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In order to develop reliable services using machine learning, it is important to understand the uncertainty of the model outputs. Often the probability distribution that the prediction target follows has a complex shape, and a mixture distribution is assumed as a distribution that uncertainty follows. Since the output of mixture density estimation is complicated, its interpretability becomes important when considering its use in real services. In this paper, we propose a method for mixture density estimation that utilizes an interpretable tree structure. Further, a fast inference procedure based on time-invariant information cache achieves both high speed and interpretability.