Nonconvex Matrix Completion with Linearly Parameterized Factors
Authors: Ji Chen, Xiaodong Li, Zongming Ma
JMLR 2022 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The effectiveness of our unified nonconvex optimization method is also empirically illustrated by extensive numerical simulations. Keywords: matrix completion, nonconvex geometry, nonconvex optimization, skew-symmetric, subspace constraints |
| Researcher Affiliation | Academia | Ji Chen EMAIL Department of Mathematics University of California, Davis Davis, CA 95616, USA Xiaodong Li EMAIL Department of Statistics University of California, Davis Davis, CA 95616, USA Zongming Ma EMAIL Department of Statistics, The Wharton School University of Pennsylvania Philadelphia, PA 19104, USA |
| Pseudocode | No | The paper describes mathematical methodologies and experimental procedures in narrative text, but it does not contain any explicitly labeled pseudocode blocks or algorithms. |
| Open Source Code | No | The paper does not provide any statement about releasing source code or a link to a code repository for the described methodology. It only mentions a license and attribution requirements for the paper itself. |
| Open Datasets | No | For simulation of nonconvex optimization for subspace-constrained matrix completion (7), the dimensions of M are set to be n1 = n2 = 500 and its rank is set as r = 2. We also set the dimensions of the prior column and row subspaces as s1 = s2 := s 40. In preparation for the construction of the column and row subspace constraints with various dimensions, we generate [u1, . . . , u40] and [v1, . . . , v40] according to the Haar measure on the manifold of 500 40 orthonormal basis matrices. The matrix to recover is fixed as M = u1v 1 +u2v 2 , which gives M 2 F = 2. |
| Dataset Splits | No | The paper describes how sampling support (Ω) is generated for observations from a matrix, using 'Model 1' and 'Model 2', and discusses 'sampling rates p'. However, it does not refer to traditional dataset splits like training, validation, or test sets for a pre-existing dataset. The data itself is generated synthetically, and 'sampling' refers to observing entries, not splitting a dataset. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware (e.g., CPU, GPU models, memory) used to conduct the experiments. |
| Software Dependencies | No | The paper mentions implementing gradient descent and using line search, but it does not specify any software names or versions (e.g., Python, PyTorch, TensorFlow, specific solvers) that would be needed to reproduce the experiment. |
| Experiment Setup | Yes | In all simulations, the sampling rate p is replaced with the empirical analog ˆp := |Ω| n1n2 . The hyperparameters are set as λ = 100 p (n1 + n2)/ˆp and α = 100. In both examples, the nonconvex objective (6) is minimized by gradient descent, with initialization for θ consisting with i.i.d. standard normal entries. At each step of the gradient descent, the step size is selected through line search. To be specific, at each update of θ, the step size is set to be max{2 k, 10 10} for k := min{t | t = 0, 1, 2, 3, , f(θ 2 t f(θ)) f(θ)}. The gradient descent iteration is terminated either after 500 iterations or as soon as the update on θ satisfied f(θ) 2 2 10 10. |