We introduce a highly expressive class of function approximators called Splat Regression Models. Model outputs are mixtures of heterogeneous and anisotropic bump functions, termed splats, each weighted by an output vector. The power of splat modeling lies in its ability to locally adjust the scale and direction of each splat, achieving both high interpretability and accuracy. Fitting splat models reduces to optimization over the space of mixing measures, which can be implemented using Wasserstein-Fisher-Rao gradient flows. As a byproduct, we recover the popular Gaussian Splatting methodology as a special case, providing a unified theoretical framework for this state-of-the-art technique that clearly disambiguates the inverse problem, the model, and the optimization algorithm. Through numerical experiments, we demonstrate that the resulting models and algorithms constitute a flexible and promising approach for solving diverse approximation, estimation, and inverse problems involving low-dimensional data.

This course teaches you about the most common & popular technique used in Data Science & Machine Learning: Linear Regression. You will learn the theory as well as applications of different types of linear regression models. At the end of the course, you will completely understand and know how to apply & implement in R linear models, how to run model's diagnostics, and how to know if the model is the best fit for your data, how to check the model's performance and to make predictions. Linear regression is the simplest machine learning (and thus deep learning) model you can learn, yet there is so much depth that you'll be returning to it for years to come. Learn how to test the model's fit, how to select the most suitable linear models for your data, and make predictions You'll start by absorbing the most valuable Linear Regression basics, and techniques and slowly moving to more complex assignments.

I still remember the day 1 of my very first job fifteen years ago. I had just finished my graduate studies and joined a global investment bank as an analyst. On my first day, I kept straightening my tie and trying to remember everything that I had studied. Meanwhile, deep down, I wondered if I was good enough for the corporate world. The only thing that you need to know is the regression modeling!"

Multiple regression analysis is tool that allows you to expand on your research question, and conduct a more rigorous test of the association between your explanatory and response variable by adding additional quantitative and/or categorical explanatory variables to your linear regression model. In this session, you will apply and interpret a multiple regression analysis for a quantitative response variable, and will learn how to use confidence intervals to take into account error in estimating a population parameter. You will also learn how to account for nonlinear associations in a linear regression model. Finally, you will develop experience using regression diagnostic techniques to evaluate how well your multiple regression model predicts your observed response variable. Note that if you have not yet identified additional explanatory variables, you should choose at least one additional explanatory variable from your data set.

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