Causal structure learning, also known as causal discovery, aims to estimate causal relationships between variables as a form of a causal directed acyclic graph (DAG) from observational data. One of the major frameworks is the order-based approach that first estimates a topological order of the underlying DAG and then prunes spurious edges from the fully-connected DAG induced by the estimated topological order. Previous studies often focus on the former ordering step because it can dramatically reduce the search space of DAGs. In practice, the latter pruning step is equally crucial for ensuring both computational efficiency and estimation accuracy. Most existing methods employ a pruning technique based on generalized additive models and hypothesis testing, commonly known as CAM-pruning. However, this approach can be a computational bottleneck as it requires repeatedly fitting additive models for all variables. Furthermore, it may harm estimation quality due to multiple testing. To address these issues, we introduce a new pruning method based on sparse additive models, which enables direct pruning of redundant edges without relying on hypothesis testing. We propose an efficient algorithm for learning sparse additive models by combining the randomized tree embedding technique with group-wise sparse regression. Experimental results on both synthetic and real datasets demonstrated that our method is significantly faster than existing pruning methods while maintaining comparable or superior accuracy.

Causal discovery from observational data is a fundamental tool in various fields of science. While existing approaches are typically designed for a single dataset, we often need to handle multiple datasets with non-identical variable sets in practice. One straightforward approach is to estimate a causal graph from each dataset and construct a single causal graph by overlapping. However, this approach identifies limited causal relationships because unobserved variables in each dataset can be confounders, and some variable pairs may be unobserved in any dataset. To address this issue, we leverage Causal Additive Models with Unobserved Variables (CAM-UV) that provide causal graphs having information related to unobserved variables. We show that the ground truth causal graph has structural consistency with the information of CAM-UV on each dataset. As a result, we propose an approach named I-CAM-UV to integrate CAM-UV results by enumerating all consistent causal graphs. We also provide an efficient combinatorial search algorithm and demonstrate the usefulness of I-CAM-UV against existing methods.

Algorithmic recourse aims to provide a recourse action for altering an unfavorable prediction given by a model into a favorable one (e.g., loan approval). In practice, it is also desirable to ensure that an action makes the real-world outcome better (e.g., loan repayment). We call this requirement improvement. Unfortunately, existing methods cannot ensure improvement unless we know the true oracle. To address this issue, we propose a framework for suggesting improvement-oriented actions from a long-term perspective. Specifically, we introduce a new online learning task of assigning actions to a given sequence of instances. We assume that we can observe delayed feedback on whether the past suggested action achieved improvement. Using the feedback, we estimate an action that can achieve improvement for each instance. To solve this task, we propose two approaches based on contextual linear bandit and contextual Bayesian optimization. Experimental results demonstrated that our approaches could assign improvement-oriented actions to more instances than the existing methods.

This paper proposes a new algorithm for learning gradient boosted decision trees while ensuring the existence of recourse actions. Algorithmic recourse aims to provide a recourse action for altering the undesired prediction result given by a model. While existing studies often focus on extracting valid and executable actions from a given learned model, such reasonable actions do not always exist for models optimized solely for predictive accuracy. To address this issue, recent studies proposed a framework for learning a model while guaranteeing the existence of reasonable actions with high probability. However, these methods can not be applied to gradient boosted decision trees, which are renowned as one of the most popular models for tabular datasets. We propose an efficient gradient boosting algorithm that takes recourse guarantee into account, while maintaining the same time complexity as the standard ones. We also propose a post-processing method for refining a learned model under the constraint of a recourse guarantee and provide a PAC-style analysis of the refined model. Experimental results demonstrated that our method successfully provided reasonable actions to more instances than the baselines without significantly degrading accuracy and computational efficiency.

Bayesian networks can deduce statistical causal relationships from observed data. When applied to a large-scale health and medical dataset, it becomes feasible to employ the deduced networks to identify potential factors related to disease onset. Factors contributing to the onset of lifestyle-related diseases, such as the social environment and habits, vary significantly among individuals. Thus, it can be hypothesized that networks illustrating disease onset mechanisms would also exhibit substantial diversity. However, typical statistical causal discovery methods challenge the analysis of relationships specific to the sub-groups in a dataset because they use the entire data. In response to this, we use a pattern mining technique for Iwaki Health Promotion Project Health Checkup data to derive subgroups exhibiting strong correlations with the target variables. We estimated the Bayesian networks for the characteristic subgroups out of those derived, and compared them with the Bayesian network estimated for the total (hereafter, base network). Our target was the onset of eight lifestyle-related diseases within three years, resulting in a total of 359 subgroups. By comparing the estimated subgroup networks with the base network, we confirmed the numerous relationships specific to the subgroup networks. These encompassed not only clinically known but also non-trivial relationships. Our approach, which uses target-wise correlation-based rule subgrouping and network estimation is beneficial for constructing hypotheses on the differences in disease onset causes among potential subgroups.

