Adaptive MCMC with online relabeling

When targeting a distribution that is artificially invariant under some permutations, Markov chain Monte Carlo (MCMC) algorithms face the label-switching problem, rendering marginal inference particularly cumbersome. Such a situation arises, for example, in the Bayesian analysis of finite mixture models. Adaptive MCMC algorithms such as adaptive Metropolis (AM), which self-calibrates its proposal distribution using an online estimate of the covariance matrix of the target, are no exception. To address the label-switching issue, relabeling algorithms associate a permutation to each MCMC sample, trying to obtain reasonable marginals. In the case of adaptive Metropolis (Bernoulli 7 (2001) 223-242), an online relabeling strategy is required. This paper is devoted to the AMOR algorithm, a provably consistent variant of AM that can cope with the label-switching problem. The idea is to nest relabeling steps within the MCMC algorithm based on the estimation of a single covariance matrix that is used both for adapting the covariance of the proposal distribution in the Metropolis algorithm step and for online relabeling. We compare the behavior of AMOR to similar relabeling methods. In the case of compactly supported target distributions, we prove a strong law of large numbers for AMOR and its ergodicity. These are the first results on the consistency of an online relabeling algorithm to our knowledge. The proof underlines latent relations between relabeling and vector quantization.Comment: Published at http://dx.doi.org/10.3150/13-BEJ578 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Adaptive Estimation of Distribution Algorithms for Low-Thrust Trajectory Optimization

A direct adaptive scheme is presented as an alternative approach for minimum-fuel low-thrust trajectory design in non-coplanar orbit transfers, utilizing fitness landscape analysis (FLA). Spacecraft dynamics is modeled with respect to modified equinoctial elements, considering $J_2$ orbital perturbations. Taking into account the timings of thrust arcs, the discretization nodes for thrust profile, and the solution of multi-impulse orbit transfer, a constrained continuous optimization problem is formed for low-thrust orbital maneuver. An adaptive method within the framework of Estimation of Distribution Algorithms (EDAs) is proposed, which aims at conserving feasibility of the solutions within the search process. Several problem identifiers for low-thrust trajectory optimization are introduced, and the complexity of the solution domain is analyzed by evaluating the landscape feature of the search space via FLA. Two adaptive operators are proposed, which control the search process based on the need for exploration and exploitation of the search domain to achieve optimal transfers. The adaptive operators are implemented in the presented EDA and several perturbed and non-perturbed orbit transfer problems are solved. Results confirm the effectiveness and reliability of the proposed approach in finding optimal low-thrust transfer trajectories.BEAZ Bizkaia, 3/12/DP/2021/00150; SPRI Group, Ekintzaile Program EK-00112-202

Non-parametric statistical thresholding for sparse magnetoencephalography source reconstructions.

Uncovering brain activity from magnetoencephalography (MEG) data requires solving an ill-posed inverse problem, greatly confounded by noise, interference, and correlated sources. Sparse reconstruction algorithms, such as Champagne, show great promise in that they provide focal brain activations robust to these confounds. In this paper, we address the technical considerations of statistically thresholding brain images obtained from sparse reconstruction algorithms. The source power distribution of sparse algorithms makes this class of algorithms ill-suited to "conventional" techniques. We propose two non-parametric resampling methods hypothesized to be compatible with sparse algorithms. The first adapts the maximal statistic procedure to sparse reconstruction results and the second departs from the maximal statistic, putting forth a less stringent procedure that protects against spurious peaks. Simulated MEG data and three real data sets are utilized to demonstrate the efficacy of the proposed methods. Two sparse algorithms, Champagne and generalized minimum-current estimation (G-MCE), are compared to two non-sparse algorithms, a variant of minimum-norm estimation, sLORETA, and an adaptive beamformer. The results, in general, demonstrate that the already sparse images obtained from Champagne and G-MCE are further thresholded by both proposed statistical thresholding procedures. While non-sparse algorithms are thresholded by the maximal statistic procedure, they are not made sparse. The work presented here is one of the first attempts to address the problem of statistically thresholding sparse reconstructions, and aims to improve upon this already advantageous and powerful class of algorithm

Enhanced localization with adaptive normal distribution transform Monte Carlo localization for map based navigation robot

Map-based navigation is the common navigation method used among the mobile robotic application. The localization plays an important role in the navigation where it estimates the robot position in an environment. Monte Carlo Localization (MCL) is found as the widely used estimation algorithm due to it non-linear characteristic. There are classifications of MCL such as Adaptive MCL (AMCL), Normal Distribution Transform MCL (NDT-MCL) which can perform better than the MCL. However, AMCL is adaptive to particles but the position estimation accuracy is not optimized. NDT-MCL has good position estimation but it requires higher number of particles which results in higher computational effort. The objective of the research is to design and develop a localization algorithm which can achieve better performance in term of position estimation and computational effort. The new MCL algorithm which is named as Adaptive Normal Distribution Transform Monte Carlo Localization (ANDT-MCL) is then designed and developed. It integrates Kullback–Leibler divergence, Normal Distribution Transform and Systematic Resampling into the algorithm. Three experiments are conducted to evaluate the performance of proposed ANDT-MCL in simulated environment. These experiments include evaluating the performance of ANDT-MCL with different path shape, distance and velocity. In the end of the research work, the proposed ANDT-MCL is successfully developed. It is adaptive to the number of particles used, higher position estimation and lower computational effort than existing algorithms. The algorithm can produce better position estimation with less computational effort in any kind paths and is consistent in long journey as well as can outperform in high speed navigation

Multimodal estimation of distribution algorithms

Taking the advantage of estimation of distribution algorithms (EDAs) in preserving high diversity, this paper proposes a multimodal EDA. Integrated with clustering strategies for crowding and speciation, two versions of this algorithm are developed, which operate at the niche level. Then these two algorithms are equipped with three distinctive techniques: 1) a dynamic cluster sizing strategy; 2) an alternative utilization of Gaussian and Cauchy distributions to generate offspring; and 3) an adaptive local search. The dynamic cluster sizing affords a potential balance between exploration and exploitation and reduces the sensitivity to the cluster size in the niching methods. Taking advantages of Gaussian and Cauchy distributions, we generate the offspring at the niche level through alternatively using these two distributions. Such utilization can also potentially offer a balance between exploration and exploitation. Further, solution accuracy is enhanced through a new local search scheme probabilistically conducted around seeds of niches with probabilities determined self-adaptively according to fitness values of these seeds. Extensive experiments conducted on 20 benchmark multimodal problems confirm that both algorithms can achieve competitive performance compared with several state-of-the-art multimodal algorithms, which is supported by nonparametric tests. Especially, the proposed algorithms are very promising for complex problems with many local optima