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Data Analysis and Machine Learning Applications

  • Course: PHYS 398MLA
  • Instructor: Prof. Mark Neubauer, msn@illinois.edu
  • Lectures: Mondays from 3-4:50 pm in 222 Loomis Laboratory of Physics
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    • Office Hours
      • Prof. Neubauer: Thursdays from 4-5 pm over Zoom

Course Description

Welcome you to the Data Analysis and Machine Learning Application (for physicists) course!

In this course, you will learn fundamentals of how to analyze and interpret scientific data and apply modern machine learning tools and techniques to problems common in physics research such as classification and regression. This course offering is very timely given the explosion of interest and rapid development of data science and artificial intelligence. Every day there are new applications of machine learning to the physical sciences in ways that are advancing our knowledge of nature.

This course is designed to be interactive and collaborative, at the same time developing your own skills and knowledge. I initiated this course in 2018 from a viewpoint that we live in an increasingly data-centric world, with both people and machines learning from vast amounts of data. There has never been a time where early-career physicists such as yourself will benefit from a solid understanding in the basics of scientific data analysis, data-driven inference and machine learning, and working knowledge of the most important tools and techniques from modern data science than today.

This is the third offering of the course. I welcome your feedback on any aspect of the course so that I can work to improve the curriculum.

Prerequisites

Courses

Hardware

  • You need a laptop for this course. It is assumed that you have a laptop running MacOS, Linux or Windows for use both inside and outside of the class.

Software

  • Some knowledge of python preferred but is not required. You do need to have a working knowledge of the basics of computer programming.

Setting up

  • The course lecture workbooks and assessments will be hoste in Prairelearn using their workspaces feature. This provides all you will need to interact with the course notebooks. You also have the option to run the Docker container for the course environment locally, which would provide faster response than the PL Workspace since the course container is rather large. See instructions for use of the PHYS398MLA Docker container at here.

Course Overview

Topics covered include:

  • Notebooks and numerical python
  • Handling and Visualizing Data
  • Finding structure in data
  • Measuring and reducing dimensionality
  • Adapting linear methods to nonlinear problems
  • Estimating probability density
  • Probability theory
  • Statistical methods
  • Bayesian statistics
  • Markov-chain Monte Carlo in practice
  • Stochastic processes and Markov-chain theory
  • Variational inference
  • Optimization
  • Computational graphs and probabilistic programming
  • Bayesian model selection
  • Learning in a probabilistic context
  • Supervised learning in Scikit-Learn
  • Cross validation
  • Neural networks
  • Deep learning

Topics will be demonstrated in-class through live-code examples/slides in Juypter notebooks.

Class Participation

The lectures will include physics and data science pedagogy, demonstrated through live examples in Jupyter notebooks that you will work through in class. You are required to attend each lecture with your laptop and working environment. Attendance will be taken.

Homework

Homework is an important part of the course where you will have an opportunity to apply the techniques you are learning to problems relevant to the analysis of scientific data. All assignments are listed within the Course Outline and distributed through PrairieLearn. You will submit your homework via your privae Github repository.

Projects

Approximately halfway through the course, you will have the opportunity to choose from a set of projects based on open scientific data and apply what you have learned in the course. You will be asked to answer certain questions about the data, supported by your analysis and written up in a Jupyter notebook which you will submit. Your notebook will also include background information about how the data is generated, its scientific relevance and your methodology.

Grading

  • Class Participation: ~20%
  • Homework: ~45%
  • Research project: ~35%

Course Outline

[Jan 17] NO LECTURE (MLK Day)

[Jan 24] Lec 01: Introduction

Goals

  • Getting overview of the course, including reading list and homework assignments
  • Setting up your environment

Lecture notebooks

Homework

  • Complete setting up your environment so that you can launch and execute notebooks

Required reading

  • A Whirlwind Tour of Python, Jake VanderPlas: free PDF, notebooks online.

