Minimizing robust density power-based divergences for general parametric density models

As the presence of outliers within observations may adversely affect the statistical inference, robust statistics has been developed for several decades (Huber and Ronchetti, 1981; Hampel et al., 1986; Maronna et al., 2006). Amongst many possible directions, the divergence-based approach, which estimates some parameters in probabilistic models by minimizing the divergence to underlying distributions, has drawn considerable attention owing to its compatibility with the probabilistically formulated problems. In particular, density power divergence (DPD), also known as β-divergence (Basu et al., 1998), extends the Kullback-Leibler divergence to enhance robustness against outliers. DPD has gained recognition as one of the most widely used divergences across disciplines. DPD finds applications in various fields, including blind source separation (Minami and Eguchi, 2002), matrix factorization (Tan and Févotte, 2012), signal processing (Basseville, 2013), Bayesian inference (Ghosh and Basu, 2016), variational inference (Futami et al., 2018), and more, contributing to the enhancement of robustness in these applications.