This paper proposes a new algorithm for learning accurate tree-based models while ensuring the existence of recourse actions. Algorithmic Recourse (AR) aims to provide a recourse action for altering the undesired prediction result given by a model. Typical AR methods provide a reasonable action by solving an optimization task of minimizing the required effort among executable actions. In practice, however, such actions do not always exist for models optimized only for predictive performance. To alleviate this issue, we formulate the task of learning an accurate classification tree under the constraint of ensuring the existence of reasonable actions for as many instances as possible. Then, we propose an efficient top-down greedy algorithm by leveraging the adversarial training techniques. We also show that our proposed algorithm can be applied to the random forest, which is known as a popular framework for learning tree ensembles. Experimental results demonstrated that our method successfully provided reasonable actions to more instances than the baselines without significantly degrading accuracy and computational efficiency.

Machine learning models need to be continually updated or corrected to ensure that the prediction accuracy remains consistently high. In this study, we consider scenarios where developers should be careful to change the prediction results by the model correction, such as when the model is part of a complex system or software. In such scenarios, the developers want to control the specification of the corrections. To achieve this, the developers need to understand which subpopulations of the inputs get inaccurate predictions by the model. Therefore, we propose correction rule mining to acquire a comprehensive list of rules that describe inaccurate subpopulations and how to correct them. We also develop an efficient correction rule mining algorithm that is a combination of frequent itemset mining and a unique pruning technique for correction rules. We observed that the proposed algorithm found various rules which help to collect data insufficiently learned, directly correct model outputs, and analyze concept drift.

In practical machine learning, models are frequently updated, or corrected, to adapt to new datasets. In this study, we pose two challenges to model correction. First, the effects of corrections to the end-users need to be described explicitly, similar to standard software where the corrections are described as release notes. Second, the amount of corrections need to be small so that the corrected models perform similarly to the old models. In this study, we propose the first model correction method for classification models that resolves these two challenges. Our idea is to use an additional decision tree to correct the output of the old models. Thanks to the explainability of decision trees, the corrections are describable to the end-users, which resolves the first challenge. We resolve the second challenge by incorporating the amount of corrections when training the additional decision tree so that the effects of corrections to be small. Experiments on real data confirm the effectiveness of the proposed method compared to existing correction methods.

Counterfactual Explanation (CE) is a post-hoc explanation method that provides a perturbation for altering the prediction result of a classifier. An individual can interpret the perturbation as an "action" to obtain the desired decision results. Existing CE methods focus on providing an action, which is optimized for a given single instance. However, these CE methods do not address the case where we have to assign actions to multiple instances simultaneously. In such a case, we need a framework of CE that assigns actions to multiple instances in a transparent and consistent way. In this study, we propose Counterfactual Explanation Tree (CET) that assigns effective actions with decision trees. Due to the properties of decision trees, our CET has two advantages: (1) Transparency: the reasons for assigning actions are summarized in an interpretable structure, and (2) Consistency: these reasons do not conflict with each other. We learn a CET in two steps: (i) compute one effective action for multiple instances and (ii) partition the instances to balance the effectiveness and interpretability. Numerical experiments and user studies demonstrated the efficacy of our CET in comparison with existing methods.

In any given machine learning problem, there may be many models that could explain the data almost equally well. However, most learning algorithms return only one of these models, leaving practitioners with no practical way to explore alternative models that might have desirable properties beyond what could be expressed within a loss function. The Rashomon set is the set of these all almost-optimal models. Rashomon sets can be extremely complicated, particularly for highly nonlinear function classes that allow complex interaction terms, such as decision trees. We provide the first technique for completely enumerating the Rashomon set for sparse decision trees; in fact, our work provides the first complete enumeration of any Rashomon set for a non-trivial problem with a highly nonlinear discrete function class. This allows the user an unprecedented level of control over model choice among all models that are approximately equally good. We represent the Rashomon set in a specialized data structure that supports efficient querying and sampling. We show three applications of the Rashomon set: 1) it can be used to study variable importance for the set of almost-optimal trees (as opposed to a single tree), 2) the Rashomon set for accuracy enables enumeration of the Rashomon sets for balanced accuracy and F1-score, and 3) the Rashomon set for a full dataset can be used to produce Rashomon sets constructed with only subsets of the data set. Thus, we are able to examine Rashomon sets across problems with a new lens, enabling users to choose models rather than be at the mercy of an algorithm that produces only a single model.

