Related papers: Iterative minimization algorithm on a mixture fami…
We generalize the generalized Arimoto-Blahut algorithm to a general function defined over Bregman-divergence system. In existing methods, when linear constraints are imposed, each iteration needs to solve a convex minimization. Exploiting…
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…
We generalize the quantum Arimoto-Blahut algorithm by Ramakrishnan et al. (IEEE Trans. IT, 67, 946 (2021)) to a function defined over a set of density matrices with linear constraints so that our algorithm can be applied to optimizations of…
This paper recalls the proximal point method. We study two iterative algorithms: the Blahut-Arimoto algorithm for computing the capacity of arbitrary discrete memoryless channels, as an example of an iterative algorithm working with…
We propose a clustering-based iterative algorithm to solve certain optimization problems in machine learning, where we start the algorithm by aggregating the original data, solving the problem on aggregated data, and then in subsequent…
Mini-batch algorithms have become increasingly popular due to the requirement for solving optimization problems, based on large-scale data sets. Using an existing online expectation-{}-maximization (EM) algorithm framework, we demonstrate…
In this paper, we will present a generalization for a minimization problem from I. Daubechies, M. Defrise, and C. Demol [3]. This generalization is useful for solving many practical problems in which more than one constraint are involved.…
In information theory, the channel capacity, which indicates how efficient a given channel is, plays an important role. The best-used algorithm for evaluating the channel capacity is Arimoto algorithm. This paper aims to reveal an…
The convergence of expectation-maximization (EM)-based algorithms typically requires continuity of the likelihood function with respect to all the unknown parameters (optimization variables). The requirement is not met when parameters…
In this paper, we investigate the convergence speed of the Arimoto-Blahut algorithm. For many channel matrices the convergence is exponential, but for some channel matrices it is slower than exponential. By analyzing the Taylor expansion of…
The Arimoto--Blahut algorithm for computing the capacity of a discrete memoryless channel is revisited. A so-called ``squeezing'' strategy is used to design algorithms that preserve its simplicity and monotonic convergence properties, but…
The EM (Expectation-Maximization) algorithm is regarded as an MM (Majorization-Minimization) algorithm for maximum likelihood estimation of statistical models. Expanding this view, this paper demonstrates that by choosing an appropriate…
Enumeration algorithms have been one of recent hot topics in theoretical computer science. Different from other problems, enumeration has many interesting aspects, such as the computation time can be shorter than the total output size, by…
The Expectation--Maximization (EM) algorithm is a simple meta-algorithm that has been used for many years as a methodology for statistical inference when there are missing measurements in the observed data or when the data is composed of…
Inference for partially observed Markov process models has been a longstanding methodological challenge with many scientific and engineering applications. Iterated filtering algorithms maximize the likelihood function for partially observed…
Finite mixture models have been widely used for the modelling and analysis of data from heterogeneous populations. Maximum likelihood estimation of the parameters is typically carried out via the Expectation-Maximization (EM) algorithm. The…
In recent years, there is a growing need to train machine learning models on a huge volume of data. Designing efficient distributed optimization algorithms for empirical risk minimization (ERM) has therefore become an active and challenging…
We present an iterative Markov chainMonte Carlo algorithm for computingreference priors and minimax risk forgeneral parametric families. Ourapproach uses MCMC techniques based onthe Blahut-Arimoto algorithm forcomputing channel capacity…
Deep learning has excelled on complex pattern recognition tasks such as image classification and object recognition. However, it struggles with tasks requiring nontrivial reasoning, such as algorithmic computation. Humans are able to solve…
Recently, the influence of potentially present symmetries has begun to be studied in complex networks. A typical way of studying symmetries is via the automorphism group of the corresponding graph. Since complex networks are often subject…