Relaxation of the EM algorithm via quantum annealing for Gaussian mixture models

Miyahara, Hidekazu; Tsumura, Koji; Sughiyama, Yuki

doi:10.1109/cdc.2016.7798981

Cited by 3 publications

(5 citation statements)

References 30 publications

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“…Finally we add a non-commutative term H nc = Γσ nc with [σ i ,σ nc ] = 0 to Eq. (38). Obviously, there are many candidates forσ nc ; however, in the numerical simulation, we adoptσ nc = k=1,...,K l=k±1…”

Section: Gaussian Mixture Modelsmentioning

confidence: 99%

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Deterministic quantum annealing expectation-maximization algorithm

Miyahara¹,

Tsumura²,

Sughiyama³

2017

J. Stat. Mech.

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Abstract. Maximum likelihood estimation (MLE) is one of the most important methods in machine learning, and the expectation-maximization (EM) algorithm is often used to obtain maximum likelihood estimates. However, EM heavily depends on initial configurations and fails to find the global optimum. On the other hand, in the field of physics, quantum annealing (QA) was proposed as a novel optimization approach. Motivated by QA, we propose a quantum annealing extension of EM, which we call the deterministic quantum annealing expectation-maximization (DQAEM) algorithm. We also discuss its advantage in terms of the path integral formulation. Furthermore, by employing numerical simulations, we illustrate how it works in MLE and show that DQAEM outperforms EM.

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Section: Gaussian Mixture Modelsmentioning

confidence: 99%

“…, K} 9 . When we work on the one-hot notation [1,2], we can formulate an equivalent quantization scheme [39]. the distribution of the GMM is written as…”

Section: Gaussian Mixture Modelsmentioning

confidence: 99%

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Deterministic quantum annealing expectation-maximization algorithm

Miyahara¹,

Tsumura²,

Sughiyama³

2017

J. Stat. Mech.

Self Cite

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show abstract

“…The Expectation-Maximization (EM) algorithm [13] provides a method for numerically obtaining the maximum likelihood estimates, although the possible multimodality of the likelihood function makes finding the global maximum challenging [4]. Extensions of the EM algorithm have been proposed for improving its speed of convergence and avoiding local optima [14,15].…”

Section: Introductionmentioning

confidence: 99%

Approximate Bayesian computation for finite mixture models

Simola

Cisewski-Kehe

Wolpert

2020

Journal of Statistical Computation and Simulation

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Finite mixture models are used in statistics and other disciplines, but inference for mixture models is challenging due, in part, to the multimodality of the likelihood function and the so-called label switching problem. We propose extensions of the Approximate Bayesian Computation-Population Monte Carlo (ABC-PMC) algorithm as an alternative framework for inference on finite mixture models. There are several decisions to make when implementing an ABC-PMC algorithm for finite mixture models, including the selection of the kernels used for moving the particles through the iterations, how to address the label switching problem and the choice of informative summary statistics. Examples are presented to demonstrate the performance of the proposed ABC-PMC algorithm for mixture modelling. The performance of the proposed method is evaluated in a simulation study and for the popular recessional velocity galaxy data.

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“…The EM algorithm (Dempster et al, 1977) provides a method for numerically retrieving the maximum likelihood estimates, although the possible multimodality of the likelihood function makes finding the global maximum challenging (Marin et al, 2005). Extensions of the EM algorithm have been proposed for improving its speed of convergence and avoiding local optima (Naim and Gildea, 2012;Miyahara et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

Approximate Bayesian Computation for Finite Mixture Models

Simola¹,

Cisewski-Kehe²,

Wolpert³

2018

Preprint

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Finite mixture models are used in statistics and other disciplines, but inference for mixture models is challenging. The multimodality of the likelihood function and the so called label switching problem contribute to the challenge. We propose extensions of the Approximate Bayesian Computation Population Monte-Carlo (ABC-PMC) algorithm as an alternative framework for inference on finite mixture models. There are several decisions to make when implementing an ABC-PMC algorithm for finite mixture models, including the selection of the kernel used for moving the particles through the iterations, how to address the label switching problem and the choice of informative summary statistics. Examples are presented to demonstrate the performance of the proposed ABC-PMC algorithm for mixture modeling.

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Relaxation of the EM algorithm via quantum annealing for Gaussian mixture models

Cited by 3 publications

References 30 publications

Deterministic quantum annealing expectation-maximization algorithm

Deterministic quantum annealing expectation-maximization algorithm

Approximate Bayesian computation for finite mixture models

Approximate Bayesian Computation for Finite Mixture Models

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