# Unbiased Estimating Equation on Inverse Divergence and Its Conditions

arXiv: https://arxiv.org/abs/2404.16519 · HTML: https://mlsanity.com/paper/2404.16519/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 25 references that are in the map.
- First posted on arXiv 25 Apr 2024.

## Builds on (most cited first, 5 of 5)

- [Pseudo-Spherical Contrastive Divergence](https://mlsanity.com/paper/2111.00780/) (2021)
- [The B-Exponential Divergence and its Generalizations with Applications to Parametric Estimation](https://mlsanity.com/paper/1810.11721/) (2018)
- [Generalized Dirichlet-process-means for f-separable distortion measures](https://mlsanity.com/paper/1901.11331/) (2019)
- [Robust Inference Using the Exponential-Polynomial Divergence](https://mlsanity.com/paper/2012.11735/) (2020)
- [Minimizing robust density power-based divergences for general parametric density models](https://mlsanity.com/paper/2307.05251/) (2023)

## Abstract (arXiv)

This paper focuses on the Bregman divergence defined by the reciprocal function, called the inverse divergence. For the loss function defined by the monotonically increasing function f and inverse divergence, the conditions for the statistical model and function f under which the estimating equation is unbiased are clarified. Specifically, we characterize two types of statistical models, an inverse Gaussian type and a mixture of generalized inverse Gaussian type distributions, to show that the conditions for the function f are different for each model. We also define Bregman divergence as a linear sum over the dimensions of the inverse divergence and extend the results to the multi-dimensional case.