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Density estimation plays a fundamental role in many areas of statistics and machine learning. Parametric, nonparametric, and semiparametric density estimation methods have been proposed in the literature. Semiparametric density models are flexible in incorporating domain knowledge and uncertainty regarding the shape of the density function. Existing literature on semiparametric density models is scattered and lacks a systematic framework. In this article, we consider a unified framework baseddoi:10.6084/m9.figshare.12327953.v2 fatcat:zy23hc3u7nbx3amlgjabomh72m