A package for the sparse identification of nonlinear dynamical systems from data

Efficient Algorithms for L0 Regularized Learning

Generalized Linear Regressions Models (penalized regressions, robust regressions, ...)

a collection of modern sparse (regularized) linear regression algorithms.

MATLAB library of gradient descent algorithms for sparse modeling: Version 1.0.3

Statistical Models with Regularization in Pure Julia

Contains a wide-ranging collection of compressed sensing and feature selection algorithms. Examples include matching pursuit algorithms, forward and backward stepwise regression, sparse Bayesian learning, and basis pursuit.

Matlab toolbox for sparse regression

Sorted L1 Penalized Estimation

Sequential adaptive elastic net (SAEN) approach, complex-valued LARS solver for weighted Lasso/elastic-net problems, and sparsity (or model) order detection with an application to single-snapshot source localization.

Nonconvex Exterior Point Operator Splitting

Variable Selection and Task Grouping for Multi-Task Learning (VSTG-MTL)

Black-box spike and slab variational inference, example with linear models

Actually Sparse Variational Gaussian Processes implemented in GPlow

locus R package - Large-scale variational inference for variable selection in sparse multiple-response regression

Sparse Identification of Truncation Errors (SITE) for Data-Driven Discovery of Modified Differential Equations

Knowledge elicitation when the user can give feedback to different features of the model with the goal to improve the prediction on the test data in a "smal n, large p" setting.

Physically-informed model discovery of systems with nonlinear, rational terms using the SINDy-PI method. Contains functionality for spectral filtering/differentiation.

MGLM Toolbox for Matlab

Sparse Bayesian ARX models with flexible noise distributions