Distributed Matrix Completion and Robust Factorization
If learning methods are to scale to the massive sizes of modern datasets, it is essential for the field of machine learning to embrace parallel and distributed computing. Inspired by the recent development of matrix factorization methods with rich theory but poor computational complexity and by the relative ease of mapping matrices onto distributed architectures, we introduce a scalable divide-and-conquer framework for noisy matrix factorization. We present a thorough theoretical analysis of this framework in which we characterize the statistical errors introduced by the "divide" step and control their magnitude in the "conquer" step, so that the overall algorithm enjoys high-probability estimation guarantees comparable to those of its base algorithm. We also present experiments in collaborative filtering and video background modeling that demonstrate the near-linear to superlinear speed-ups attainable with this approach.
Code (0)
등록된 구현이 없습니다.
Tasks
Collaborative FilteringDistributed ComputingMatrix CompletionSimilar Papers 제목 키워드 기반
Matrix Completion and Low-Rank SVD via Fast Alternating Least Squares
The matrix-completion problem has attracted a lot of attention, largely as a result of the celebrated Netflix competition. Two popular approaches for solving the problem are nuclear-norm-regularized matrix approximation …
Matrix CompletionApproximate Method of Variational Bayesian Matrix Factorization/Completion with Sparse Prior
We derive analytical expression of matrix factorization/completion solution by variational Bayes method, under the assumption that observed matrix is originally the product of low-rank dense and sparse matrices with addi…
Matrix CompletionScalable Bayesian Non-linear Matrix Completion
Matrix completion aims to predict missing elements in a partially observed data matrix which in typical applications, such as collaborative filtering, is large and extremely sparsely observed. A standard solution is matr…
Collaborative FilteringMatrix CompletionMissing ElementsFederated Knowledge Graph Completion via Latent Embedding Sharing and Tensor Factorization
Knowledge graphs (KGs), which consist of triples, are inherently incomplete and always require completion procedure to predict missing triples. In real-world scenarios, KGs are distributed across clients, complicating co…
Knowledge Graph CompletionKnowledge GraphsAdaptive Matrix Completion for the Users and the Items in Tail
Recommender systems are widely used to recommend the most appealing items to users. These recommendations can be generated by applying collaborative filtering methods. The low-rank matrix completion method is the state-o…
Collaborative FilteringLow-Rank Matrix CompletionMatrix CompletionRecommendation Systems