OpenNovelty.org

Covariate-Guided Clusterwise Linear Regression for Generalization to Unseen Data

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
Clusterwise Linear Regression (CLR)Covariate-Guided AssignmentProxy NetworkVector QuantizationConvergence Guarantee
Abstract:

In many tabular regression tasks, the relationships between covariates and response can often be approximated as linear only within localized regions of the input space; a single global linear model therefore fails to capture these local relationships. Conventional Clusterwise Linear Regression (CLR) mitigates this issue by learning KK local regressors. However, existing algorithms either optimize latent binary indicators, (i) providing no explicit rule for assigning an unseen\textit{unseen} covariate vector to a cluster at test time, or rely on heuristic mixture of experts approaches, (ii) lacking convergence guarantees. To address these limitations, we propose covariate-guided\textit{covariate-guided} CLR, an end-to-end framework that jointly learns an assignment function and KK linear regressors within a single gradient-based optimization loop. During training, a proxy network iteratively predicts coefficient vectors for inputs, and hard vector quantization assigns samples to their nearest codebook regressors. This alternating minimization procedure yields monotone descent of the empirical risk, converges under mild assumptions, and enjoys a PAC-style excess-risk bound. By treating the covariate data from all clusters as a single concatenated design matrix, we derive an FF-test statistic from a nested linear model, quantitatively characterizing the effective model complexity. As KK varies, our method spans the spectrum from a single global linear model to instance-wise fits. Experimental results show that our method exactly reconstructs synthetic piecewise-linear surfaces, achieves accuracy comparable to strong black-box models on standard tabular benchmarks, and consistently outperforms existing CLR and mixture-of-experts approaches.

Disclaimer
This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
If you have any questions, please contact: mingzhang23@m.fudan.edu.cn

Overview

Overall Novelty Assessment

The paper proposes an end-to-end framework for covariate-guided clusterwise linear regression, jointly learning an assignment function and K local regressors through gradient-based optimization with hard vector quantization. It occupies the 'End-to-End Gradient-Based Assignment Learning' leaf within the 'Covariate-Driven Cluster Assignment Methods' branch, where it is currently the sole paper in that leaf. This positioning reflects a relatively sparse research direction focused on unified gradient descent for both assignment and regression, distinguishing it from iterative alternating schemes and distance-based methods that populate neighboring branches.

The taxonomy reveals several neighboring directions: 'Iterative Clustering and Local Model Estimation' contains fuzzy and distance-based methods that alternate between assignment and parameter updates, while 'Model-Based Clustering with Linear Regression Components' adopts probabilistic mixture frameworks. The paper diverges from these by treating assignment as a differentiable function learned end-to-end rather than through EM-style alternation or fixed distance metrics. Its use of hard vector quantization and proxy networks contrasts with fuzzy membership approaches in 'Fuzzy Clustering with Takagi-Sugeno Local Models' and the semi-supervised metric learning in 'Distance-Based Clustering with Local Regressors', emphasizing direct gradient flow over heuristic assignment rules.

Among 27 candidates examined, the end-to-end framework contribution (10 candidates, 0 refutable) appears novel within the limited search scope, with no prior work combining gradient-based assignment learning and hard quantization in this manner. The convergence guarantees contribution (7 candidates, 2 refutable) shows more substantial overlap, suggesting existing theoretical analyses of alternating minimization may cover similar ground. The model complexity quantification via F-test (10 candidates, 0 refutable) appears less explored in the examined literature. These statistics reflect a targeted semantic search rather than exhaustive coverage, indicating the framework's novelty is conditional on the top-27 matches retrieved.

Based on the limited search scope of 27 semantically similar papers, the work introduces a distinctive combination of differentiable assignment and local regression within a sparse taxonomy leaf. However, the convergence analysis overlaps with prior theoretical work, and the search does not capture the full breadth of gradient-based clustering or neural mixture-of-experts literature. The novelty assessment is thus provisional, contingent on the semantic retrieval strategy and the specific papers indexed in the taxonomy.

