Code for Conformal Mirror Descent (Information Geometry 2022).
Install the requirements into a local virtual environment using:
pip install -r requirements.txt
To run the Student t-distribution example (with k = 3), run the following command:
python student_online.py --k 3
Similarly, the Dirichlet perturbation example can be run with
python dirichlet_perturbation_model.py. The Dirichlet transport
examples in Section 5 can be run with
python dirichlet_transport --name NAME
where NAME can be one of center, dirichlet-1, dirichlet-2 or
random.
If you find this useful, please consider citing:
@Article{kainth2022cmd,
abstract={The logarithmic divergence is an extension of the Bregman divergence motivated by optimal
transport and a generalized convex duality, and satisfies many remarkable properties. Using the geometry
induced by the logarithmic divergence, we introduce a generalization of continuous time mirror descent
that we term the conformal mirror descent. We derive its dynamics under a generalized mirror map, and
show that it is a time change of a corresponding Hessian gradient flow. We also prove convergence results
in continuous time. We apply the conformal mirror descent to online estimation of a generalized
exponential family, and construct a family of gradient flows on the unit simplex via the Dirichlet
optimal transport problem.},
author={Kainth, Amanjit Singh and Wong, Ting-Kam Leonard and Rudzicz, Frank},
doi={10.1007/s41884-022-00089-3},
journal={Information Geometry},
language={en},
month={12},
publisher={Springer Science and Business Media LLC},
title={Conformal mirror descent with logarithmic divergences},
url={http://dx.doi.org/10.1007/s41884-022-00089-3},
year={2022}
}