# Math 3094

Honors Undergraduate Course on Machine Learning

View the Project on GitHub jeremy9959/Math-3094-Spring-2021

# Course outline

See this page for help on Anaconda, Jupyter, and Python.

## Part One

### Linear Regression (1/18/21-1/29/21)

Goals

• Learn the mathematics of Linear Regression (ordinary least squares) using Linear Algebra

• Lab:

• get a working installation of anaconda, python, and jupyter on your computer.
• a basic introduction to working with the Jupyter notebook
• fundamentals of Python
• calculations and plotting examples of linear regression

References

### Gradient Descent (2/2/21 - 2/12/21)

Goals:

• Learn the basic theory of gradient descent and how it is applied to find maxima and minima of functions
• Apply Gradient Descent to some specific examples.
• Learn Newton’s method and apply it to some examples.

References

• Gradient Descent html pdf
• Gradient Descent lab - includes datafiles and ipynb file. zip tgz

### Probability

Goals:

References

• Probability Notes html pdf
• Naive Bayes Notes html pdf
• Naive Bayes Lab - includes datafiles and ipynb file. zip tgz

### Logistic Regression

Goals:

• Understand the statistical model underlying logistic regression
• See how the ideas of likelihood and gradient descent combine to solve the logistic regression problem
• Do some sample computations to see Logistic Regression in action
• Generalize binary logistic regression to multi-class logistic regression

References

• Logistic Regression html pdf
• Logistic Regression lab - includes datafiles and ipynb file. zip tgz

### Principal Component Analysis

Goals:

References

• Principal Component Analysis html pdf
• PCA Lab – includes notebook(s) and data zip tgz

### Bayesian Regression

Goals:

• Learn the process of Bayesian inference (see also the notes on probability above).
• Understand over-fitting in linear regression
• Study Bayesian linear regression
• Understand the ideas of linear discriminant analysis

References

• Bayesian Regression Lab – includes notebook(s) and data zip tgz

### Support Vector Machines

Goals:

• Learn the ideas behind support vector machine classifiers
• Understand the relationship between convex hulls, supporting hyperplanes, and support vector machines
• Formulate the convex optimization problem yielding the optimal margin classifier
• Learn the sequential minimum optimization algorithm
• Further ideas

References:

• Notes on support vector machines html pdf
• Support Vector Machines Lab (includes jupyter notebook and data files) zip tgz

### Neural Networks

Goals:

• Learn the ideas of neural networks and understand forward-propagation and back-propagation
• Derive the back-propagation formula
• Learn the mechanisms of basic convolutional neural networks

References

• Neural Networks Lab – includes notebook(s) and data zip tgz