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What is Learnable in Valiant's Theory of the Learnable? Learning Perturbations to Extrapolate Your LLM Byzantine-Robust Distributed Sparse Learning Revisited The Sample Complexity of Multiple Change Point Identification under Bandit Feedback A proximal gradient algorithm for composite log-concave sampling Model-based Bootstrap of Controlled Markov Chains Approximation of Maximally Monotone Operators : A Graph Convergence Perspective Posterior Contraction Rates for Sparse Kolmogorov-Arnold Networks in Anisotropic Besov Spaces MIST: Reliable Streaming Decision Trees for Online Class-Incremental Learning via McDiarmid Bound A Spectral Framework for Closed-Form Relative Density Estimation Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability Higher-Order Equilibrium Tracking for EM-Compressible Online Estimation Scaling Limits of Long-Context Transformers A Note on Non-Negative $L_1$-Approximating Polynomials Susceptibilities and Patterning: A Primer on Linear Response in Bayesian Learning Linear Response Estimators for Singular Statistical Models Statistical inference with belief functions: A survey Robust stochastic first order methods in heavy-tailed noise via medoid mini-batch gradient sampling Every Feedforward Neural Network Definable in an o-Minimal Structure Has Finite Sample Complexity Adaptive auditing of AI systems with anytime-valid guarantees Locally Near Optimal Piecewise Linear Regression in High Dimensions via Difference of Max-Affine Functions Risk-Controlled Post-Processing of Decision Policies Covariate Balancing and Riesz Regression Should Be Guided by the Neyman Orthogonal Score in Debiased Machine Learning A Unified Pair-GRPO Family: From Implicit to Explicit Preference Constraints for Stable and General RL Alignment Time-Inhomogeneous Preconditioned Langevin Dynamics A Fine-Grained Understanding of Uniform Convergence for Halfspaces CITE: Anytime-Valid Statistical Inference in LLM Self-Consistency Ratio-based Loss Functions Optimal Confidence Band for Kernel Gradient Flow Estimator A renormalization-group inspired lattice-based framework for piecewise generalized linear models
Sample-efficient inductive matrix completion with noise a...
Yuepeng Yang, Cong Ma · 2026-05-17 · via math.ST updates on arXiv.org

Inductive matrix completion (IMC) is a variant of low-rank matrix completion that incorporates row and column side-information. In principle, it can reduce the effective dimension of the recovery problem from the ambient matrix size to the dimension of the side-information features. Existing theory, however, does not fully realize this advantage in the noisy setting: sample-efficient guarantees only apply to noiseless recovery, while noisy guarantees require sample sizes comparable to ordinary matrix completion. This paper closes this gap for noisy IMC. We analyze a nonconvex projected gradient descent algorithm with spectral initialization and prove that, under exact side-information, it achieves linear convergence and stable recovery at a sample complexity governed by the effective side-information dimension rather than the ambient matrix dimension. The key technical ingredient is a local regularity condition for the IMC loss that holds at this reduced sample size, despite the mismatch between the observation pattern and the side-information subspaces. We further extend the analysis to inexact side-information, showing that the same reduced sample complexity is preserved and that the estimation error degrades optimally with the level of subspace misspecification. Motivated by this trade-off, we also propose a penalized interpolation between IMC and ordinary matrix completion that balances sample efficiency against robustness to imperfect side-information. Simulations and experiments on the MovieLens dataset support the theoretical findings and illustrate the practical benefits of exploiting side-information in low-sample regimes.