About this project

This is freelance research about how to find model $M$ transforming observed values $x_1, x_2, ... x_n$ into a target scalar $y$, which is known as regression problem, or into set of labels $A,B,...$, which is known as classification problem.

The research covers also stochastic modelling where target $y$ is a random value or labels $A,B,...$ have different input dependent probabilities.

The difference of this project from other forms of deep machine learning is that it presents a completely new solution, different in principal. In the foundation of all stochastic and deterministic models lays Kolmogorov-Arnold representation
$$ M(x_1, x_2, x_3, ... , x_n) = \sum_{q=0}^{2n} \Phi_q\left(\sum_{p=1}^{n} \phi_{q,p}(x_{p})\right), $$ where $\Phi_q, \phi_{q,p}$ are unspecified functions that are determined in a modelling process. The theoretical part is published in peer reviewed journals, but this site offers a reader friendly form along with coding samples. The site provides also many details that are not included in journal publications due to certain requirements and traditions. The research started by Andrew Polar and Mike Poluektov but hopefully will be continued by other contributors as well.

The basic model is chosen not because authors like it or because they wish to be different and not cross path with others. According to big number of tests, presented on this site further in content, it showed higher accuracy and better performance compared to traditional approaches.

The content is designed for reading top to bottom. Some prerequisites are required. It is assumed that readers are familiar with basic data modelling techniques by minimizing residual errors such as least mean squares, neural networks, tree type algorithms like random forest, stochastic methods such as Bayesian neural networks, types of data set uncertainties (epistemic, aleatoric) and so on.

Good luck

Andrew Polar