Bayesian Nonparametric Models for Multiway Data Analysis
Bayesian Nonparametric Models for Multiway Data Analysis
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DOI：
10.1109/tpami.2013.201
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发表时间：
2015-02
影响因子：
23.6
通讯作者：
Zenglin Xu;Feng Yan;Y. Qi
中科院分区：
文献类型：
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作者：
Zenglin Xu;Feng Yan;Y. Qi
张量分解是一种强大的多路数据分析计算工具。许多流行的张量分解方法——如Tucker分解和CANDECOMP/PARAFAC （CP）——相当于多线性分解。它们不足以模拟(i)数据实体之间复杂的相互作用，（ii）各种数据类型（例如缺失数据和二进制数据），以及（iii）嘈杂的观测值和异常值。为了解决这些问题，我们提出了用于多路数据分析的张量变量潜在非参数贝叶斯模型。我们将这些模型命名为InfTucker。这些新模型本质上是在无限特征空间中进行Tucker分解。与经典张量分解模型不同，我们的新方法在概率框架中处理连续和二进制数据。与之前的矩阵和张量贝叶斯模型不同，我们的模型基于具有非线性协方差函数的潜在高斯或$t$过程。此外，在网络数据上，我们的模型简化为非参数随机块模型，可用于发现潜在组和预测缺失的相互作用。为了有效地从数据中学习模型，我们开发了一种变分推理技术，并探索了计算效率的Kronecker积的性质。与经典的变分实现相比，该技术将时间和空间复杂性降低了几个数量级。在真实的多路和网络数据上，我们的新模型取得了比最先进的张量分解方法和块模型更高的预测精度。
Tensor decomposition is a powerful computational tool for multiway data analysis. Many popular tensor decomposition approaches—such as the Tucker decomposition and CANDECOMP/PARAFAC (CP)—amount to multi-linear factorization. They are insufficient to model (i) complex interactions between data entities, (ii) various data types (e.g., missing data and binary data), and (iii) noisy observations and outliers. To address these issues, we propose tensor-variate latent nonparametric Bayesian models for multiway data analysis. We name these models InfTucker. These new models essentially conduct Tucker decomposition in an infinite feature space. Unlike classical tensor decomposition models, our new approaches handle both continuous and binary data in a probabilistic framework. Unlike previous Bayesian models on matrices and tensors, our models are based on latent Gaussian or $t$ processes with nonlinear covariance functions. Moreover, on network data, our models reduce to nonparametric stochastic blockmodels and can be used to discover latent groups and predict missing interactions. To learn the models efficiently from data, we develop a variational inference technique and explore properties of the Kronecker product for computational efficiency. Compared with a classical variational implementation, this technique reduces both time and space complexities by several orders of magnitude. On real multiway and network data, our new models achieved significantly higher prediction accuracy than state-of-art tensor decomposition methods and blockmodels.