# Sparse Estimation of Generalized Linear Models (GLM) via Approximated Information Criteria

arXiv: https://arxiv.org/abs/1607.05169 · HTML: https://mlsanity.com/paper/1607.05169/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jul 2016.

## Built on by (most cited first, 1 of 1)

- [Constraint- and Score-Based Nonlinear Granger Causality Discovery with Kernels](https://mlsanity.com/paper/2601.09579/) (2026)

## Abstract (arXiv)

We propose a new sparse estimation method, termed MIC (Minimum approximated Information Criterion), for generalized linear models (GLM) in fixed dimensions. What is essentially involved in MIC is the approximation of the ℓ0-norm with a continuous unit dent function. Besides, a reparameterization step is devised to enforce sparsity in parameter estimates while maintaining the smoothness of the objective function. MIC yields superior performance in sparse estimation by optimizing the approximated information criterion without reducing the search space and is computationally advantageous since no selection of tuning parameters is required. Moreover, the reparameterization tactic leads to valid significance testing results that are free of post-selection inference. We explore the asymptotic properties of MIC and illustrate its usage with both simulated experiments and empirical examples.