Systems and methods for mathematical regression with inexact feedback

The present invention provides methods for providing mathematical regression analysis. In particular, the method for conducting regression analysis comprises the steps of: selecting a regression model; selecting an initial set of regression parameters; applying the regression model to the initial set of regression parameters to create an initial set of regression values; selecting an improved set of regression values, wherein the improved set of regression values is selected from the set of initial regression values; generating a loss function based on the improved set; applying an iterative optimization method to the loss function and the improved set of regression values to generate a resultant set of regression values; and outputting the resultant set of regression values.