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UofT STA410/2102 Statistical Computation

Programming Portfolio Assignments

  1. Assignment 0 introduces Python through the following foundational computational and statistical computation problems:

    1. Bit string representation of integer value numbers
    2. Pseudorandom integer generation with modulus
    3. Floating-point error accumulation reduction
    4. High precision single pass variance calculations

  2. Assignment 1 practices linear algebra computations with numpy through the following foundational computational and statistical computation problems:

    1. The Gram-Schmidt to orthogonalize vectors
    2. Regression fits from a X=QR decomposition
    3. The Cholesky covariance matrix decomposition
    4. Conjugate gradient methods

  3. Assignment 2 explores the quintessential algorithms underlying the computational efficiency of the following standard use cases for function:

    1. Interpolation with Lagrange piecewise polynomials
    2. Convolution theorem with the fast Fourier transform
    3. Orthogonal polynomial recurrence formula evaluation
    4. Time-benchmarking commonly used built-in functions

  4. Assignment 3 addresses optimization with a particular focus on Newton's Method and TensorFlow for Gradient and Hessian (Jacobian) computations.

    1. Root-finding with Newton-Raphson and fixed-point iteration and acceleration
    2. Iteratively reweighted least squares for fitting logistic regression models
    3. Nonlinear Gauss-Seidel using TensorFlow for partial derivative calculations
    4. Newton's method for arbitrary dimension gradients/Hessians with TensorFlow

  5. Assignment 4 addresses sampling from statistical distributions using PyMC3, TensorFlow, and classes and custom code.

    1. (Bayesian) probabilistic programming is introduced through the official PyMC3 tutorial
    2. Adaptive (squeezed) rejection sampling is introduced through a custom python class
    3. Hidden Markov models are fit via sequential importance sampling with bootstrap resampling
    4. Normalizing flow (bijection) generative modeling of arbitrary distributions is demonstrated

Submitting Programming Portfolio Assignments

Submit .ipynb files on MarkUs before the end of the calendar day (EoD) on the due date.

Accessing Programming Portfolio Assignments

UofT students may access STA410 Programming Portfolio Assignment coding problems with UofT JupyterHub or JupyterLab or google colab via

[JupyterHub] https://jupyter.utoronto.ca/hub/user-redirect/git-pull?repo=https://github.com/pointOfive/sta410hw<#>&branch=<master|main>

[JupyterLab] https://jupyter.utoronto.ca/hub/user-redirect/git-pull?repo=https://github.com/pointOfive/sta410hw<#>&branch=<master|main>&urlpath=/lab/tree/sta410hw<#>

or

https://colab.research.google.com/github/pointOfive/sta410hw0/blob/<master|main>/sta410hw<#>.ipynb

where <#> above is replaced with the Programming Portfolio Assignment number and <master|main> is replaced by master for hw0 and hw1 and main for all others.

Additional Information and Requirements

Some notes to faciltate getting started in this environment are available on the UofT JupyterHub support page.

If for some reason JupyterHub/Lab is not loading the repository, you can delete and reload repositories (after downloading and saving what you need).

From JupyterLab or JupyterHub, open a new terminal with New > Terminal and then use yes y | rm -r <path to directory to delete> to a delete the repository directory.

If you're working in some other environment, the versioning there must support notebook format 4.5, e.g., JupyterLab >= 3.0.13 (for "JupyterLab UI") or Jupyter Notebook >= 6.2 (for "Jupyter classic UI"); otherwise, your notebook cell-ids will not be supported and you will not get any credit for your submitted work.

You may check if cell ids are present or changing at each save with ! grep '"id":' <path/to/notebook>.ipynb