/Divergence_in_tensors

Primary LanguageMATLAB

Divergence_in_tensors

Alexander Litvinenko, RWTH Aachen, Germany

THE SUBJECT SOFTWARE IS PROVIDED "AS IS" WITHOUT ANY WARRANTY

This project contains numerical examples for this article "Computing f-Divergences and Distances of High-Dimensional Probability Density Functions -- Low-Rank Tensor Approximations", available at https://arxiv.org/abs/2111.07164

The user needs, first, to install TT-Toolbox from here https://github.com/oseledets/TT-Toolbox .

Then to run TT-Toolbox/setup.m

Only after that the user can run single Matlabs files from this repository

The following functionality is available:

  1. Tensor train (TT) approximation of a probability characteristic function (pcf)
  2. TT approximation of a probability density function (pdf)
  3. Computation of the log() function of a pdf and then the KL distance
  4. Computation of the square root of a pdf and then the Hellinger distance

For example:

my_pdf_tensor_ex1.m was used for Example 6.1 and to generate data from Table 5, i.e. for the computation of $D_{H}(\alpha_1,\alpha_2)$ between two \alpha-stable distributions (\alpha=1.5 and \alpha=0.9) for different AMEn tolerances.

my_H2dist_tensor.m was used to compute $D_{H}(\alpha_1,\alpha_2)$ between two \alpha - stable distributions for different dimensions d and resolutions n.

my_KLD_tensor.m was used for computing $D_KL(\alpha_1,\alpha_2)$ between two \alpha-stable distributions for various \alpha with fixed d=8 and n=64.

Other useful files:

KLD_simplified.m computes KLD between two \alpha stable distributions. Different ways are tested and compared with the analyticc solution.

Plese write me an email if you have any questions litvinenko@uq.rwth-aachen.de