Search

Bayesian structure learning in Gaussian graphical models is often done by search algorithms over the graph space.The conjugate prior for the precision matrix satisfying graphical constraints is the well-known G-Wishart.With this prior, the transition probabilities in the search algorithms necessitate evaluating the ratios of the prior normalizing constants of G-Wishart.In moderate to high-dimensions, this ratio is often approximated by using sampling-based methods as computationally expensive updates in the search algorithm.Calculating this ratio so far has been a major computational bottleneck.We overcome this issue by representing a search algorithm in which the ratio of normalizing constants is carried out by an explicit closed-form approximation.Using this approximation within our search algorithm yields significant improvement in the scalability of structure learning without sacrificing structure learning accuracy.We study the conditions under which the approximation is valid.We also evaluate the efficacy of our method with simulation studies.We show that the new search algorithm with our approximation outperforms state-of-the-art methods in both computational efficiency and accuracy.The implementation of our work is available in the R package BDgraph. [ABSTRACT FROM AUTHOR]

In this paper, we propose two kernel distribution estimators based on a data transformation. We study the properties of these estimators and we compare them with two conventional estimators. It appears that with an appropriate choice of the parameters of the two proposed estimators, the convergence rate of two estimators will be faster than that of the two conventional estimators and the Mean Integrated Square Error will be smaller than the two conventional estimators. We corroborate these theoretical results through simulations as well as a real data set. [ABSTRACT FROM AUTHOR]

Fuzzy testing is the most effective method for vulnerability mining, which can deal with complex programmes better than other vulnerability mining techniques and has strong scalability. However, in the large-scale vulnerability analysis test, the fuzzy test input sample set faces the challenges of low quality, high repeatability and low availability etc. Therefore, this paper studies the input sample set and proposes heuristic genetic algorithm. By using 0–1 matrix, the genetic algorithm is improved with a consideration of practical problems and the execution path for sample set is selected and compressed through approximation algorithm, thus obtaining a smallest sample set and accelerating the efficiency of fuzzy test. Experimental results show that the proposed method is effective. [ABSTRACT FROM AUTHOR]

This work deals with the robust maximum weighted independent set problem, i.e. finding a subset of graph vertices that are not adjacent to each other and whose sum of weights is as large as possible. Uncertainty in problem formulation is restricted to vertex weights and expressed explicitly by a finite set of scenarios. Three criteria of robustness are considered: absolute robustness (max-min), robust deviation (min-max regret), and relative robustness (relative min-max regret). Since the conventional maximum weighted independent set problem is already NP-hard, finding the exact solution of its robust counterpart should obviously have a prohibitive computational complexity. Therefore, we propose an approximate algorithm for solving the considered robust problem, which is based on evolutionary computing and on various crossover and mutation operators. The algorithm is experimentally evaluated on appropriate problem instances. It is shown that satisfactory solutions can be obtained for any of the three robustness criteria in reasonable time. [ABSTRACT FROM AUTHOR]

This article presents an elementary informal technique for deriving the convergence of known distributions to limiting normal or non-normal distributions. The presentation should be of interest to teachers and students of first year graduate level courses in probability and statistics. [ABSTRACT FROM PUBLISHER]

In this paper, we introduce modified (p, q)-Bernstein-Schurer operators and discuss their statistical approximation properties based on Korovkin's type approximation theorem. We compute the rate of convergence and also prove a Voronovskaja-type theorem. [ABSTRACT FROM AUTHOR]

Many models of interest in the natural and social sciences have no closed-form likelihood function, which means that they cannot be treated using the usual techniques of statistical inference. In the case where such models can be efficiently simulated, Bayesian inference is still possible thanks to the approximate Bayesian computation (ABC) algorithm. Although many refinements have been suggested, ABC inference is still far from routine. ABC is often excruciatingly slow due to very low acceptance rates. In addition, ABC requires introducing a vector of “summary statistics”s(y), the choice of which is relatively arbitrary, and often require some trial and error, making the whole process laborious for the user. We introduce in this work the EP-ABC algorithm, which is an adaptation to the likelihood-free context of the variational approximation algorithm known asexpectation propagation. The main advantage of EP-ABC is that it is faster by a few orders of magnitude than standard algorithms, while producing an overall approximation error that is typically negligible. A second advantage of EP-ABC is that it replaces the usual global ABC constraint ‖s(y) −s(y⋆)‖ ⩽ ϵ, wheres(y⋆) is the vector of summary statistics computed on the whole dataset, bynlocal constraints of the form ‖si(yi) −si(y⋆i)‖ ⩽ ϵ that apply separately to each data point. In particular, it is often possible to takesi(yi) =yi, making it possible to do away with summary statistics entirely. In that case, EP-ABC makes it possible to approximate directly the evidence (marginal likelihood) of the model. Comparisons are performed in three real-world applications that are typical of likelihood-free inference, including one application in neuroscience that is novel, and possibly too challenging for standard ABC techniques. [ABSTRACT FROM AUTHOR]

We consider the problem of approximating a sequence of data points with a 'nearly-isotonic,' or nearly-monotone function. This is formulated as a convex optimization problem that yields a family of solutions, with one extreme member being the standard isotonic regression fit. We devise a simple algorithm to solve for the path of solutions, which can be viewed as a modified version of the well-known pool adjacent violators algorithm, and computes the entire path in O( n log n) operations ( n being the number of data points). In practice, the intermediate fits can be used to examine the assumption of monotonicity. Nearly-isotonic regression admits a nice property in terms of its degrees of freedom: at any point along the path, the number of joined pieces in the solution is an unbiased estimate of its degrees of freedom. We also extend the ideas to provide 'nearly-convex' approximations. [ABSTRACT FROM AUTHOR]

This note considers the single-machine total weighted tardiness problem. Three new heuristic algorithms are suggested and compared with other competing heuristics from the literature, such as Apparent Tardiness Cost, Weighted Covert and Weighted Modified Due Date. The experimental tests show that the suggested heuristic algorithms outperform the existing heuristics. [ABSTRACT FROM AUTHOR]

The generalized robust colouring problem (GRCP) deals with a robust colouring for a given graph with a fixed number of colours, not necessarily the chromatic number and considers the distance between colours as the penalization of complementary edges. This problem provides a way to solve timetabling problems that consider 'event spread constraints' such as 'there must be at least d days between two events'. Because this problem is NP-hard, a heuristic approach is necessary to produce good solutions in a reasonable amount of time for large instances. In this work a greedy randomized adaptive search procedure (GRASP) is proposed to solve GRCP, which was used in instances to schedule course lectures requiring from 30 to 120 h per week in total, in which the bound of the optimal solution is reached in almost every instance. [ABSTRACT FROM AUTHOR]

The author discusses weighted average derivatives estimation and dimension asymptomatics and semiparametrics. The author states that the average derivatives estimation offers new first-order asymptomatic approximation according to quadratic expansion of the estimating equation. He also focuses on the jackknife methodology.