This paper mainly tends to investigate finite-time stability and stabilization of impulsive stochastic delayed neural networks with randomly occurring uncertainties (ROUs) and randomly occurring nonlinearities (RONs). Firstly, by constructing the proper Lyapunov-Krasovskii functional and employing the average impulsive interval method, several novel criteria for ensuring the finite-time stability of impulsive stochastic delayed neural networks are obtained by means of linear matrix inequalities (LMIs). Then, some conditions about the state feedback controller are derived to ensure the finite-time stabilization of impulsive stochastic delayed neural networks with ROUs and RONs. Finally, numerical examples are provided to demonstrate the effectiveness and feasibility of the proposed results.

In many scenarios of security analysis, Bayesian methods are often used for assessing harmful factors like attacks, as Bayesian causal model can estimate or predict the effect from the observed factors. To distinguish which ones are direct or significant causal (harmful) factors to the target systems, we often need to calculate a (local) causal network, but the existing methods usually return Markov equivalence classes instead of an actual causal structure. In this paper, a new approach for inferring causal direction from multidimensional causal networks for assessing harmful factors in security analysis is proposed based on a split-and-merge strategy. The method first decomposes an n-dimensional network into induced subnetworks, each of which corresponds to a node in the network. We show that each induced subnetwork can be subsumed into one of the three substructures: one-degree, non-triangle, and triangle-existence substructures. Three effective algorithms are developed to infer causalities from the three substructures. The whole causal structure of the multi-dimensional network is obtained by learning these induced subnetworks separately. Experimental results demonstrate that our method is more general and effective than the state-of-the-art methods.

Exploring and detecting the causal relations among variables have shown huge practical values in recent years, with numerous opportunities for scientific discovery, and have been commonly seen as the core of data science. Among all possible causal discovery methods, causal discovery based on a constraint approach could recover the causal structures from passive observational data in general cases, and had shown extensive prospects in numerous real world applications. However, when the graph was sufficiently large, it did not work well. To alleviate this problem, an improved causal structure learning algorithm named brain storm optimization (BSO), is presented in this paper, combining K2 with brain storm optimization (K2-BSO). Here BSO is used to search optimal topological order of nodes instead of graph space. This paper assumes that dataset is generated by conforming to a causal diagram in which each variable is generated from its parent based on a causal mechanism. We designed an elaborate distance function for clustering step in BSO according to the mechanism of K2. The graph space therefore was reduced to a smaller topological order space and the order space can be further reduced by an efficient clustering method. The experimental results on various real-world datasets showed our methods outperformed the traditional search and score methods and the state-of-the-art genetic algorithm-based methods.

In the problem of causal discovery, conditional independence (CI) tests are generally used to detect the causal relationships among observed data. Due to the curse of dimensionality and the limitation of causal direction learning based on V -structure learning, it is difficult for constraint-based methods to distinguish the actual graph from a set of Markov equivalence classes. To alleviate this problem, in this work, a novel regression-based method to test CIs over linear Non-Gaussian data is proposed. The main purpose of this proposal is to relax the CI test of x±yǀZ to two unconditional independence tests x – f (Z)±y – g (Z) + ∑H (Z) and x – f (Z) + ∑H (Z)±y – g (Z), where f and g can be estimated by linear regression independently. In addition, we further show that x – f (Z)±y – g (Z) + ∑H (Z) ( or x – f (Z) + ∑H (Z)±y – g (Z) ) can lead to x← Z ( or y ← Z ). According to this regression-based method, we design a causal structure learning algorithm to learn the actual graph instead of a set of Markov equivalence classes over the observed data. Experiments indicate that our method can detect much more causal relationships than other existing methods, especially in large-scale cases.

The brain storm optimization (BSO) algorithm has received increased attention in the field of evolutionary computation. While BSO has been applied in numerous industrial scenarios due to its effectiveness and accessibility, there are few theoretical analysis results about its running time. Running-time analysis can be conducted through the estimation of the upper bounds of the expected first hitting time to evaluate the efficiency of BSO. This study estimates the upper bounds of the expected first hitting time on six single individual BSO variants (BSOs with one individual) based on the average gain model. The theoretical analysis indicates the following results. (1) The time complexity of the six BSO variants is $\mathrm{O}\left(\sqrt{n}\right)$ in equal coefficient linear functions regardless of the presence or absence of the disrupting operator, where n is the number of the dimensions. Moreover, the coefficient of the upper bounds on the expected first hitting time shows that the single individual BSOs with the disrupting operator require fewer iterations to obtain the target solution than the single individual BSOs without the disrupting operator. (2) The upper bounds on the expected first hitting time of single individual BSOs with the standard normally distributed mutation operator are lower than those of BSOs with the uniformly distributed mutation operator. (3) The upper bounds on the expected first hitting time of single individual BSOs with the $U\left(-\frac{1}{2},\frac{1}{2}\right)$ mutation operator are approximately twice those of BSOs with the $U(-1,1)$ mutation operator. The corresponding numerical results are also consistent with the theoretical analysis results.