
EM Algorithm and Stochastic Control in Economics
Generalising the idea of the classical EM algorithm that is widely used ...
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Relaxation of the EM Algorithm via Quantum Annealing
The EM algorithm is a novel numerical method to obtain maximum likelihoo...
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Geometry of Arimoto Algorithm
This paper aims to reveal information geometric structure of Arimoto alg...
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Convergence of the ForwardBackward Algorithm: Beyond the Worst Case with the Help of Geometry
We provide a comprehensive study of the convergence of forwardbackward ...
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Derivatives of partial eigendecomposition of a real symmetric matrix for degenerate cases
This paper presents the forward and backward derivatives of partial eige...
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Efficient Inference in Markov Control Problems
Markov control algorithms that perform smooth, nongreedy updates of the...
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The MLEM algorithm in continuum: sparse measure solutions
Linear inverse problems A μ = δ with Poisson noise and nonnegative unkn...
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Forward and Backward Bellman equations improve the efficiency of EM algorithm for DECPOMDP
Decentralized partially observable Markov decision process (DECPOMDP) models sequential decision making problems by a team of agents. Since the planning of DECPOMDP can be interpreted as the maximum likelihood estimation for the latent variable model, DECPOMDP can be solved by the EM algorithm. However, in EM for DECPOMDP, the forward–backward algorithm needs to be calculated up to the infinite horizon, which impairs the computational efficiency. In this paper, we propose the Bellman EM algorithm (BEM) and the modified Bellman EM algorithm (MBEM) by introducing the forward and backward Bellman equations into EM. BEM can be more efficient than EM because BEM calculates the forward and backward Bellman equations instead of the forward–backward algorithm up to the infinite horizon. However, BEM cannot always be more efficient than EM when the size of problems is large because BEM calculates an inverse matrix. We circumvent this shortcoming in MBEM by calculating the forward and backward Bellman equations without the inverse matrix. Our numerical experiments demonstrate that the convergence of MBEM is faster than that of EM.
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