Elastic net – based K2 algorithm for Bayesian network structure learning

An empirical comparison of popular structure learning algorithms with a view to gene network inference

Bayesian network is an important model for reasoning in an uncertain environment. A reliable node rank is required by K2 algorithm to learn Bayesian network structure better. To provide a high-quality node rank tailored for K2 algorithm, we propose a node priority-based sorting algorithm. Given observable data only, our algorithm can be employed to learn a node rank without expert knowledge. Specifically, MCMC algorithm is first utilized to yield some Bayesian network structures that can sufficiently fit the observed data. We then define the priority of each node in these network structures. Node rank is finally obtained through weighted scoring based on the priority. The empirical results show that our sorting algorithm performs significantly better than commonly used methods, e.g., randomly sorting and MCMC algorithm, on an Asia network-learning dataset.

A hybrid algorithm for Bayesian network structure learning with application to multi-label learning

Bayesian Network is a knowledge representation formalism that has been proven to be valuable in gene regulatory network reconstruction. However, it is showed that the structure learning of Bayesian networks is an NP-hard problem. Several heuristic searching techniques have been used to find better network structures. Among these algorithms, K2 algorithm has been found to be the most successful. However, the performance of K2 algorithm is greatly affected by a prior ordering of input nodes. If using inappropriate orderings, the accuracy of the learned structures will be relatively low. This paper represents a new structure learning method to reconstruct gene networks from the observational gene expression data. The proposed method is based on Binary Particle Swarm Optimization and K2 algorithm. It firstly identifies nodes ordering from the experimental data by using Binary Particle Swarm Optimization algorithm. Then, the nodes ordering information is used as an input of K2 algorithm so as to improve the performance and efficiency of the K2 algorithm in determining the network structure. Our method is evaluated using two benchmark network datasets with known structures. Experimental studies show that the proposed method can identify networks more efficiently and accurately than comparable methods reported in the literature.

In order to solve the problems that the intelligence algorithm falls into the local optimum easily and has a slow convergence in Bayesian networks (BN) structure learning, an algorithm based on adaptive selection operator with simulated annealing is proposed. This chapter conducts the adaptive selection rule in combination with conditional independence tests of BN nodes to guide the generation of neighbor. In order to better compare the adaptive effect, an algorithm based on selection operator with simulated annealing (SOSA) is proposed; at the same time 15 data sets in the three typical networks are accessed as learning samples. The results of the Bayesian Dirichlet (BD) score, Hamming distance (HD), and evolution time of the network after learning show that it has the quicker convergence and it searches the optimal solution more easily compared with simulated annealing (SA) and SOSA.

The Covid-19 pandemic has an impact on all aspects of life, including the social life of elementary school children. This study aims to determine the effectiveness of the structure learning (SLA) approach to improve teacher competence in independent elementary school students who are rejected in the KKG Kapanewon Sleman area. This research uses quantitative research with pre-experimental method with one group pretest-posttest design which is by comparing the condition before being given treatment and the condition after being given treatment. This study involved 25 teachers who were members of the teacher working group (KKG) in Kapanewon Sleman, Yogyakarta Special Region which was held in July-September 2022. This improvement used the lecture, question and answer, discussion, simulation and project methods. The data collection technique used is observation and the structure learning approach (SLA) scale. While the technical analysis of the data using the Wilcoxon Test. The Structure Learning Approach (SLA) has 5 hierarchical intervention techniques, namely; instruction, modeling, role playing, feedback, and ownwork/applying skills outside the group setting. The results of the implementation of this training based on a pre-post questionnaire showed an increase in pre-post results from an average of 28 to an average of 41.08. While the results of data processing using SPSS obtained the value of Sig. 0.05 this indicates a significant difference between the pretest and posttest. Thus, SLA can increase the independence of rejected elementary school students

