# Structured Learning via Logistic Regression

arXiv: https://arxiv.org/abs/1407.0754 · HTML: https://mlsanity.com/paper/1407.0754/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jul 2014.

## Built on by (most cited first, 2 of 2)

- [Language Independent Neuro-Symbolic Semantic Parsing for Form Understanding](https://mlsanity.com/paper/2305.04460/) (2023)
- [Heatmap Regression without Soft-Argmax for Facial Landmark Detection](https://mlsanity.com/paper/2508.14929/) (2025)

## Abstract (arXiv)

A successful approach to structured learning is to write the learning objective as a joint function of linear parameters and inference messages, and iterate between updates to each. This paper observes that if the inference problem is "smoothed" through the addition of entropy terms, for fixed messages, the learning objective reduces to a traditional (non-structured) logistic regression problem with respect to parameters. In these logistic regression problems, each training example has a bias term determined by the current set of messages. Based on this insight, the structured energy function can be extended from linear factors to any function class where an "oracle" exists to minimize a logistic loss.