Mathematical Methods for Machine Learning

Lecturer

Dr.  Zdravko Botev, The University of New South Wales

Course Purpose

To someone starting to learn data science, the multitude of computational techniques and mathematical ideas may seem overwhelming. Some may be satisfied with only learning how to use off-the-shelf recipes to apply to practical situations. But what if the assumptions of the black-box recipe are violated? Can we still trust the results? How should the algorithms be adapted?

The purpose of this short course is to provide an accessible introduction to the basic ideas in data science and machine learning. It is intended for anyone interested in gaining a better understanding of the mathematics and statistics that underpin the rich variety of ideas and machine learning algorithms in data science. This understanding is needed, because computer implementations come and go, but the underlying key ideas and algorithms will remain, and will form the basis for ongoing research and future practice.

Course Topics

(dependent on time and level of study)

  • Handling Data
  • Fundamentals of Supervised Learning and Regression
  • Monte Carlo Methods for Bayesian Learning
  • Unsupervised Learning (clustering and mixture modelling)
  • Kernel Methods and Support Vector Machines for Classification
  • Deep Learning and Neural Networks

Assessment

  • Mid-school assignment: 40%
  • Final examination: 60%

Prerequisites

  • Honours level calculus and statistics: students who do not have the necessary background will be provided with detailed background lecture notes and expected to fill in the gaps in their knowledge in their spare time.
  • Familiarity with a programming language for statistics, such as MATLAB, R or Python. Students who do not have this background will be provided with an introductory tutorial lecture notes on using these progamming languages.

Resources

  • Trevor J.. Hastie, Tibshirani, R. J., & Friedman, J. H. (2011). The elements of statistical learning: data mining, inference, and prediction. Springer.
  • D. P. Kroese, Z. I. Botev, S. Vaisman, T. Taimre (2018) Lecture notes on “Mathematical and Statistical Methods for Data Science and Machine Learning”
Mathematical Methods for Machine Learning

Biography

Dr.  Zdravko Botev, The University of New South Wales

Dr. Botev is a Lecturer in statistics and applied probability at UNSW Sydney. Previously he was a postdoctoral researcher at the University of Montreal, Canada. His research interests include Monte Carlo computational methods, efficient rare and high-cost event computer simulation, and nonparametric density estimation (unsupervised learning).

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