Kento Uemura

Shuyu Dong, Kento Uemura, Akito Fujii et al.

Learning causal structures from observational data is a fundamental problem facing important computational challenges when the number of variables is large. In the context of linear structural equation models (SEMs), this paper focuses on learning causal structures from the inverse covariance matrix. The proposed method, called ICID for Independence-preserving Decomposition from Inverse Covariance matrix, is based on continuous optimization of a matrix decomposition model that preserves the nonzero patterns of the inverse covariance matrix. Through theoretical and empirical evidences, we show that ICID efficiently identifies the sought directed acyclic graph (DAG) assuming the knowledge of noise variances. Moreover, ICID is shown empirically to be robust under bounded misspecification of noise variances in the case where the noise variances are non-equal. The proposed method enjoys a low complexity, as reflected by its time efficiency in the experiments, and also enables a novel regularization scheme that yields highly accurate solutions on the Simulated fMRI data (Smith et al., 2011) in comparison with state-of-the-art algorithms.

Shuyu Dong, Michèle Sebag, Kento Uemura et al.

Causal learning tackles the computationally demanding task of estimating causal graphs. This paper introduces a new divide-and-conquer approach for causal graph learning, called DCILP. In the divide phase, the Markov blanket MB($X_i$) of each variable $X_i$ is identified, and causal learning subproblems associated with each MB($X_i$) are independently addressed in parallel. This approach benefits from a more favorable ratio between the number of data samples and the number of variables considered. In counterpart, it can be adversely affected by the presence of hidden confounders, as variables external to MB($X_i$) might influence those within it. The reconciliation of the local causal graphs generated during the divide phase is a challenging combinatorial optimization problem, especially in large-scale applications. The main novelty of DCILP is an original formulation of this reconciliation as an integer linear programming (ILP) problem, which can be delegated and efficiently handled by an ILP solver. Through experiments on medium to large scale graphs, and comparisons with state-of-the-art methods, DCILP demonstrates significant improvements in terms of computational complexity, while preserving the learning accuracy on real-world problem and suffering at most a slight loss of accuracy on synthetic problems.

Kentaro Kanamori, Takuya Takagi, Ken Kobayashi et al.

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.