Since the MPLE objective function for LDFA-H given in Eq. (9) is not guaranteed convex, an EM-algorithm may find a local minimum according to a choice of the initial value. Hence a good initialization is crucial to a successful estimation. According to the equivalence between CCA and probablistic CCA shown by A. Anonymous, it gives (r 1) (r 1) (r 1) (r 1) Lasso problem is solved by the P-GLASSO algorithm by Mazumder et al. (2010). We simulated realistic data with known cross-region connectivity as follows. Notice that the amplitudes of the top four factors dominate the others.

Since the MPLE objective function for LDFA-H given in Eq. (9) is not guaranteed convex, an EM-algorithm may find a local minimum according to a choice of the initial value. Hence a good initialization is crucial to a successful estimation. According to the equivalence between CCA and probablistic CCA shown by A. Anonymous, it gives (r 1) (r 1) (r 1) (r 1) Lasso problem is solved by the P-GLASSO algorithm by Mazumder et al. (2010). We simulated realistic data with known cross-region connectivity as follows. Notice that the amplitudes of the top four factors dominate the others.

This paper has provided global convergence analyses, with convergence rates, of stochastic EM-algorithms which include incremental (iEM) and variance reduced (sEM-VR) versions of EM-algorithms. Especially, the paper has given a convergence rate of O(n/\epsilon) for iEM by applying the theory developed by Miral(2015) and a convergence rate of O(n {2/3}/\epsilon) for sEM-VR by showing sEM-VR is a special case of stochastic scaled-gradient methods. In addition, a new variance reduced EM-algorithm named fiEM based on SAGA has been proposed with its convergence analysis as well as sEM-VR. Finally, the superiority of variance reduced variants (sEM-VR and fiEM) has been shown via numerical experiments. Clarity: The paper is clear and well written.

Parametric policy search algorithms are one of the methods of choice for the optimisation of Markov Decision Processes, with Expectation Maximisation and natural gradient ascent being popular methods in this field. In this article we provide a unifying perspective of these two algorithms by showing that their searchdirections in the parameter space are closely related to the search-direction of an approximate Newton method. This analysis leads naturally to the consideration of this approximate Newton method as an alternative optimisation method for Markov Decision Processes. We are able to show that the algorithm has numerous desirable properties, absent in the naive application of Newton's method, that make it a viable alternative to either Expectation Maximisation or natural gradient ascent. Empirical results suggest that the algorithm has excellent convergence and robustness properties, performing strongly in comparison to both Expectation Maximisation and natural gradient ascent.