Apesar do nome bem complicado o paper fala de uma modificação do mecanismo do algoritmo de cluster Expectation-Maximization (EM) em que o mesmo tem o incremento de uma meta-heurísica similar ao Simulated Annealing (arrefecimento simulado) para eliminar duas deficiências do EM que é de depender muito dos dados de início (atribuições iniciais) e o fato de que as vezes há problemas de mínimos locais.

**Relaxation of the EM Algorithm via Quantum Annealing for Gaussian Mixture Models**

**Abstract**: We propose a modified expectation-maximization algorithm by introducing the concept of quantum annealing, which we call the deterministic quantum annealing expectation-maximization (DQAEM) algorithm. The expectation-maximization (EM) algorithm is an established algorithm to compute maximum likelihood estimates and applied to many practical applications. However, it is known that EM heavily depends on initial values and its estimates are sometimes trapped by local optima. To solve such a problem, quantum annealing (QA) was proposed as a novel optimization approach motivated by quantum mechanics. By employing QA, we then formulate DQAEM and present a theorem that supports its stability. Finally, we demonstrate numerical simulations to confirm its efficiency.

**Conclusion**: In this paper, we have proposed the deterministic quantum annealing expectation-maximization (DQAEM) algorithm for Gaussian mixture models (GMMs) to relax the problem of local optima of the expectation-maximization (EM) algorithm by introducing the mechanism of quantum fluctuations into EM. Although we have limited our attention to GMMs in this paper to simplify the discussion, the derivation presented in this paper can be straightforwardly applied to any models which have discrete latent variables. After formulating DQAEM, we have presented the theorem that guarantees its convergence. We then have given numerical simulations to show its efficiency compared to EM and DSAEM. It is expect that the combination of DQAEM and DSAEM gives better performance than DQAEM. Finally, one of our future works is a Bayesian extension of this work. In other words, we are going to propose a deterministic quantum annealing variational Bayes inference.

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