Understanding and evaluating directed acyclic graphs (DAGs) is crucial for causal discovery, particularly in high-dimensional and small-sample datasets such as microbial abundance data. This study introduces DAGMetrics, an R package designed to comprehensively evaluate and compare DAGs. The package provides descriptive and comparative metrics, streamlining the assessment of outputs from various structure learning algorithms. It was applied to datasets generated for potato tubers and soils from different terroirs (continental and island) and stages (at harvest and post-harvest). Using a comprehensive set of descriptive and comparative metrics, DAGMetrics facilitated model selection by identifying balanced and robust DAGs. The PC algorithm with Spearman correlation produced DAGs with moderate complexity and high stability across scaling and transformation setups. Additionally, the package enabled detailed exploration of the Markov blanket space, revealing small Markov blankets (up to seven nodes) and numerous isolated nodes. Identified matching edges between Markov blankets across different terroirs and stages aligned with known microbial interactions, highlighting the package’s utility in facilitating the discovery of biologically meaningful relationships. This study illustrates the utility of DAGMetrics in providing objective and reproducible tools for DAG evaluation along with its potential application in agronomic and other domains involving complex structured data.

Towards efficient and effective discovery of Markov blankets for feature selection

Causal learning tackles the computationally demanding task of estimating causal graphs. This paper introduces a new divide-and-conquer approach for causal graph learning, called DCILP. In the divide phase, the Markov blanket MB(Xi) of each variable Xi is identified, and causal learning subproblems associated with each MB(Xi) are independently addressed in parallel. This approach benefits from a more favorable ratio between the number of data samples and the number of variables considered. In counterpart, it can be adversely affected by the presence of hidden confounders, as variables external to MB(Xi) might influence those within it. The reconciliation of the local causal graphs generated during the divide phase is a challenging combinatorial optimization problem, especially in large-scale applications. The main novelty of DCILP is an original formulation of this reconciliation as an integer linear programming (ILP) problem, which can be delegated and efficiently handled by an ILP solver. Through experiments on medium to large scale graphs, and comparisons with state-of-the-art methods, DCILP demonstrates significant improvements in terms of computational complexity, while preserving the learning accuracy on real-world problem and suffering at most a slight loss of accuracy on synthetic problems.

Local search algorithm in ordering space is a good method which can effectively improve the efficiency of bayesian network structure learning. However, the existing algorithms usually have problems such as insufficient order optimization, low learning accuracy, and easy stop at a local optimal. In order to solve these problems, the local search algorithm in ordering space is studied, and a new method to improve the accuracy of bayesian network structure learning by optimizing order search operator is proposed. Combining the iterative local search algorithm with the window operator to search the neighborhood of a given order in the ordering space, the probability of the algorithm falling into the local optimal value is reduced, and the network structure with higher quality is obtained. Experimental results show that comparing with the bayesian network structure learning algorithm in network structure space, the learning efficiency of the present algorithm is improved by 54.12%. Comparing with the bayesian network structure learning algorithm in ordering space, the learning accuracy of the present algorithm is improved by 2.33%.

The recent advances in hardware and software has led to development of applications generating a large amount of data in real-time. To keep abreast with latest trends, learning algorithms need to incorporate novel data continuously. One of the efficient ways is revising the existing knowledge so as to save time and memory. In this paper, we proposed an incremental algorithm for Bayesian network structure learning. It could deal with high dimensional domains, where whole dataset is not completely available, but grows continuously. Our algorithm learns local models by limiting search space and performs a constrained greedy hill-climbing search to obtain a global model. We evaluated our method on different datasets having several hundreds of variables, in terms of performance and accuracy. The empirical evaluation shows that our method is significantly better than existing state of the art methods and justifies its effectiveness for incremental use.

