Learning nonparametric DAGs with incremental information via high-order HSIC

Score-based methods for learning Bayesain networks(BN) aim to maximizing the global score functions. However, if local variables have direct and indirect dependence simultaneously, the global optimization on score functions misses edges between variables with indirect dependent relationship, of which scores are smaller than those with direct dependent relationship. In this paper, we present an identifiability condition based on a determined subset of parents to identify the underlying DAG. By the identifiability condition, we develop a two-phase algorithm namely optimal-tuning (OT) algorithm to locally amend the global optimization. In the optimal phase, an optimization problem based on first-order Hilbert-Schmidt independence criterion (HSIC) gives an estimated skeleton as the initial determined parents subset. In the tuning phase, the skeleton is locally tuned by deletion, addition and DAG-formalization strategies using the theoretically proved incremental properties of high-order HSIC. Numerical experiments for different synthetic datasets and real-world datasets show that the OT algorithm outperforms existing methods. Especially in Sigmoid Mix model with the size of the graph being ${\rm\bf d=40}$, the structure intervention distance (SID) of the OT algorithm is 329.7 smaller than the one obtained by CAM, which indicates that the graph estimated by the OT algorithm misses fewer edges compared with CAM.Source code of the OT algorithm is available at https://github.com/YafeiannWang/optimal-tune-algorithm

Interleukin-6 gene -572G/C polymorphism and prostate cancer risk

Background: The aim of the present study was to determine whether the interleukin-6 (IL-6) -572G/C polymorphism correlates with prostate cancer.Methods: According to inclusion and exclusion criteria, the association of the IL-6 -572G/C polymorphism with prostate cancer was searched in databases and analyzed using comprehensive meta-analysis software. Odds ratios (ORs) with 95% confidence intervals (CIs) were used to assess the strength of the associations.Results: We considered a total of six case-control studies including 2237 patients and 1754 controls and the meta-analysis results showed significant association between the IL-6 -572G/C polymorphism and prostate cancer risk(CC vs GG: OR = 0.49, 95% CI =0.37-0.65;CG vs GG: OR =0.71, 95% CI = 0.58-0.87; the dominant model: OR =0.65, 95% CI = 0.54-0.79;the recessive model: OR =0.70, 95% CI = 0.58-0.85). In stratified analyses by ethnicity, significant associations were found among Asian populations. However, no significant association was found in Caucasian populations.Conclusion: Our findings demonstrated that the -572G/C polymorphism of the IL-6 gene may be a risk factor for the development of prostate cancer in Asians.Keywords: Prostate cancer, IL-6 polymorphisms, risk

Effect of Investment in Environmental Protection on Green Development of Industrial Enterprises: Evidence from Central China

China\u27s industrialization and urbanization process is advancing rapidly. While using natural resources, the country also generates a large amount of waste, causing serious environmental pollution and affecting further development of human society. Expanding the scale of investment in environmental protection has gradually become an effective means to address the problem. China is continuously increasing investment in environmental protection, actively improving environmental conditions, and achieving the dual goals of promoting high-quality development and environmental protection. Six provinces in central China were taken as research objects and the regional differences in their investments in environmental protection were analyzed. A panel entropy weight model was used to calculate the green development level of industrial enterprises, and a panel regression model was employed to calculate the impact of investment in environmental protection on the degree of influence of the green development of industrial enterprises. Results show that the six provinces in central China have significant differences in their investment in industrial environmental pollution control. The unreasonable allocation of environmental protection investment funds has led to the insignificant improvement of environmental pollution caused by industrial enterprises in the six central provinces of investment in environmental protection. R&D expenditure of industrial enterprises, the total import, and export volume of foreign-invested enterprises, and the fixed asset investment of the entire society have a positive role in promoting the green development of industrial enterprises. The added value of the secondary industry has a significant negative effect on the green development of industrial enterprises. Conclusions can be used as a reference for encouraging industrial enterprises to increase investment in environmental protection and promote green development