique to give similar results for DNF formulae.

Decision trees are surprisingly adaptive in three important respects: They automatically (1) adapt to favorable conditions near the Bayes decision boundary; (2) focus on data distributed on lower dimensional manifolds; (3) reject irrelevant features. In this paper we examine a decision tree based on dyadic splits that adapts to each of these conditions to achieve minimax optimal rates of convergence. The proposed classifier is the first known to achieve these optimal rates while being practical and im- plementable.

Many computer aided diagnosis (CAD) problems can be best modelled as a multiple-instance learning (MIL) problem with unbalanced data: i.e., the training data typically consists of a few positive bags, and a very large number of negative instances. Existing MIL algorithms are much too computationally expensive for these datasets. We describe CH, a framework for learning a Convex Hull representation of multiple instances that is significantly faster than existing MIL algorithms. Our CH framework applies to any standard hyperplane-based learning algorithm, and for some algorithms, is guaranteed to find the global optimal solution. Experimental studies on two different CAD applications further demonstrate that the proposed algorithm significantly improves diagnostic accuracy when compared to both MIL and traditional classifiers.

This paper introduces timeline trees, which are partial models of partially observable environments. Timeline trees are given some specific predictions to make and learn a decision tree over history. The main idea of timeline trees is to use temporally abstract features to identify and split on features of key events, spread arbitrarily far apart in the past (whereas previous decision-tree-based methods have been limited to a finite suffix of history). Experiments demonstrate that timeline trees can learn to make high quality predictions in complex, partially observable environments with high-dimensional observations (e.g. an arcade game).

In this note, we establish the hardness of approximation of the problem of computing the minimal size of a $\delta$-sufficient reason for decision trees.

The recent boom in AI has clearly shown the power of deep neural networks in various tasks, especially in the field of classification problems where the data is high-dimensional and has complex, non-linear relationships with the target variables. However, explaining the decisions of any neural classifier is an incredibly hard problem. While many post-hoc methods such as DeepLift [2] and Layer-Wise Relevance Propagation [3] can help with explaining individual decisions, explaining the global decision mechanisms (or what the model generally looks for) is much more difficult. Because of this, many practitioners in high-stakes fields instead opt for more interpretable models like basic Decision Trees since the decision hierarchy can be clearly visualized and understood by stakeholders. However, basic trees by themselves often do not provide enough accuracy for the task at hand and often ensemble methods like Bagging or Boosting are used to improve the model's performance.

Counterfactual fairness alleviates the discrimination between the model prediction toward an individual in the actual world (observational data) and that in counterfactual world (i.e., what if the individual belongs to other sensitive groups). The existing studies need to pre-define the structural causal model that captures the correlations among variables for counterfactual inference; however, the underlying causal model is usually unknown and difficult to be validated in real-world scenarios. Moreover, the misspecification of the causal model potentially leads to poor performance in model prediction and thus makes unfair decisions. In this research, we propose a novel minimax game-theoretic model for counterfactual fairness that can produce accurate results meanwhile achieve a counterfactually fair decision with the relaxation of strong assumptions of structural causal models. In addition, we also theoretically prove the error bound of the proposed minimax model. Empirical experiments on multiple real-world datasets illustrate our superior performance in both accuracy and fairness. Source code is available at \url{https://github.com/tridungduong16/counterfactual_fairness_game_theoretic}.

Data-driven artificial intelligence models require explainability in intelligent manufacturing to streamline adoption and trust in modern industry. However, recently developed explainable artificial intelligence (XAI) techniques that estimate feature contributions on a model-agnostic level such as SHapley Additive exPlanations (SHAP) have not yet been evaluated for semi-supervised fault diagnosis and prognosis problems characterized by class imbalance and weakly labeled datasets. This paper explores the potential of utilizing Shapley values for a new clustering framework compatible with semi-supervised learning problems, loosening the strict supervision requirement of current XAI techniques. This broad methodology is validated on two case studies: a heatmap image dataset obtained from a semiconductor manufacturing process featuring class imbalance, and a benchmark dataset utilized in the 2021 Prognostics and Health Management (PHM) Data Challenge. Semi-supervised clustering based on Shapley values significantly improves upon clustering quality compared to the fully unsupervised case, deriving information-dense and meaningful clusters that relate to underlying fault diagnosis model predictions. These clusters can also be characterized by high-precision decision rules in terms of original feature values, as demonstrated in the second case study. The rules, limited to 1-2 terms utilizing original feature scales, describe 12 out of the 16 derived equipment failure clusters with precision exceeding 0.85, showcasing the promising utility of the explainable clustering framework for intelligent manufacturing applications.