Statistical Machine Learning Implementations

A collection of machine-learning methods implemented largely from the underlying math rather than off-the-shelf, spanning convolutional networks, one-class anomaly detection, autoencoders, and transformers. Built for a graduate statistical-computing course; each piece stands on its own.

What's here

Method	File	Idea
Convolutional neural network	code/cnn_convolution.Rmd	Convolution and a CNN for image-style classification
SVDD for directional data	code/svdd_directional_kernels.py	Support Vector Data Description with four directional-data kernels (von Mises–Fisher, geodesic/Laplacian, heat/diffusion, Watson), solving the kernelized dual as a QP with CVXOPT
Least-squares SVDD	code/lssvdd_ionosphere.py	LS-SVDD variant, demonstrated on the Ionosphere dataset
Autoencoder anomaly detection	code/autoencoder_outlier_detection.py	PyTorch autoencoder flagging outliers by reconstruction error, on network firewall logs
Transformers	code/transformers.Rmd	Attention / transformer mechanics

The SVDD work is the most involved: it derives the kernel dual and implements four different kernels suited to data that lives on a sphere (directions/angles), rather than assuming ordinary Euclidean geometry.

Datasets

Two public datasets are bundled in data/:

• Ionosphere (ionosphere.data, ionosphere.names) — radar returns, Johns Hopkins University / UCI Machine Learning Repository.
• Firewall log (firewall_log.csv) — network traffic with allow/deny/drop actions, UCI Machine Learning Repository ("Internet Firewall Data").

The directional-SVDD script (svdd_directional_kernels.py) expects a data/twitter.csv of geotagged coordinates. That file is not included (large and of uncertain redistribution rights); the script documents the expected columns (longitude, latitude) so you can supply your own directional data.

Running

The Python scripts read their data via relative paths and are meant to be run from the code/ directory, e.g.:

cd code
python lssvdd_ionosphere.py
python autoencoder_outlier_detection.py

Dependencies: numpy, pandas, scipy, scikit-learn, cvxopt (SVDD), torch (autoencoder). The .Rmd files knit in R/RStudio.

Repository Contents

.
├── README.md
├── code/      # one file per method
├── data/      # bundled public datasets
└── report/    # the written project report

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Author: Katrina Stephenson