Post-hoc explanation methods for machine learning models have been widely used to support decision-making. One of the popular methods is Counterfactual Explanation (CE), also known as Actionable Recourse, which provides a user with a perturbation vector of features that alters the prediction result. Given a perturbation vector, a user can interpret it as an "action" for obtaining one's desired decision result. In practice, however, showing only a perturbation vector is often insufficient for users to execute the action. The reason is that if there is an asymmetric interaction among features, such as causality, the total cost of the action is expected to depend on the order of changing features. Therefore, practical CE methods are required to provide an appropriate order of changing features in addition to a perturbation vector. For this purpose, we propose a new framework called Ordered Counterfactual Explanation (OrdCE). We introduce a new objective function that evaluates a pair of an action and an order based on feature interaction. To extract an optimal pair, we propose a mixed-integer linear optimization approach with our objective function. Numerical experiments on real datasets demonstrated the effectiveness of our OrdCE in comparison with unordered CE methods.

Counterfactual Explanation (CE) is one of the post-hoc explanation methods that provides a perturbation vector so as to alter the prediction result obtained from a classifier. Users can directly interpret the perturbation as an "action" for obtaining their desired decision results. However, an action extracted by existing methods often becomes unrealistic for users because they do not adequately care about the characteristics corresponding to the empirical data distribution such as feature-correlations and outlier risk. To suggest an executable action for users, we propose a new framework of CE for extracting an action by evaluating its reality on the empirical data distribution. The key idea of our proposed method is to define a new cost function based on the Mahalanobis' distance and the local outlier factor. Then, we propose a mixed-integer linear optimization approach to extracting an optimal action by minimizing our cost function. By experiments on real datasets, we confirm the effectiveness of our method in comparison with existing methods for CE.

The suffix trees are fundamental data structures for various kinds of string processing. The suffix tree of a string T of length n has O(n) nodes and edges, and the string label of each edge is encoded by a pair of positions in T. Thus, even after the tree is built, the input text T needs to be kept stored and random access to T is still needed. The linear-size suffix tries (LSTs), proposed by Crochemore et al. [Linear-size suffix tries, TCS 638:171-178, 2016], are a "stand-alone" alternative to the suffix trees. Namely, the LST of a string T of length n occupies O(n) total space, and supports pattern matching and other tasks in the same efficiency as the suffix tree without the need to store the input text T. Crochemore et al. proposed an offline algorithm which transforms the suffix tree of T into the LST of T in O(n log sigma) time and O(n) space, where sigma is the alphabet size. In this paper, we present two types of online algorithms which "directly" construct the LST, from right to left, and from left to right, without constructing the suffix tree as an intermediate structure. Both algorithms construct the LST incrementally when a new symbol is read, and do not access to the previously read symbols. The right-to-left construction algorithm works in O(n log sigma) time and O(n) space and the left-to-right construction algorithm works in O(n (log sigma + log n / log log n)) time and O(n) space. The main feature of our algorithms is that the input text does not need to be stored.

We analyze the grammar generation algorithm of the RePair compression algorithm and show the relation between a grammar generated by RePair and maximal repeats. We reveal that RePair replaces step by step the most frequent pairs within the corresponding most frequent maximal repeats. Then, we design a novel variant of RePair, called MR-RePair, which substitutes the most frequent maximal repeats at once instead of substituting the most frequent pairs consecutively. We implemented MR-RePair and compared the size of the grammar generated by MR-RePair to that by RePair on several text corpora. Our experiments show that MR-RePair generates more compact grammars than RePair does, especially for highly repetitive texts.

We consider fully-online construction of indexing data structures for multiple texts. Let T = {T_1, ..., T_K} be a collection of texts. By fully-online, we mean that a new character can be appended to any text in T at any time. This is a natural generalization of semi-online construction of indexing data structures for multiple texts in which, after a new character is appended to the kth text T_k, then its previous texts T_1, ..., T_k-1 will remain static. Our fully-online scenario arises when we maintain dynamic indexes for multi-sensor data. Let N and sigma denote the total length of texts in T and the alphabet size, respectively. We first show that the algorithm by Blumer et al. [Theoretical Computer Science, 40:31-55, 1985] to construct the directed acyclic word graph (DAWG) for T can readily be extended to our fully-online setting, retaining O(N log sigma)-time and O(N)-space complexities. Then, we give a sophisticated fully-online algorithm which constructs the suffix tree for T in O(N log sigma) time and O(N) space. A key idea of this algorithm is synchronized maintenance of the DAWG and the suffix tree.