α-Geodesical Skew Divergence

Official PyTorch Implementation of "α-Geodesical Skew Divergence".

[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.

Installation

From PyPi

$ pip install gs_divergence

From GitHub

$ git clone https://github.com/nocotan/geodesical_skew_divergence
$ python setup.py install

Usage

import torch
from gs_divergence import gs_div

a = torch.Tensor([0.1, 0.2, 0.3, 0.4])
b = torch.Tensor([0.2, 0.2, 0.4, 0.2])

div = gs_div(a, b, alpha=-1, lmd=0.5)

Definition of α-Geodesical Skew Divergence

Visualizations of the α-Geodesical Skew Divergence

Monotonicity of the α-geodesical skew divergence with respect to α

Continuity of the α-geodesical skew divergence with respect to α and λ.

Citation

@misc{kimura2021geodesical,
    title={$α$-Geodesical Skew Divergence},
    author={Masanari Kimura and Hideitsu Hino},
    year={2021},
    eprint={2103.17060},
    archivePrefix={arXiv},
    primaryClass={cs.IT}
}