- Introduction to Python
- Getting started with Python and the IPython notebook
- Functions are first class objects
- Data science is OSEMN
- Working with text
- Preprocessing text data
- Working with structured data
- Using SQLite3
- Using HDF5
- Using numpy
- Using Pandas
- Computational problems in statistics
- Computer numbers and mathematics
- Algorithmic complexity
- Linear Algebra and Linear Systems
- Linear Algebra and Matrix Decompositions
- Change of Basis
- Optimization and Non-linear Methods
- Practical Optimizatio Routines
- Finding roots
- Optimization Primer
- Using scipy.optimize
- Gradient deescent
- Newton’s method and variants
- Constrained optimization
- Curve fitting
- Finding paraemeters for ODE models
- Optimization of graph node placement
- Optimization of standard statistical models
- Fitting ODEs with the Levenberg–Marquardt algorithm
- 1D example
- 2D example
- Algorithms for Optimization and Root Finding for Multivariate Problems
- Expectation Maximizatio (EM) Algorithm
- Monte Carlo Methods
- Resampling methods
- Resampling
- Simulations
- Setting the random seed
- Sampling with and without replacement
- Calculation of Cook’s distance
- Permutation resampling
- Design of simulation experiments
- Example: Simulations to estimate power
- Check with R
- Estimating the CDF
- Estimating the PDF
- Kernel density estimation
- Multivariate kerndel density estimation
- Markov Chain Monte Carlo (MCMC)
- Using PyMC2
- Using PyMC3
- Using PyStan
- C Crash Course
- Code Optimization
- Using C code in Python
- Using functions from various compiled languages in Python
- Julia and Python
- Converting Python Code to C for speed
- Optimization bake-off
- Writing Parallel Code
- Massively parallel programming with GPUs
- Writing CUDA in C
- Distributed computing for Big Data
- Hadoop MapReduce on AWS EMR with mrjob
- Spark on a local mahcine using 4 nodes
- Modules and Packaging
- Tour of the Jupyter (IPython3) notebook
- Polyglot programming
- What you should know and learn more about
- Wrapping R libraries with Rpy
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Expectation Maximizatio (EM) Algorithm
- Review of Jensen’s inequality
- Concavity of log function
- Example of coin tossing with missing informaiton to provide context
- Derivation of EM equations
- Illustration of EM convergence
- Derivation of update equations of coin tossing example
- Code for coin tossing example
- Derivation of update equatiosn for mixture of Gaussians
- Code for mixture of Gaussians
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