Skip to content

GLM Algorithm Arena · Phase I

An encyclopedia of algorithms for generalized linear models.

Every estimator for linear and generalized linear models — classical, penalized, high-dimensional, and online — reduced to one precise mapping and documented under one unified notation. From OLS to debiased Lasso to streaming stochastic approximation.

Browse the catalogue Read the framework

The one question every card answers

Given a design matrix \(X\), a response vector \(y\), and a link function \(g\), how does this algorithm produce a coefficient estimate \(\hat\beta\) ?

Each method can be viewed as the same essential mapping \((X, y, g) \mapsto \hat\beta\) and written against the shared template \(\;\hat\beta=\arg\min_\beta \mathcal L(\beta)+\lambda P(\beta)\), so estimators defined across decades of literature can be read, compared, and — in later phases — benchmarked on equal footing.

Explore

  •   Notation & framework

    The shared mathematical language: exponential family, link functions, loss, score and Fisher information, penalties, and the optimization primitives every card builds on.

    Read the framework

  •   Taxonomy

    How hundreds of solvers stay navigable, from classical closed forms to online stochastic approximation.

    See the taxonomy

  •   Card schema

    The exact, faithful template each algorithm follows — machine-readable metadata plus nine fixed sections, with a strict faithfulness rule.

    View the schema

  •   Algorithm catalogue

    The growing collection: OLS, Ridge, Lasso, Elastic Net, SCAD, MCP, LARS, FISTA, debiased Lasso, SGD, and many more.

    Open the catalogue

Project construction

  • I · Documentation   current

    Faithful algorithm cards — exact mathematics only. Each defines the estimator, the algorithm, its hyperparameters, and the precise \((X,y,g)\mapsto\hat\beta\) contract.

  • II · Implementation   planned

    Python solvers behind one interface, fit(X, y, link, **config) -> beta_hat, mirroring each method's official construction.

  • III · The Arena   planned

    Run every solver across many datasets; study performance, agreement, and the correlations between their outputs.

Contributing a card

Copy the stub in the card schema, drop it in docs/algorithms/<id>.md, fill the fixed sections faithfully from the source paper, and add the bibkey to reference.bib. Run python scripts/validate_cards.py, and it appears in the catalogue.