Machine Learning Cloud Regression The Swiss Army Knife Of Optimization Vincent Granville by Vincent Granville instant download after payment.

This article is not about regression performed in the cloud. It is about considering your data set as a cloud of points or observations, where the concepts of dependent and independent variables (the response and the features) are blurred. It is a very general type of regression, offering backward-compatibility with existing methods. Treating a variable as the response amounts to setting a constraint on the multivariate parameter, and results in an optimization algorithm with Lagrange multipliers. The originality comes from unifying and bringing under a same umbrella, a number of disparate methods each solving a part of the general problem and originating from various fields. I also propose a novel approach to logistic regression, and a generalized R-squared adapted to shape fitting, model fitting, feature selection and dimensionality reduction. In one example, I show how the technique can perform unsupervised clustering, with confidence regions for the cluster centers obtained via parametric bootstrap. 

Besides ellipse fitting and its importance in computer vision, an interesting application is non-periodic sum of periodic time series. While rarely discussed in machine learning circles, such models explain many phenomena, for instance ocean tides. It is particular useful in time-continuous situations where the error is not a white noise, but instead smooth and continuous everywhere. For instance, granular temperature forecast. Another curious application is modeling meteorite shapes. Finally, my methodology is model free and data driven, with a focus on numerical stability. Prediction intervals and confidence regions are obtained via bootstrapping. I provide Python code and synthetic data generators for replication purposes.