秩正则化与张量完备化和外推的贝叶斯推断
Rank regularization and Bayesian inference for tensor completion and extrapolation
摘要：
本文提出了一种新的正则化的PARAFAC分解因子捕获张量的秩，作为完成的三路数据阵列的缺失条目的关键使能器。在贝叶斯框架中，张量完成方法结合了先验信息，以增强其平滑和预测能力。这种概率方法可以自然地适应数据分布的一般模型，从而适应各种拟合标准，从而在最大后验意义上产生最佳估计。特别是，两个算法的高斯分布和泊松分布的数据，最小化秩正则化最小二乘误差和Kullback-Leibler发散，分别设计。所提出的技术是能够恢复“地面实况”的张量秩测试时，合成数据，并完成脑成像和酵母基因表达数据集分别与50%和15%的缺失条目，导致在-10 dB和-15 dB的恢复误差。
英文摘要：
A novel regularizer of the PARAFAC decomposition factors capturing the tensor's rank is proposed in this paper, as the key enabler for completion of three-way data arrays with missing entries. Set in a Bayesian framework, the tensor completion method incorporates prior information to enhance its smoothing and prediction capabilities. This probabilistic approach can naturally accommodate general models for the data distribution, lending itself to various fitting criteria that yield optimum estimates in the maximum-a-posteriori sense. In particular, two algorithms are devised for Gaussian- and Poisson-distributed data, that minimize the rank-regularized least-squares error and Kullback-Leibler divergence, respectively. The proposed technique is able to recover the "ground-truth'' tensor rank when tested on synthetic data, and to complete brain imaging and yeast gene expression datasets with 50% and 15% of missing entries respectively, resulting in recovery errors at -10dB and -15dB.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
