# α-Geodesical Skew Divergence

arXiv: https://arxiv.org/abs/2103.17060 · HTML: https://mlsanity.com/paper/2103.17060/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 45 references that are in the map.
- First posted on arXiv 31 Mar 2021.

## Builds on (most cited first, 4 of 4)

- [On a generalization of the Jensen-Shannon divergence and the JS-symmetrization of distances relying on abstract means](https://mlsanity.com/paper/1904.04017/) (2019)
- [Generalized Bhattacharyya and Chernoff upper bounds on Bayes error using quasi-arithmetic means](https://mlsanity.com/paper/1401.4788/) (2014)
- [Annealed Importance Sampling with q-Paths](https://mlsanity.com/paper/2012.07823/) (2020)
- [Controllable Dual Skew Divergence Loss for Neural Machine Translation](https://mlsanity.com/paper/1908.08399/) (2019)

## Built on by (most cited first, 6 of 6)

- [On permutation-invariant neural networks](https://mlsanity.com/paper/2403.17410/) (2024)
- [Information Geometrically Generalized Covariate Shift Adaptation](https://mlsanity.com/paper/2304.09387/) (2023)
- [Statistical and Geometrical properties of regularized Kernel Kullback-Leibler divergence](https://mlsanity.com/paper/2408.16543/) (2024)
- [Information Geometry of Dropout Training](https://mlsanity.com/paper/2206.10936/) (2022)
- [Fashion-Specific Attributes Interpretation via Dual Gaussian Visual-Semantic Embedding](https://mlsanity.com/paper/2210.17417/) (2022)
- [Graph-Smoothed Bayesian Black-Box Shift Estimator and Its Information Geometry](https://mlsanity.com/paper/2505.16251/) (2025)

## Abstract (arXiv)

The asymmetric skew divergence smooths one of the distributions by mixing it, to a degree determined by the parameter λ, with the other distribution. Such divergence is an approximation of the KL divergence that does not require the target distribution to be absolutely continuous with respect to the source distribution. In this paper, an information geometric generalization of the skew divergence called the α-geodesical skew divergence is proposed, and its properties are studied.