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 also can be employed to minimize other density power-based $\gamma$-divergences, by leveraging unnormalized models.

翻译：密度幂散度（DPD）旨在存在异常值的情况下鲁棒地估计观测数据的潜在分布。然而，DPD涉及待估计参数密度模型幂次的积分；该积分项的显式形式仅能针对特定密度（如正态分布和指数分布）推导得出。尽管我们可以在优化算法的每次迭代中进行数值积分，但计算复杂度阻碍了基于DPD的估计方法在实际中应用于更一般的参数密度。为解决这一问题，本研究引入一种随机化方法，用于最小化一般参数密度模型下的DPD。该方法还可通过利用非归一化模型，最小化其他基于密度幂的$\gamma$-散度。