Yutong Chao, Resat Gökhan, Jalal Etesami, Ali Habibnia
arXiv 25 May 2026 · Statistics — Machine Learning
arXiv:2605.26271 · PDF · DOI · OpenAlex · Extracted main text
We study a nonlinear factor model in which observed responses depend on low-rank latent factors through an unknown monotone link function. This setting is challenging and largely underexplored due to severe nonconvexity and identifiability issues. The link function is assumed to lie in a reproducing kernel Hilbert space (RKHS), enabling flexible nonparametric modeling while preserving identifiability. We formulate the problem as the joint recovery of the low-rank factors, loadings, and the nonlinear link function from possibly incomplete and noisy observations and propose a projected block coordinate descent (BCD) algorithm with explicit regularization to address scale and rotational ambiguities. Under mild incoherence of factors and standard sampling conditions, we establish convergence guarantees in both noiseless and noisy regimes, along with sublinear regret bounds for the link-function updates. Our results extend classical linear factor models to a broad nonlinear regime and provide a principled framework for learning nonlinear latent structures. We evaluate the proposed approach using controlled synthetic experiments, indicating promising performance.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Zheng, Qinqing and Lafferty, John (2016) Convergence analysis for rectangular matrix completion using Burer-Monteiro factorization and gradient descent | 0.894 | 7 | 5 | 71% |
| 2 | Sankagiri, Suryanarayana and Etesami, Jalal and Grossglauser, Matthias (2025) Recommendations from Sparse Comparison Data: Provably Fast Convergence for Nonconvex Matrix Factorization self | 0.874 | 6 | 2 | 100% |
| 3 | Candès, Emmanuel and Recht, Benjamin (2009) Exact Matrix Completion via Convex Optimization | 0.737 | 3 | 2 | 100% |
| 4 | Chen, Yudong and Wainwright, Martin J (2015) Fast low-rank estimation by projected gradient descent: General statistical and algorithmic guarantees | 0.737 | 3 | 2 | 100% |
| 5 | Sun, Ruoyu and Luo, Zhi-Quan (2016) Guaranteed matrix completion via non-convex factorization | 0.737 | 3 | 2 | 100% |
| 6 | Candes, Emmanuel J and Plan, Yaniv (2010) Matrix completion with noise | 0.644 | 2 | 2 | 100% |
| 7 | Caner, Mehmet and Daniele, Maurizio (2025) Deep learning based residuals in non-linear factor models: Precision matrix estimation of returns with low signal-to-noise ratio | 0.644 | 2 | 2 | 100% |
| 8 | Fan, Jianqing and Liao, Yuan and Mincheva, Martina (2013) Large covariance estimation by thresholding principal orthogonal complements | 0.644 | 2 | 2 | 100% |
| 9 | Scholkopf, Bernhard and Smola, Alexander J (2018) Learning with kernels: support vector machines, regularization, optimization, and beyond | 0.585 | 3 | 1 | 100% |
| 10 | Chen, Mingli and Fernández-Val, Iván and Weidner, Martin (2014) Nonlinear panel models with interactive effects | 0.511 | 2 | 1 | 100% |
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