We provide a comprehensive study of the convergence of the forward-backwardalgorithm under suitable geometric conditions, such as conditioning or Lojasiewicz properties. These geometrical notions are usually local by...
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We provide a comprehensive study of the convergence of the forward-backwardalgorithm under suitable geometric conditions, such as conditioning or Lojasiewicz properties. These geometrical notions are usually local by nature, and may fail to describe the fine geometry of objective functions relevant in inverse problems and signal processing, that have a nice behaviour on manifolds, or sets open with respect to a weak topology. Motivated by this observation, we revisit those geometric notions over arbitrary sets. In turn, this allows us to present several new results as well as collect in a unified view a variety of results scattered in the literature. Our contributions include the analysis of infinite dimensional convex minimization problems, showing the first Lojasiewicz inequality for a quadratic function associated to a compact operator, and the derivation of new linear rates for problems arising from inverse problems with low-complexity priors. Our approach allows to establish unexpected connections between geometry and a priori conditions in inverse problems, such as source conditions, or restricted isometry properties.
In this paper, we study the backwardforwardalgorithm as a splitting method to solve structured monotone inclusions, and convex minimization problems in Hilbert spaces. It has a natural link with the forwardbackward...
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In this paper, we study the backwardforwardalgorithm as a splitting method to solve structured monotone inclusions, and convex minimization problems in Hilbert spaces. It has a natural link with the forward backward algorithm and has the same computational complexity, since it involves the same basic blocks, but organized differently. Surprisingly enough, this kind of iteration arises when studying the time discretization of the regularized Newton method for maximally monotone operators. First, we show that these two methods enjoy remarkable involutive relations, which go far beyond the evident inversion of the order in which the forward and backward steps are applied. Next, we establish several convergence properties for both methods, some of which were unknown even for the forward backward algorithm. This brings further insight into this well-known scheme. Finally, we specialize our results to structured convex minimization problems, the gradient projection algorithms, and give a numerical illustration of theoretical interest. (C) 2016 Elsevier Inc. All rights reserved.
Mixed hidden Markov models have been recently defined in the literature as an extension of hidden Markov models for dealing with population studies. The notion of mixed hidden Markov models is particularly relevant fo...
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Mixed hidden Markov models have been recently defined in the literature as an extension of hidden Markov models for dealing with population studies. The notion of mixed hidden Markov models is particularly relevant for modeling longitudinal data collected during clinical trials, especially when distinct disease stages can be considered. However, parameter estimation in such models is complex, especially due to their highly nonlinear structure and the presence of unobserved states. Moreover, existing inference algorithms are extremely time consuming when the model includes several random effects. New inference procedures are proposed for estimating population parameters, individual parameters and sequences of hidden states in mixed hidden Markov models. The main contribution consists of a specific version of the stochastic approximation EM algorithm coupled with the Baum-Welch algorithm for estimating population parameters. The properties of this algorithm are investigated via a Monte-Carlo simulation study, and an application of mixed hidden Markov models to the description of daily seizure counts in epileptic patients is presented. (C) 2012 Elsevier B.V. All rights reserved.
The detection of change-points in heterogeneous sequences is a statistical challenge with applications across a wide variety of fields. In bioinformatics, a vast amount of methodology exists to identify an ideal set o...
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The detection of change-points in heterogeneous sequences is a statistical challenge with applications across a wide variety of fields. In bioinformatics, a vast amount of methodology exists to identify an ideal set of change-points for detecting Copy Number Variation (CNV). While considerable efficient algorithms are currently available for finding the best segmentation of the data in CNV, relatively few approaches consider the important problem of assessing the uncertainty of the change-point location. Asymptotic and stochastic approaches exist but often require additional model assumptions to speed up the computations, while exact methods generally have quadratic complexity which may be intractable for large data sets of tens of thousands points or more. A hidden Markov model, with constraints specifically chosen to correspond to a segment-based change-point model, provides an exact method for obtaining the posterior distribution of change-points with linear complexity. The methods are implemented in the R package postCP, which uses the results of a given change-point detection algorithm to estimate the probability that each observation is a change-point. The results include an implementation of postCP on a publicly available CNV data set (n = 120). Due to its frequentist framework, postCP obtains less conservative confidence intervals than previously published Bayesian methods, but with linear complexity instead of quadratic. Simulations showed that postCP provided comparable loss to a Bayesian MCMC method when estimating posterior means, specifically when assessing larger scale changes, while being more computationally efficient. On another high-resolution CNV data set (n = 14,241), the implementation processed information in less than one second on a mid-range laptop computer. (C) 2013 Elsevier B.V. All rights reserved.
In this world of technology, consumption of electrical energy is increasing day by day. Distributed generation is one of the solution for this increased power requirement with minimal power system losses. Distributed ...
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ISBN:
(纸本)9781538681138
In this world of technology, consumption of electrical energy is increasing day by day. Distributed generation is one of the solution for this increased power requirement with minimal power system losses. Distributed generators(DG) cannot place randomly in the network which may lead to reliability issues. This paper proposes a multi-objective algorithm for finding the optimal location and size of DG for radial distribution system, considering two objectives, power loss minimization and voltage stability enhancement. Non-dominated Sorting Genetic algorithms II (NSGA-II) is used to obtain the set of Pareto optimal solutions. The algorithm is tested on IEEE33 bus system to analyse the performance
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