Vertically Shifted Exponential Best-Fit

Abstract :

Exponentially decreasing data examples can be found all over in the world. While most of these decrease to zero, there are some examples that decrease with a vertical shift. Data in this form can be difficult to fit to a mathematical model. Iterative algorithms, such as Levenberg-Marquardt for nonlinear least squares curve-fitting, exist to fit the data to a curve, but have some constrains that need to be considered, some hyperparameters that need to be tuned and convergence can be slow.?A new method will be presented in this paper that is not using the above mentioned iterative algorithms, while maintaining the accuracy; has no hyperparameters and the only constraint it has is that the data needs to roughly[1]follow the exponential decay curve: Ae?αx + B with A,α and B >= 0. This method was tested on both simulated and real data, and performed equally well in both cases much like the curve fit method from the Python library Scipy, but having no hyperparameters and converging faster.

[1] Data can be noisy.