Ergodic Set Regression Models

Multivariate polynomial regression (MPR) is a traditional machine learning method. it has been widely used in the past decades. However, the high-order interaction information in its model is incomplete. Moreover, it is difficult to visually understand its decision logic and to determine which factor contributes more to the result. In this work, we propose a special set of power terms named ergodic set, which considers more complete high-order interaction information. Based on this set, Ergodic Set Regression (ESR) and Curve Ergodic Set Regression (CESR) models are constructed, the first model for accurately prediction and another model for visualizing the influences of various factors on result. The experiment results on a small-scale data set show that the performance of ESR is better than that of MPR and even some neural networks methods dedicated to small-scale data sets. CESR shows the influence curve of each factor on result with the premise of obtaining certain accuracy.