Supplemental reading

  • None

[Jan 31] Lec 02: Data Science

Goals

  • Gain familiarity with Jupyter Notebooks and Numerical python
  • Learn about handling and describing data

Lecture notebook(s)

Homework

[Feb 07] Lec 03: Visualizing & Finding Structure in Data

Goals

  • Learn about visualizing data
  • Learn about the importance of clustering data in physics
  • Learn how to find structure in data (clustering)
    • KMeans, Spectral Clustering, DBSCAN

Lecture notebook(s)

Homework

  • Homework 1: Numerical python and data handling
    • Released via Prairelearn on Monday, Feb 7
    • Due by 3:00 pm CDT on Monday, Feb 14

Supplemental reading

[Feb 14] Lec 04: Dimensionality & Linearity

Goals

  • Measure and reduce dimensionality
  • Adapt linear models to nonlinear problems

Lecture notebook(s)

Homework

  • Homework 2: Visualization, Covariance and Correlation
    • Released via Prairelearn on Monday, Feb 14
    • Due by 3:00 pm CDT on Monday, Feb 21

Supplemental reading

[Feb 21] Lec 05: Kernel Functions & Probability Theory

Goals

  • Learn about Kernel functions
  • Learn about Probability Theory

Lecture notebook(s)

Homework

  • Homework 3: Expectation-Maximization Algorithm, K-Means, Principle Component Analysis
    • Released via Prairelearn on Monday, Feb 21
    • Due by 3:00 pm CDT on Monday, Feb 28

Supplemental reading

[Feb 28] Lec 06: Probability Density Estimation & Statistics

Goals

  • Estimate probability density
  • Learn about Statistical Methods

Lecture notebook(s)

Homework

  • Homework 4: Probability
    • Released via Prairelearn on Monday, Feb 28
    • Due by 3:00 pm CDT on Monday, Mar 07

Supplemental reading

[Mar 07] Lec 07: Bayesian Statistics & Markov-chain Monte Carlo

Goals

Homework

  • Homework 5: Kernel Density Estimation
    • Released via Prairelearn on Monday, Mar 07
    • Due by 3:00 pm CDT on Monday, Mar 21

Supplemental reading

[Mar 14] NO LECTURE (Spring Break)

[Mar 21] Lec 08: Stochastic Processes, Markov Chains & Variational Inference

Goals

  • Learn about Stochastic processes in the realm of Data Science
  • Learn about Markov-chain Theory
  • Learn about the Variational Inference Method

Lecture notebook(s)

Homework

  • Homework 6: Bayesian Statistics and Markov Chain Monte Carlo
    • Released via Prairelearn on Monday, Mar 21
    • Due by 3:00 pm CDT on Monday, Mar 28

Supplemental reading

[Mar 28] Lec 09: Optimization, Comput. Graphs & Prob. Prog.

Goals

  • Learn about Optimization and Stochastic Gradient Descent
  • Learn about Frameworks for Computational Graphs
  • Learn about Probabilistic Programming methods

Lecture notebook(s)

Homework

  • Homework 7: Markov Chains
    • Released via Prairelearn on Monday, Mar 28
    • Due by 3:00 pm CDT on Monday, Apr 18

Supplemental reading

[Apr 04] Lec 10: Bayesian Models & Probabilistic Learning

Goals

Lecture notebook(s)

Homework

  • None

Supplemental reading

[Apr 11] Lec 11: Supervised Learning & Cross Validation

Goals

  • Learn about Cross Validation

Lecture notebook(s)

Homework

  • None

Supplemental reading

[Apr 18] Lec 12: Artificial Neural Networks

Goals

  • Learning and Inference using Neural Networks

Lecture notebook(s)

Homework

  • Homework 8: Cross Validation and Artificial Neural Networks
    • Released via Prairelearn on Monday, Apr 18
    • Due by 3:00 pm CDT on Monday, May 13

Supplemental reading

[Apr 25] Lec 13: Deep Learning

Goals

  • Learn about Deep Learning

Lecture notebook(s)

Homework

  • None

[May 02] Lec 14: Deep Learning

Goals

Lecture notebook(s)

  • Deep learning

Homework

  • None

Resources

References

Tools

Git and GitHub

Anaconda and Conda

Project Jupyter

Acknowledgements

I would like to acknowledge David Kirby at the University of California at Irvine for the materials and setup for which this course is based and the helpful discussions we have had. I would like to thank Matthew Feickert and Dewen Zhong for their guidance and contributions to the course. I also acknowledge the course at github.com/advanced-js for which the syllabus template was utilized.

_________________

Material for a University of Illinois course offered by the Physics Department.

Content is maintained on github and distributed under a BSD3 license.

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