*Article* **Soft Randomized Machine Learning Procedure for Modeling Dynamic Interaction of Regional Systems**

## **Yuri S. Popkov 1,2,3,4**


Received: 19 March 2019; Accepted: 11 April 2019; Published: 20 April 2019

**Abstract:** The paper suggests a randomized model for dynamic migratory interaction of regional systems. The locally stationary states of migration flows in the basic and immigration systems are described by corresponding entropy operators. A soft randomization procedure that defines the optimal probability density functions of system parameters and measurement noises is developed. The advantages of soft randomization with approximate empirical data balance conditions are demonstrated, which considerably reduces algorithmic complexity and computational resources demand. An example of migratory interaction modeling and testing is given.

**Keywords:** soft randomization; entropy; entropy operator; migration; immigration; empirical balance; empirical risk
