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

arXiv: https://arxiv.org/abs/2307.05251 · HTML: https://mlsanity.com/paper/2307.05251/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 49 references that are in the map.
- First posted on arXiv 11 Jul 2023.

## Builds on (most cited first, 11 of 11)

- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [How to Escape Saddle Points Efficiently](https://mlsanity.com/paper/1703.00887/) (2017)
- [Variational Inference based on Robust Divergences](https://mlsanity.com/paper/1710.06595/) (2017)
- [General Bayesian Loss Function Selection and the use of Improper Models](https://mlsanity.com/paper/2106.01214/) (2021)
- [Adaptation of the Tuning Parameter in General Bayesian Inference with Robust Divergence](https://mlsanity.com/paper/2106.06902/) (2021)
- [Robust sparse Gaussian graphical modeling](https://mlsanity.com/paper/1508.05571/) (2015)
- [Robust Graph Embedding with Noisy Link Weights](https://mlsanity.com/paper/1902.08440/) (2019)
- [Generalized Wald-type Tests based on Minimum Density Power Divergence Estimators](https://mlsanity.com/paper/1403.7616/) (2014)
- [Robust and Sparse Regression in GLM by Stochastic Optimization](https://mlsanity.com/paper/1802.03127/) (2018)
- [Robust Inference for Skewed data in Health Sciences](https://mlsanity.com/paper/1909.10285/) (2019)
- [Minimum Density Power Divergence Estimation for the Generalized Exponential Distribution](https://mlsanity.com/paper/2206.08216/) (2022)

## Built on by (most cited first, 1 of 1)

- [Unbiased Estimating Equation on Inverse Divergence and Its Conditions](https://mlsanity.com/paper/2404.16519/) (2024)

## Abstract (arXiv)

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 γ-divergences, by leveraging unnormalized models. We provide verb|R| package for implementation of the proposed approach in urlhttps://github.com/oknakfm/sgdpd.