Impact statement: The proposed PID algorithm can be applied in various fields because it provides knowledge about a domain. Any researcher who needs to design experiments might benefit from our proposed algorithm in the sense that it can help researchers formulate hypotheses that could lead to new data collection and experiments. For example, PID can help us discover the combined effects of drugs on human body: By utilizing PID on patients’ records, we might find using Phenelzine togther with Fluoxetine has a strong interaction effect towards serotonin syndrome. Thus, PID has great potential in helping the development of new therapies for saving lives. Also, this project will lead to effective and efficient algorithms for finding useful any-order crossing features in an automated way. Finding useful crossing features is one of the most crucial task in the Recommender Systems. Engineers and Scientists in E-commerce companies may benefit from our results that our algorithm can alleviate the human effect on finding these useful patterns in the data.