L. Gross page at UTK - Math 589 Fall 2020

Math 589 and EEB 589 - Fall 2020 - Mathematics of Machine Learning Methods in Ecology and Environmental Science

Louis Gross, Chancellor's Professor of Ecology and Evolutionary Biology and Mathematics

Machine learning methods have blossomed over the recent decade as a means to analyze patterns in data using a training set that is understood and expanding the knowledge from this to a broader context. A key concept is that there is a method applied that automatically adjusts the choice of model based on its performance in meeting the goals of the model as there is exposure of the model to additional data. Underlying this is the agreement on appropriate performance metrics and that the process of adjustment of a model, sometimes through choice of parameters, sometimes through choice of the underlying model, proceeds through an algorithm that is automatic. The entire process is inherently related to the issue of model evaluation, encoded through the performance metrics. There are hosts of mathematical concepts underlying machine learning algorithm development and assessment of performance, including virtually every area of classic applied mathematics (e.g. calculus, optimization, linear algebra, probability, numerical analysis).

The objective of this one-credit-hour seminar is to provide an overview of the variety of applications of machine learning to ecology, broadly construed. The focus is on the underlying mathematical ideas, not on the coding or detailed implementation of the algorithm. We will start with an overview of key ideas (e.g differences between supervised, unsupervised, reinforcement and deep learning), discuss some of the main problems for which machine learning methods have been applied (e.g. regression, prediction, dimensionality reduction, regularization, probability distribution estimation, clustering, classification), and throughout will use examples of applications in ecology (ecological forecasting, neural net methods to estimate parameters in process models, image analysis for species classification, prediction of invasive species outbreaks).

Participants are assumed to have some of the underlying undergraduate-level background in mathematics, and will be expected to choose a particular application of machine learning in an area of interest to their research, become knowledgeable about associated articles or books inform the instructor regularly about what they are reading, and be prepared as the semester progresses to comment in class about what they have learned about their chosen topic. The instructor will provide an extensive list of papers and other references, provide a conceptual overview of each of the approaches with a bit of mathematical detail, and guide discussions in collaboration with course participants.

This course is offered online synchronously and the course meeting time is 1:10-2:00PM. We will use Zoom for class meetings and will share documents using the Basecamp site for the seminar. In addition to attending class, registered participants are expected to share their understanding of the topic they have chosen. At the end of the semester, each participant is expected to produce a short report on some application of machine learning to a problem of interest to them. This could include use of one of the many available tools (in Matlab, R, Python, TensorFlow, etc.) available to apply machine learning, or it could be a discussion of an application and the mathematics.