# Consistent Collective Matrix Completion under Joint Low Rank Structure

@article{Gunasekar2015ConsistentCM, title={Consistent Collective Matrix Completion under Joint Low Rank Structure}, author={Suriya Gunasekar and Makoto Yamada and Dawei Yin and Yi Chang}, journal={ArXiv}, year={2015}, volume={abs/1412.2113} }

We address the collective matrix completion problem of jointly recovering a collection of matrices with shared structure from partial (and potentially noisy) observations. To ensure well--posedness of the problem, we impose a joint low rank structure, wherein each component matrix is low rank and the latent space of the low rank factors corresponding to each entity is shared across the entire collection. We first develop a rigorous algebra for representing and manipulating collective--matrix…

## 25 Citations

A PAC bound for joint matrix completion based on Partially Collective Matrix Factorization

- Computer Science2016 23rd International Conference on Pattern Recognition (ICPR)
- 2016

A first PAC generalization error bound for joint matrix completion based on the Partially Collective Matrix Factorization model is presented, which not only justifies the theoretical soundness of P-CMF, but also reveals its several insights.

Collective Matrix Completion

- Computer Science, Mathematics
- 2021

This work considers the problem of collective matrix completion with multiple and heterogeneous matrices, which can be count, binary, continuous, etc, and investigates the setting where, for each source, the matrix entries are sampled from an exponential family distribution.

Collective Matrix Completion

- Computer Science, MathematicsJ. Mach. Learn. Res.
- 2019

This work investigates the setting where, for each source, the matrix entries are sampled from an exponential family distribution and investigates the distribution-free case, and proves that the proposed estimators achieve fast rates of convergence under the two considered settings.

Robust Matrix Completion with Mixed Data Types

- Computer ScienceArXiv
- 2020

This work proposes a computationally feasible statistical approach with strong recovery guarantees along with an algorithmic framework suited for parallelization to recover a low rank matrix with partially observed entries for mixed data types in one step.

Co-Regularized Collective Matrix Factorization for Joint Matrix Completion

- Computer Science
- 2016

This paper introduces a novel joint matrix completion method based on a relaxed assumption that allows the matrix structures to be different, but assume their induced subspaces lie close to each other, and proposes a method that penalizes the distance between these subspaced while learning different factorization models for different matrices.

Partial Collective Matrix Factorization and its PAC Bound

- Computer ScienceISAIM
- 2016

This paper promoted a prior solution to the theoretical level and formalized an assumption-free factorization model called partial collective matrix factorization (pCMF), based on the fact that any two matrices (of the same row) admit some joint factorization such that their factors are partially shared.

Towards a Theoretical Understanding of Negative Transfer in Collective Matrix Factorization

- Computer ScienceUAI
- 2016

Under the statistical mini-max framework, lower bounds for the CMF estimator are derived and two insights are gained that suggest n.t. may be more effectively addressed via model construction other than model selection.

Convex Coupled Matrix and Tensor Completion

- Computer ScienceNeural Computation
- 2018

A set of convex low-rank inducing norms for coupled matrices and tensors are proposed, which can be used to find a globally optimal solution, whereas existing methods for coupled learning are nonconvex.

Convex Factorization Machine for Regression

- Computer ScienceArXiv
- 2015

The convex factorization machine (CFM) is proposed, which is a convex variant of the widely used Factorization Machines (FMs), and it is shown that CFM outperforms a state-of-the-art tensor factorization method in a toxicogenomics prediction task.

Convex Factorization Machine for Toxicogenomics Prediction

- Computer ScienceKDD
- 2017

It is shown in a toxicogenomics prediction task that CFM predicts the toxic outcomes of a collection of drugs better than a state-of-the-art tensor factorization method.

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