Related papers: Bayesian Low-rank Matrix Completion with Dual-graph Embedding: Prior Analysis and Tuning-free Inference

Bayesian Low-rank Matrix Completion with Dual-graph Embedding: Prior Analysis and Tuning-free Inference

URL: http://arxiv.org/abs/2203.10044v1
Date: Fri, 18 Mar 2022 16:38:30 GMT
Title: Bayesian Low-rank Matrix Completion with Dual-graph Embedding: Prior Analysis and Tuning-free Inference
Authors: Yangge Chen, Lei Cheng, Yik-Chung Wu
Abstract summary: We propose a novel Bayesian learning algorithm that automatically learns the hyper- parameters associated with dual-graph regularization. A novel prior is devised to promote the low-rankness of the matrix and encode the dual-graph information simultaneously. Experiments using synthetic and real-world datasets demonstrate the state-of-the-art performance of the proposed learning algorithm.
Score: 16.82986562533071
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: Recently, there is a revival of interest in low-rank matrix completion-based unsupervised learning through the lens of dual-graph regularization, which has significantly improved the performance of multidisciplinary machine learning tasks such as recommendation systems, genotype imputation and image inpainting. While the dual-graph regularization contributes a major part of the success, computational costly hyper-parameter tunning is usually involved. To circumvent such a drawback and improve the completion performance, we propose a novel Bayesian learning algorithm that automatically learns the hyper-parameters associated with dual-graph regularization, and at the same time, guarantees the low-rankness of matrix completion. Notably, a novel prior is devised to promote the low-rankness of the matrix and encode the dual-graph information simultaneously, which is more challenging than the single-graph counterpart. A nontrivial conditional conjugacy between the proposed priors and likelihood function is then explored such that an efficient algorithm is derived under variational inference framework. Extensive experiments using synthetic and real-world datasets demonstrate the state-of-the-art performance of the proposed learning algorithm for various data analysis tasks.

Related papers

Fast Dual-Regularized Autoencoder for Sparse Biological Data [65.268245109828]
We develop a shallow autoencoder for the dual neighborhood-regularized matrix completion problem. We demonstrate the speed and accuracy advantage of our approach over the existing state-of-the-art in predicting drug-target interactions and drug-disease associations.
arXiv Detail & Related papers (2024-01-30T01:28:48Z)
Efficiently Learning the Graph for Semi-supervised Learning [4.518012967046983]
We show how to learn the best graphs from the sparse families efficiently using the conjugate gradient method. Our approach can also be used to learn the graph efficiently online with sub-linear regret, under mild smoothness assumptions. We implement our approach and demonstrate significant ($sim$10-100x) speedups over prior work on semi-supervised learning with learned graphs on benchmark datasets.
arXiv Detail & Related papers (2023-06-12T13:22:06Z)
Representation Learning with Multi-Step Inverse Kinematics: An Efficient and Optimal Approach to Rich-Observation RL [106.82295532402335]
Existing reinforcement learning algorithms suffer from computational intractability, strong statistical assumptions, and suboptimal sample complexity. We provide the first computationally efficient algorithm that attains rate-optimal sample complexity with respect to the desired accuracy level. Our algorithm, MusIK, combines systematic exploration with representation learning based on multi-step inverse kinematics.
arXiv Detail & Related papers (2023-04-12T14:51:47Z)
Transductive Matrix Completion with Calibration for Multi-Task Learning [3.7660066212240757]
We propose a transductive matrix completion algorithm that incorporates a calibration constraint for the features under the multi-task learning framework. The proposed algorithm recovers the incomplete feature matrix and target matrix simultaneously. Several synthetic data experiments are conducted, which show the proposed algorithm out-performs other existing methods.
arXiv Detail & Related papers (2023-02-20T08:47:23Z)
Improved Algorithms for Neural Active Learning [74.89097665112621]
We improve the theoretical and empirical performance of neural-network(NN)-based active learning algorithms for the non-parametric streaming setting. We introduce two regret metrics by minimizing the population loss that are more suitable in active learning than the one used in state-of-the-art (SOTA) related work.
arXiv Detail & Related papers (2022-10-02T05:03:38Z)
Bayesian Graph Contrastive Learning [55.36652660268726]
We propose a novel perspective of graph contrastive learning methods showing random augmentations leads to encoders. Our proposed method represents each node by a distribution in the latent space in contrast to existing techniques which embed each node to a deterministic vector. We show a considerable improvement in performance compared to existing state-of-the-art methods on several benchmark datasets.
arXiv Detail & Related papers (2021-12-15T01:45:32Z)
Matrix completion based on Gaussian belief propagation [5.685589351789462]
We develop a message-passing algorithm for noisy matrix completion problems based on matrix factorization. We derive a memory-friendly version of the proposed algorithm by applying a perturbation treatment commonly used in the literature of approximate message passing. Experiments on synthetic datasets show that while the proposed algorithm quantitatively exhibits almost the same performance under settings where the earlier algorithm is optimal, it is advantageous when the observed datasets are corrupted by non-Gaussian noise.
arXiv Detail & Related papers (2021-05-01T12:16:49Z)
Deep Learning Approach for Matrix Completion Using Manifold Learning [3.04585143845864]
This paper introduces a new latent variables model for data matrix which is a combination of linear and nonlinear models. We design a novel deep-neural-network-based matrix completion algorithm to address both linear and nonlinear relations among entries of data matrix.
arXiv Detail & Related papers (2020-12-11T01:01:54Z)
Single-Timescale Stochastic Nonconvex-Concave Optimization for Smooth Nonlinear TD Learning [145.54544979467872]
We propose two single-timescale single-loop algorithms that require only one data point each step. Our results are expressed in a form of simultaneous primal and dual side convergence.
arXiv Detail & Related papers (2020-08-23T20:36:49Z)
A Scalable, Adaptive and Sound Nonconvex Regularizer for Low-rank Matrix Completion [60.52730146391456]
We propose a new non scalable low-rank regularizer called "nuclear Frobenius norm" regularizer, which is adaptive and sound. It bypasses the computation of singular values and allows fast optimization by algorithms. It obtains state-of-the-art recovery performance while being the fastest in existing matrix learning methods.
arXiv Detail & Related papers (2020-08-14T18:47:58Z)

This list is automatically generated from the titles and abstracts of the papers in this site.