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Directed acyclic graphs are widely used to describe directional pairwise relations. Such relations are estimated by reconstructing a directed acyclic graph's structure, which is challenging when the ordering of nodes of the graph is unknown. In such a situation, existing methods such as the neighbourhood and search-and-score methods have high estimation errors or computational complexities, especially when a local or sequential approach is used to enumerate edge directions by testing or optimizing a criterion locally, as a local method may break down even for moderately sized graphs. We propose a novel approach to simultaneously identifying all estimable directed edges and model parameters, using constrained maximum likelihood with nonconvex constraints. We develop a constraint reduction method that constructs a set of active constraints from super-exponentially many constraints. This, coupled with an alternating direction method of multipliers and a difference convex method, permits efficient computation for large-graph learning. We show that the proposed method consistently reconstructs identifiable directions of the true graph and achieves the optimal performance in terms of parameter estimation. Numerically, the method compares favourably with competitors. A protein network is analysed to demonstrate that the proposed method can make a difference in identifying the network's structure. [ABSTRACT FROM AUTHOR]

Location awareness has become one of the most popular areas for mobile internet applications. Normally, the method of maximum likelihood estimation (MLE) can be used to estimate the position of the unknown nodes. However, when the number of anchor nodes is small within the communication range, the traditional methods cannot work very well. This paper provides a novel location approach to estimate the position by selecting valuable neighbors (both anchor and regular nodes) with Minimized Error Propagation Location method based on Error estimation (MEPLE). The simulation results show that the MEPLE outperforms the MLE overall, especially when the number of anchor nodes is relatively small such as between 10 and 20, MEPLE can reduce 50-80% estimation error on average. [ABSTRACT FROM AUTHOR]

We explore the estimation of uncertainty in evolutionary parameters using a recently devised approach for resampling entire additive genetic variance-covariance matrices ( G). Large-sample theory shows that maximum-likelihood estimates (including restricted maximum likelihood, REML) asymptotically have a multivariate normal distribution, with covariance matrix derived from the inverse of the information matrix, and mean equal to the estimated G. This suggests that sampling estimates of G from this distribution can be used to assess the variability of estimates of G, and of functions of G. We refer to this as the REML- MVN method. This has been implemented in the mixed-model program WOMBAT. Estimates of sampling variances from REML- MVN were compared to those from the parametric bootstrap and from a Bayesian Markov chain Monte Carlo ( MCMC) approach (implemented in the R package MCMCglmm). We apply each approach to evolvability statistics previously estimated for a large, 20-dimensional data set for Drosophila wings. REML- MVN and MCMC sampling variances are close to those estimated with the parametric bootstrap. Both slightly underestimate the error in the best-estimated aspects of the G matrix. REML analysis supports the previous conclusion that the G matrix for this population is full rank. REML- MVN is computationally very efficient, making it an attractive alternative to both data resampling and MCMC approaches to assessing confidence in parameters of evolutionary interest. [ABSTRACT FROM AUTHOR]

The estimation of species trees using multiple loci has become increasingly common. Because different loci can have different phylogenetic histories (reflected in different gene tree topologies) for multiple biological causes, new approaches to species tree estimation have been developed that take gene tree heterogeneity into account. Among these multiple causes, incomplete lineage sorting (ILS), modeled by the multi-species coalescent, is potentially the most common cause of gene tree heterogeneity, and much of the focus of the recent literature has been on how to estimate species trees in the presence of ILS. Despite progress in developing statistically consistent techniques for estimating species trees when gene trees can differ due to ILS, there is substantial controversy in the systematics community as to whether to use the new coalescent-based methods or the traditional concatenation methods. One of the key issues that has been raised is understanding the impact of gene tree estimation error on coalescent-based methods that operate by combining gene trees. Herewe explore the mathematical guarantees of coalescent-based methods when analyzing estimated rather than true gene trees. Our results provide some insight into the differences between promise of coalescent-based methods in theory and their performance in practice. [ABSTRACT FROM AUTHOR]