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Special Issue: Artificial Intelligence and Pattern Recognition

• Regular Paper •

### A Heuristic Sampling Method for Maintaining the Probability Distribution

Jiao-Yun Yang1,2,3, Member, CCF, Jun-Da Wang1,2,4,*, Yi-Fang Zhang1,2,3, Wen-Juan Cheng1,2,3, and Lian Li1,2,3, Member, CCF

1. 1 Key Laboratory of Knowledge Engineering with Big Data of Ministry of Education, Hefei University of Technology Hefei 230601, China;
2 National Smart Eldercare International Science and Technology Cooperation Base, Hefei University of Technology Hefei 230601, China;
3 School of Computer Science and Information Engineering, Hefei University of Technology, Hefei 230601, China;
4 School of Mathematics, Hefei University of Technology, Hefei 230601, China
• Received:2019-10-05 Revised:2020-08-15 Online:2021-07-05 Published:2021-07-30
• Contact: Jun-Da Wang E-mail:jwang212@ur.rochester.edu
• About author:Jiao-Yun Yang received his B.S. degree and Ph.D. degree in computer science from University of Science and Technology of China, Hefei, in 2009 and 2014, respectively. He is an associate professor in the School of Computer Science and Information Engineering, Hefei University of Technology, Hefei. His research interests include heuristic search, machine learning and health computing. He is a member of CCF.
• Supported by:
This work was supported by the National Key Research and Development Program of China under Grant No. 2018YFB1003204, Anhui Provincial Key Technologies Research and Development Program under Grant Nos. 1804b06020378 and 1704e1002221, and the National 111 Project of China under Grant No. B14025.

Sampling is a fundamental method for generating data subsets. As many data analysis methods are developed based on probability distributions, maintaining distributions when sampling can help to ensure good data analysis performance. However, sampling a minimum subset while maintaining probability distributions is still a problem. In this paper, we decompose a joint probability distribution into a product of conditional probabilities based on Bayesian networks and use the chi-square test to formulate a sampling problem that requires that the sampled subset pass the distribution test to ensure the distribution. Furthermore, a heuristic sampling algorithm is proposed to generate the required subset by designing two scoring functions: one based on the chi-square test and the other based on likelihood functions. Experiments on four types of datasets with a size of 60 000 show that when the significant difference level, α, is set to 0.05, the algorithm can exclude 99.9%, 99.0%, 93.1% and 96.7% of the samples based on their Bayesian networks—ASIA, ALARM, HEPAR2, and ANDES, respectively. When subsets of the same size are sampled, the subset generated by our algorithm passes all the distribution tests and the average distribution difference is approximately 0.03; by contrast, the subsets generated by random sampling pass only 83.8% of the tests, and the average distribution difference is approximately 0.24.

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