Bayesian Matrix Completion via Adaptive Relaxed Spectral Regularization
Bayesian matrix completion has been studied based on a low-rank matrix factorization formulation with promising results. However, little work has been done on Bayesian matrix completion based on the more direct spectral regularization formulation. We fill this gap by presenting a novel Bayesian matrix completion method based on spectral regularization. In order to circumvent the difficulties of dealing with the orthonormality constraints of singular vectors, we derive a new equivalent form with relaxed constraints, which then leads us to design an adaptive version of spectral regularization feasible for Bayesian inference. Our Bayesian method requires no parameter tuning and can infer the number of latent factors automatically. Experiments on synthetic and real datasets demonstrate encouraging results on rank recovery and collaborative filtering, with notably good results for very sparse matrices.
Code (1)
Tasks
Bayesian InferenceCollaborative FilteringMatrix CompletionSimilar Papers 제목 키워드 기반
Concentration properties of fractional posterior in 1-bit matrix completion
The problem of estimating a matrix based on a set of its observed entries is commonly referred to as the matrix completion problem. In this work, we specifically address the scenario of binary observations, often termed …
Matrix CompletionPAC-Bayesian Matrix Completion with a Spectral Scaled Student Prior
We study the problem of matrix completion in this paper. A spectral scaled Student prior is exploited to favour the underlying low-rank structure of the data matrix. We provide a thorough theoretical investigation for ou…
Image InpaintingMatrix CompletionPAC-Bayesian matrix completion with a spectral scaled Student prior
We study the problem of matrix completion in this paper. A spectral scaled Student prior is exploited to favour the underlying low-rank structure of the data matrix. We provide a thorough theoretical investigation for ou…
Image InpaintingMatrix CompletionProbabilistic Low-Rank Matrix Completion with Adaptive Spectral Regularization Algorithms
We propose a novel class of algorithms for low rank matrix completion. Our approach builds on novel penalty functions on the singular values of the low rank matrix. By exploiting a mixture model representation of this pe…
Low-Rank Matrix CompletionMatrix CompletionBayesian Parametric Matrix Models: Principled Uncertainty Quantification for Spectral Learning
Scientific machine learning increasingly uses spectral methods to understand physical systems. Current spectral learning approaches provide only point estimates without uncertainty quantification, limiting their use in s…
Computational Efficiency