Foundations of Data and Models: Regression Analytics
Overview:
Introduction
This course aims to teach a suite of algorithms and concepts to a diverse set of participants interested in the general concept of fitting data to models. It starts with mostly simple linear algebra and computational methods, and introduces some more difficult mathematical concepts towards the end. This method also, by design, fits in with our approach of morning lectures and afternoon practice on personal computers. The combined teaching system provides opportunities for much hands-on learning and participants leave the course with practical knowledge of the basic algorithms.
It is such a foundational course in data and models. Through the lens of regression analysis, a far-reaching discipline with roots in mathematics, statistics, and optimization, Foundations of Data and Models introduces students to the quantitative and (to a lesser degree) computational realms of data science.
Course Objectives
At the end of this course, the participants will be able to:
- Examine how to fit data to models
- Define linear least squares, non-linear least squares, singular value decomposition, sensitivity analysis, experiment design, and parameter error estimation
- Appreciate grid search, random search, simulated annealing, genetic algorithms, neural networks, and large inverse systems
- Investigate principles leading to rapid application of methods
- Evaluate the results of pre-programmed computer exercises
Targeted Audience
This course is ideal for anyone who fits data to models. Participants from different fields: engineering, business, natural sciences, geoscience, medicine, statistics, and economics.
Course Outline
Unit 1:
- Philosophy of Data and Models
- Least Squares
- Levenberg-Marquardt & Ridge Regression
Unit 2:
- Damped Least Squares Comparison
- Least Squares with Constraints
- Stochastic Inverse
Unit 3:
- Singular Value Decomposition
- Random and Grid Search Methods
Unit 4:
- Simulated Annealing and Genetic Algorithms
- Neural Networks
Unit 5:
- Experimental Design
- Parameter Error Estimates
- Large Inverse Problems