This study was carried out to evaluate the advantage of preselecting SNP markers using Markov blanket algorithm regarding the accuracy of genomic prediction for carcass and meat quality traits in Nellore cattle. This study considered 3675, 3680, 3660 and 524 records of rib eye area (REA), back fat thickness (BF), rump fat (RF), and Warner-Bratzler shear force (WBSF), respectively, from the Nellore Brazil Breeding Program. The animals have been genotyped using low-density SNP panel (30 k), and subsequently imputed for arrays with 777 k SNPs. Four Bayesian specifications of genomic regression models, namely Bayes A, Bayes B, Bayes Cπ and Bayesian Ridge Regression methods were compared in terms of prediction accuracy using a five folds cross-validation. Prediction accuracy for REA, BF and RF was all similar using the Bayesian Alphabet models, ranging from 0.75 to 0.95. For WBSF, the predictive ability was higher using Bayes B (0.47) than other methods (0.39 to 0.42). Although the prediction accuracies using Markov blanket of SNP markers were lower than those using all SNPs, for WBSF the relative gain was lower than 13%. With a subset of informative SNPs markers, identified using Markov blanket, probably, is possible to capture a large proportion of the genetic variance for WBSF. The development of low-density and customized arrays using Markov blanket might be cost-effective to perform a genomic selection for this trait, increasing the number of evaluated animals, improving the management decisions based on genomic information and applying genomic selection on a large scale.

Constructing the structure of protein signaling networks by Bayesian network technology is a key issue in the field of bioinformatics. The primitive structure learning algorithms of the Bayesian network take no account of the causal relationships between variables, which is unfortunately important in the application of protein signaling networks. In addition, as a combinatorial optimization problem with a large searching space, the computational complexities of the structure learning algorithms are unsurprisingly high. Therefore, in this paper, the causal directions between any two variables are calculated first and stored in a graph matrix as one of the constraints of structure learning. A continuous optimization problem is constructed next by using the fitting losses of the corresponding structure equations as the target, and the directed acyclic prior is used as another constraint at the same time. Finally, a pruning procedure is developed to keep the result of the continuous optimization problem sparse. Experiments show that the proposed method improves the structure of the Bayesian network compared with the existing methods on both the artificial data and the real data, meanwhile, the computational burdens are also reduced significantly.

Learning the structure of Bayesian networks (BNs) from high dimensional discrete data is common nowadays but a challenging task, due to the large parameter space, the acyclicity constraint placed on the graphical structures and the difficulty in searching for a sparse structure. In this article, we propose a sparse structure learning algorithm (SSLA) to solve this problem. The algorithm uses the negative log-likelihood function of multi-logit regression as a loss function, adding the adaptive group lasso as a penalty term for sparsity, with a new penalty term to ensure that the learned graph is a directed acyclic graph. A block coordinate descent algorithm (BCD) combining with the alternating direction multiplier method (ADMM) algorithm is developed to solve the proposed model. The learned graph is proved theoretically to be a Bayesian network. In order to evaluate the proposed SSLA and compare with its competitors, we conducted intensive simulation studies and applied them to the benchmark Bayesian networks. The results indicate that the SSLA is superior to the hill climbing (HC) algorithm, the CD algorithm and the BFO-B algorithm respectively, and is competitive with K2 algorithm when the order of the nodes is given.

Faster feature selection algorithms become a necessity as Big Data dictates the zeitgeist. An important class of feature selectors are Markov Blanket (MB) learning algorithms. They are Causal Discovery algorithms that learn the local causal structure of a target variable. A common assumption in their theoretical basis, yet often violated in practice, is causal sufficiency: the requirement that all common causes of the measured variables in the dataset are also in the dataset. Recently, Yu et al. (2018) proposed the M3B algorithm, the first to directly learn the MB without demanding causal sufficiency. The main drawback of M3B is that it is time inefficient, being intractable for high-dimensional inputs. In this paper, we derive the Fast Markov Blanket Discovery Algorithm (FMMB). Empirical results that compare FMMB to M3B on the structural learning task show that FMMB outperforms M3B in terms of time efficiency while preserving structural accuracy. Five real-world datasets where used to contrast both algorithms as feature selectors. Applying NB and SVM classifiers, FMMB achieved a competitive outcome. This method mitigates the curse of dimensionality and inspires the development of local-toglobal algorithms.