# A Unified Framework for Regularized Estimating Equations via Fixed-Point and Variational Inequality Problems

arXiv: https://arxiv.org/abs/2110.11074 · HTML: https://mlsanity.com/paper/2110.11074/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Oct 2021.

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

- [Generalized Random Forests using Fixed-Point Trees](https://mlsanity.com/paper/2306.11908/) (2023)

## Abstract (arXiv)

Many statistics problems are formulated within an estimating equation framework instead of a minimization framework. However, the regularized estimating equations (REE) have been much less extensively studies than regularized minimization problems. In this paper, we study an improved regularized estimating equation formulation and explore its subsequent equivalences in terms of (1) fixed-point problem specified via the proximal operator of the corresponding regularizer, and (2) generalized variational inequality problems. Such equivalences hold under general conditions and accommodate nonconvex regularizers. Moreover, these equivalences open up new possibilities in theoretical analysis and computational algorithms when studying the REE.