CS7300: Final Project

Jaryt Salvo

Date: 12/13/24

Fall 2024 | CS 7300 Unsupervised Learning

Statistical Computing: A Functional Approach

Foundations and Implementation

This work presents a rigorous implementation of fundamental statistical algorithms through the lens of functional programming. By leveraging Clojure’s immutable data structures and pure functions, we develop a robust framework for numerical computing that emphasizes both mathematical precision and computational efficiency.

Descriptive Statistics

Statistical measures form the cornerstone of numerical computing. Our implementation establishes fundamental operations with careful attention to numerical stability and computational efficiency. The descriptive namespace provides:

  • Robust implementations of central tendency and dispersion measures
  • Numerically stable algorithms for variance computation
  • Efficient matrix operations for covariance analysis

Eigendecomposition

The eigen namespace demonstrates the synthesis of mathematical theory with practical computation through:

  • Power iteration for dominant eigenvalue computation
  • QR algorithm for complete eigendecomposition
  • Inverse iteration for eigenvector determination

Principal Component Analysis

The pca namespace builds directly on these foundations, implementing PCA with:

  • Theoretical development from covariance analysis
  • Efficient matrix transformations for high-dimensional data
  • Comprehensive comparison with industry-standard implementations

Implementation Validation

Systematic validation ensures correctness through comparison with established tools:

  • Baseline implementation in Python using scikit-learn
  • Comprehensive test suite ensuring numerical accuracy
  • Performance analysis and optimization strategies

Technical Architecture

The implementation leverages modern Clojure libraries while maintaining functional purity:

  • Neanderthal for efficient numerical operations
  • Property-based testing for robust validation
  • Comprehensive documentation integrated with code

This work serves dual purposes: as a practical implementation of statistical algorithms and as an exploration of functional programming’s capabilities in numerical computing. Through careful attention to both mathematical rigor and computational efficiency, we demonstrate the viability of functional programming for serious statistical computing.

source: src/index.clj