README.Rmd

---
output: github_document
bibliography: references.bib
nocite: '@*'
---
  
```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

# IRLS repository

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This repository provides a from‑first‑principles implementation of the
**Iteratively Reweighted Least Squares (IRLS)** algorithm for logistic regression.
It is designed for graduate students, advanced undergraduates, and practitioners 
with a strong interest in computational statistics, numerical optimization, and 
the theoretical foundations of generalized linear models. In addition to a 
detailed mathematical derivation, the repository includes annotated R code and 
a real‑world case study using stock market data, offering both theoretical
insight and practical application.

By visiting the website (`vadimtyuryaev.github.io/IRLS/`) and following the 
accompanying calculations and code implementations, you will:

1. **Understand the exponential‑family formulation** of the binomial distribution, 
and derive the log‑likelihood, score vector, and Fisher information from
first principles.  

2. **See how Newton–Raphson** algorithm applied to the binomial log‑likelihood
can be recast as weighted least squares, laying the theoretical foundation 
for the IRLS. 

3. **Walk through the IRLS algorithm** with an easy-to-follow mathematical
derivation and clear matrix formulation.

4. **Examine an R implementation** (`IRLS_logistic_binomial`) with detailed
annotations, illustrating how to initialize, iterate, and stabilize your fits in
practice. 

5. **Apply IRLS to real data** (the `S&P Daily Smarket dataset`), and directly 
verify that results obtained reproduce the same coefficients as R's built-in 
function `glm(..., family=binomial)`.  

# References