  Density power divergence (DPD) is designed to robustly estimate the
underlying distribution of observations, in the presence of outliers. However,
DPD involves an integral of the power of the parametric density models to be
estimated; the explicit form of the integral term can be derived only for
specific densities, such as normal and exponential densities. While we may
perform a numerical integration for each iteration of the optimization
algorithms, the computational complexity has hindered the practical application
of DPD-based estimation to more general parametric densities. To address the
issue, this study introduces a stochastic approach to minimize DPD for general
parametric density models. The proposed approach can also be employed to
minimize other density power-based $\gamma$-divergences, by leveraging
unnormalized models. We provide \verb|R| package for implementation of the
proposed approach in \url{https://github.com/oknakfm/sgdpd}.