Taxonomy

Core-task Taxonomy Papers
13
3
Claimed Contributions
27
Contribution Candidate Papers Compared
2
Refutable Paper

Research Landscape Overview

Core task: learning local linear regressors with covariate-based cluster assignment for tabular regression. The field addresses heterogeneity in tabular data by partitioning observations into clusters, each governed by its own linear model, with cluster membership determined by covariates rather than fixed labels. The taxonomy reveals several complementary perspectives. Covariate-Driven Cluster Assignment Methods emphasize learning assignment rules directly from input features, often via gradient-based or distance-metric approaches. Iterative Clustering and Local Model Estimation focuses on alternating optimization schemes that refine both cluster boundaries and regression parameters. Multi-View and Multi-Source Regression Clustering tackles scenarios with multiple feature representations or data sources, as seen in Scalable Multi-View Regression[1]. Model-Based Clustering with Linear Regression Components adopts probabilistic mixture frameworks, while Nonparametric Local Smoothing for Clustered and Longitudinal Data leverages kernel or spline methods for flexible local fits, exemplified by Local Polynomial Clustered[11]. Finally, Partial Linear and Hybrid Regression Models with Clustering blend parametric and nonparametric components, illustrated by Clustered Partial Linear[6]. A central tension across these branches is the trade-off between interpretability and flexibility: hard assignment rules yield simpler cluster structures but may miss smooth transitions, whereas soft or fuzzy methods, such as Incremental Fuzzy Regression[3], capture gradual membership at the cost of added complexity. Another active theme is scalability and convergence guarantees, with works like Cluster Linear Consistency[8] exploring theoretical properties of iterative schemes. The original paper, Covariate-Guided Clusterwise[0], sits within the End-to-End Gradient-Based Assignment Learning sub-branch of Covariate-Driven methods. It emphasizes jointly optimizing cluster assignment functions and local regressors through backpropagation, contrasting with older alternating schemes like Split-and-Merge Clustering[9] and differing from distance-metric learning approaches such as Semi-supervised Distance Metric[7] by directly parameterizing assignment via neural layers. This positioning highlights a modern trend toward differentiable, end-to-end pipelines that unify clustering and prediction in a single optimization objective.

Claimed Contributions

End-to-end covariate-guided clusterwise linear regression framework

The authors introduce CG-CLR, a framework that simultaneously trains both a data-driven assignment rule (via a proxy network) and K local linear regressors through joint gradient-based optimization. This addresses the limitation of existing CLR methods that lack explicit rules for assigning unseen covariates at test time.

10 retrieved papers
Convergence guarantees for alternating minimization with dual loss

The authors prove that their alternating update procedure achieves monotone descent of a dual loss function and establishes linear convergence toward optimal parameters under stated assumptions. They also derive PAC-style generalization bounds for the non-realizable setting.

7 retrieved papers
Can Refute
Model complexity quantification via F-test statistic

The authors develop an F-test based criterion that treats all K regressors as a nested linear model, enabling principled statistical selection of the number of clusters K and providing transparent quantification of effective degrees of freedom.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Within the taxonomy built over the current TopK core-task papers, the original paper is assigned to a leaf with no direct siblings and no cousin branches under the same grandparent topic. In this retrieved landscape, it appears structurally isolated, which is one partial signal of novelty, but still constrained by search coverage and taxonomy granularity.

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

End-to-end covariate-guided clusterwise linear regression framework

The authors introduce CG-CLR, a framework that simultaneously trains both a data-driven assignment rule (via a proxy network) and K local linear regressors through joint gradient-based optimization. This addresses the limitation of existing CLR methods that lack explicit rules for assigning unseen covariates at test time.

Contribution

Convergence guarantees for alternating minimization with dual loss

The authors prove that their alternating update procedure achieves monotone descent of a dual loss function and establishes linear convergence toward optimal parameters under stated assumptions. They also derive PAC-style generalization bounds for the non-realizable setting.

Contribution

Model complexity quantification via F-test statistic

The authors develop an F-test based criterion that treats all K regressors as a nested linear model, enabling principled statistical selection of the number of clusters K and providing transparent quantification of effective degrees of freedom.

Table of Contents

Covariate-Guided Clusterwise Linear Regression for Generalization to Unseen Data | Novelty Validation