Iterative minimization algorithm on a mixture family
arXiv:2302.06905 · doi:10.1007/s41884-024-00140-5
Abstract
Iterative minimization algorithms appear in various areas including machine learning, neural networks, and information theory.The em algorithm is one of the famous iterative minimization algorithms in the area of machine learning, and the Arimoto-Blahut algorithm is a typical iterative algorithm in the area of information theory.However, these two topics had been separately studied for a long time. In this paper, we generalize an algorithm that was recently proposed in the context of the Arimoto-Blahut algorithm.Then, we show various convergence theorems, one of which covers the case when each iterative step is done approximately.Also, we apply this algorithm to the target problem of the em algorithm, and propose its improvement. In addition, we apply it to other various problems in information theory.
References in corpus (9)
- The information bottleneck method
- Exponential decreasing rate of leaked information in universal random privacy amplification
- Secure Multiplex Coding with Dependent and Non-Uniform Multiple Messages
- Quantum wiretap channel with non-uniform random number and its exponent and equivocation rate of leaked information
- Computing Quantum Channel Capacities
- Efficient Approximation of Quantum Channel Capacities
- Bregman divergence based em algorithm and its application to classical and quantum rate distortion theory
- Efficient algorithms for quantum information bottleneck
- Secure list decoding and its application to bit-string commitment