Research map / Learning theory and algorithms / Matrix and tensor methods

Group-Aware Matrix Estimation and Latent Subspace Recovery

NeurIPS 2026 · Learning theory and algorithms › Matrix and tensor methods · approach: Matrix completion and factorization · 0 citations (OpenAlex)

Read the paperCheck your idea against 108,967 papers

AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.

Proposes GAME, a convex matrix completion estimator with overlapping per-meta-category nuclear-norm penalties, solved via proximal averaging, with finite-sample error and subspace guarantees and experiments on synthetic, MovieLens, BirdSet, and Neuropixels data.

Problem

Matrix completion with heterogeneous rows that belong to overlapping meta-categories; global low-rank estimators smooth away subgroup-specific latent structure, especially for weakly observed groups.

Approach

Penalize the nuclear norm of each overlapping category-specific row-submatrix in a single convex objective (weighted sum of per-category nuclear norms), optimized with proximal averaging instead of ADMM, giving local rank-dependent error bounds and per-category subspace recovery.

Key results

• On MovieLens-100k under block-wise missingness, GAME attains the lowest test RMSE across nearly all block-missingness levels, with the gap widening as subgroup missingness increases; FNNM is the strongest competitor.
• On synthetic crossed-group data at 60% masking, GAME nearly matches the fully observed oracle clustering at small and moderate beta and outperforms all baselines.
• On Svoboda Neuropixels striatum recovery, GAME attains the lowest mean Grassmann distance to the fully observed subspace across masking probabilities.

Surprising findings

• On BirdSet top-1 accuracy, modern tabular imputation baselines (MissForest/TabImpute) perform slightly better than GAME at some masking levels.

Limitations

• Advantages depend on meta-categories capturing meaningful subgroup-specific low-rank structure; uninformative metadata gives limited gains.
• Theory assumes block-wise uniform i.i.d. sampling and requires each category to be sufficiently sampled.
• Theoretical gains over global nuclear norm are shown mainly in the tall-matrix regime with distinct block subspaces.

Experimental setup

Datasets: MovieLens-100k BirdSet HSN Svoboda Lab Neuropixels synthetic hierarchical group data

Benchmarks: MovieLens-100k BirdSet HSN Svoboda Lab Neuropixels synthetic clustering

Metrics: ARI NMI RMSE AUROC cmAP top-1 accuracy Grassmann distance

Baselines: singular value thresholding alternating least squares DirtyIMC Maxide FNNM OCMC MissForest TabImpute

Builds on: nuclear-norm matrix completion (Negahban-Wainwright) proximal average algorithm (Bauschke et al.) Maxide FNNM DirtyIMC

Closest papers by meaning

• Non-Negative Inductive Matrix Completion for Discrete Dyadic Data (AAAI 2017 · similarity 0.86)
• Dynamic matrix recovery from incomplete observations under an exact low-rank constraint (NeurIPS 2016 · similarity 0.86)
• Thy Friend is My Friend: Iterative Collaborative Filtering for Sparse Matrix Estimation (NeurIPS 2017 · similarity 0.86)
• Connectivity Shapes Implicit Regularization in Matrix Factorization Models for Matrix Completion (NeurIPS 2024 · similarity 0.85)
• A Pairwise Pseudo-likelihood Approach for Matrix Completion with Informative Missingness (NeurIPS 2024 · similarity 0.84)
• FasMe: Fast and Sample-efficient Meta Estimator for Precision Matrix Learning in Small Sample Settings (NeurIPS 2024 · similarity 0.84)