TY - GEN

T1 - A Note on the Estimation Method of Intervention Effects based on Statistical Decision Theory

AU - Horii, Shunsuke

AU - Suko, Tota

N1 - Funding Information:
ACKNOWLEDGMENT We would like to acknowledge all members of Matsushima Lab. and Goto Lab. in Waseda Univ. for their helpful suggestions to this work. This research is partially supported by No. 16K00417 of Grant-in-Aid for Scientific Research Category (C) and No. 18H03642 of Grant-in-Aid for Scientific Research Category (A), Japan Society for the Promotion of Science.

PY - 2019/4/16

Y1 - 2019/4/16

N2 - In this paper, we deal with the problem of estimating the intervention effect in the statistical causal analysis using the structural equation model and the causal diagram. The intervention effect is defined as a causal effect on the response variable Y when the causal variable X is fixed to a certain value by an external operation and is defined based on the causal diagram. The intervention effect is defined as a function of the probability distributions in the causal diagram, however, generally these probability distributions are unknown, so it is required to estimate them from data. In other words, the steps of the estimation of the intervention effect using the causal diagram are as follows: 1. Estimate the causal diagram from the data, 2. Estimate the probability distributions in the causal diagram from the data, 3. Calculate the intervention effect. However, if the problem of estimating the intervention effect is formulated in the statistical decision theory framework, estimation with this procedure is not necessarily optimal. In this study, we formulate the problem of estimating the intervention effect for the two cases, the case where the causal diagram is known and the case where it is unknown, in the framework of statistical decision theory and derive the optimal decision method under the Bayesian criterion. We show the effectiveness of the proposed method through numerical simulations.

AB - In this paper, we deal with the problem of estimating the intervention effect in the statistical causal analysis using the structural equation model and the causal diagram. The intervention effect is defined as a causal effect on the response variable Y when the causal variable X is fixed to a certain value by an external operation and is defined based on the causal diagram. The intervention effect is defined as a function of the probability distributions in the causal diagram, however, generally these probability distributions are unknown, so it is required to estimate them from data. In other words, the steps of the estimation of the intervention effect using the causal diagram are as follows: 1. Estimate the causal diagram from the data, 2. Estimate the probability distributions in the causal diagram from the data, 3. Calculate the intervention effect. However, if the problem of estimating the intervention effect is formulated in the statistical decision theory framework, estimation with this procedure is not necessarily optimal. In this study, we formulate the problem of estimating the intervention effect for the two cases, the case where the causal diagram is known and the case where it is unknown, in the framework of statistical decision theory and derive the optimal decision method under the Bayesian criterion. We show the effectiveness of the proposed method through numerical simulations.

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U2 - 10.1109/CISS.2019.8692816

DO - 10.1109/CISS.2019.8692816

M3 - Conference contribution

AN - SCOPUS:85065192272

T3 - 2019 53rd Annual Conference on Information Sciences and Systems, CISS 2019

BT - 2019 53rd Annual Conference on Information Sciences and Systems, CISS 2019

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 53rd Annual Conference on Information Sciences and Systems, CISS 2019

Y2 - 20 March 2019 through 22 March 2019

ER -