BIOSTAT 257: Statistical Computing

• Tue/Thu 1pm-2:50pm @ CHS 33-105A
• Instructor: Dr. Hua Zhou, huazhou@ucla.edu

What is statistics?

• Statistics, the science of data analysis, is the applied mathematics in the 21st century.

• People (scientists, goverment, health professionals, companies) collect data in order to answer certain questions. Statisticians's job is to help them extract knowledge and insights from data.

• Must-read for (bio)statistics students:

  • 50 years of data sicence, by David Donoho.

• If existing software tools readily solve the problem, all the better.

• Often statisticians need to implement their own methods, test new algorithms, or tailor classical methods to new types of data (big, streaming).

• This entails at least two essential skills: programming and fundamental knowledge of algorithms.

What is this course about?

• Not a course on statistical packages. It does not answer questions such as How to fit a linear mixed model in R, Julia, SAS, SPSS, or Stata?

• Not a pure programming course, although programming is important and we do homework in Julia.
  BIOSTAT 203A (Data Management) in fall quarter focuses on programming in R and SAS.

• Not a course on data science. BIOSTAT 203B (Introduction to Data Science) in winter quarter focuses on some software tools for data scientists.

• This course focuses on algorithms, mostly those in numerical linear algebra and numerical optimization.

Learning objectives

1. Be highly appreciative of this quote by James Gentle

   The form of a mathematical expression and the way the expression should be evaluated in actual practice may be quite different.

   Examples: $\mathbf{X}^T \mathbf{W} \mathbf{X}$, $\operatorname{tr} (\mathbf{A} \mathbf{B})$, $\operatorname{diag}(\mathbf{A} \mathbf{B})$, multivariate normal density,...

2. Become memory-conscious. You care about looping order. You do benchmarking on hot functions fanatically to make sure it's not allocating.
   

   Image source

3. No inversion mentality. Whenever you see a matrix inverse in mathematical expression, your brain reacts with matrix decomposition, iterative solvers, etc. For R users, that means you almost never use the solve(M) function to obtain inverse of a matrix $\boldsymbol{M}$.

   Examples: $(\mathbf{X}^T \mathbf{X})^{-1} \mathbf{X}^T \mathbf{y}$, $\mathbf{y}^T \boldsymbol{\Sigma}^{-1} \mathbf{y}$, Newton-Raphson algorithm, ...
   

   Image source

4. Know some basic strategies to solve big data problems.

   Examples: how Google solve the PageRank problem with $10^{9}$ webpages, linear regression with $10^7$ observations, etc.

5. No afraid of optimizations and treat it as a technology. Be able to recognize some major optimization classes and choose the best solver(s) correspondingly.

6. Be immune to the language fight.

Course logistics

• Course webpage: https://ucla-biostat-257.github.io/2022spring or http://ucla-biostat-257.com.

• Syllabus.

• Check the Schedule page frequently.

• Jupyter notebooks will be posted/updated before each lecture.

How to get started

All course materials are in GitHub repo https://github.com/ucla-biostat-257/2022spring. Lecture notes are Jupyter Notebooks (.ipynb files) under the slides folder. It is a good idea to learn by running through the code examples. You can do this in several ways.

Run Jupyter Notebook in Binder

A quick and easy way to run the Jupyter Notebooks is Binder, a free service that allows us to run Jupyter Notebooks in cloud. Simply follow the Binder link at https://ucla-biostat-257.github.io/2022spring/schedule/schedule.html.

If you want the JupyterLab interface, replace the tree by lab in the URL.

Run Jupyter Notebook locally on your own computer

1. Download and install Julia v1.7.2 from https://julialang.org/downloads/. On Mac, use Bash command

   sudo ln -s /Applications/Julia-1.7.app/Contents/Resources/julia/bin/julia /usr/local/bin/julia
   

   to create a symbolic link so julia command is available anywhere in the terminal.

2. Git clone the course material.

   git clone https://github.com/ucla-biostat-257/2022spring.git biostat-257-2022spring
   

   You can change biostat-257-2022spring to another directory name you prefer.

3. Enter the folder biostat-257-2022spring on Terminal.

4. Open Julia within that folder, type ] to enter the package mode, then type

   activate .
   instantiate
   

   to install necessary packages.

5. In Julia REPL, type

   using IJulia
   jupyterlab(dir = pwd())
   

   to open the JupyterLab in browser or

   using IJulia
   notebook(dir = pwd())
   

   to open a Jupyter notebook.

6. Course material is updated frequently. Remember to git pull to obtain the most recent material.