# Partition-wise Linear Models

arXiv: https://arxiv.org/abs/1410.8675 · HTML: https://mlsanity.com/paper/1410.8675/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Oct 2014.

## Built on by (most cited first, 3 of 3)

- [ParsNets: A Parsimonious Orthogonal and Low-Rank Linear Networks for Zero-Shot Learning](https://mlsanity.com/paper/2312.09709/) (2023)
- [Improving Uncertainty Quantification of Variance Networks by Tree-Structured Learning](https://mlsanity.com/paper/2212.12658/) (2022)
- [Joint Optimization of Piecewise Linear Ensembles](https://mlsanity.com/paper/2405.00303/) (2024)

## Abstract (arXiv)

Region-specific linear models are widely used in practical applications because of their non-linear but highly interpretable model representations. One of the key challenges in their use is non-convexity in simultaneous optimization of regions and region-specific models. This paper proposes novel convex region-specific linear models, which we refer to as partition-wise linear models. Our key ideas are 1) assigning linear models not to regions but to partitions (region-specifiers) and representing region-specific linear models by linear combinations of partition-specific models, and 2) optimizing regions via partition selection from a large number of given partition candidates by means of convex structured regularizations. In addition to providing initialization-free globally-optimal solutions, our convex formulation makes it possible to derive a generalization bound and to use such advanced optimization techniques as proximal methods and decomposition of the proximal maps for sparsity-inducing regularizations. Experimental results demonstrate that our partition-wise linear models perform better than or are at least competitive with state-of-the-art region-specific or locally linear models.