Bregman divergence based em algorithm and its application to classical and quantum rate distortion theory
arXiv:2201.02447 · doi:10.1109/TIT.2023.3239955
Abstract
We formulate em algorithm in the framework of Bregman divergence, which is a general problem setting of information geometry. That is, we address the minimization problem of the Bregman divergence between an exponential subfamily and a mixture subfamily in a Bregman divergence system. Then, we show the convergence and its speed under several conditions. We apply this algorithm to rate distortion and its variants including the quantum setting, and show the usefulness of our general algorithm. In fact, existing applications of Arimoto-Blahut algorithm to rate distortion theory make the optimization of the weighted sum of the mutual information and the cost function by using the Lagrange multiplier. However, in the rate distortion theory, it is needed to minimize the mutual information under the constant constraint for the cost function. Our algorithm directly solves this minimization. In addition, we have numerically checked the convergence speed of our algorithm in the classical case of rate distortion problem.
References in corpus (10)
- Fundamental bound on the reliability of quantum information transmission
- On the strong converses for the quantum channel capacity theorems
- Quantum rate distortion, reverse Shannon theorems, and source-channel separation
- Finite-length Analysis on Tail probability for Markov Chain and Application to Simple Hypothesis Testing
- Uniform Random Number Generation from Markov Chains: Non-Asymptotic and Asymptotic Analyses
- Computing Quantum Channel Capacities
- Squeezing the Arimoto-Blahut algorithm for faster convergence
- Efficient Approximation of Quantum Channel Capacities
- Information Geometry Approach to Parameter Estimation in Markov Chains
- Efficient Approximation of Channel Capacities