Bayesian streaming sparse Tucker decomposition
Bayesian streaming sparse Tucker decomposition
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发表时间：
2021
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通讯作者：
Shikai Fang;Robert M. Kirby;Shandian Zhe
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作者：
Shikai Fang;Robert M. Kirby;Shandian Zhe
塔克分解是一种经典的张量分解模型。与应用最广泛的CP分解相比，塔克模型更加灵活且更具可解释性，因为它考虑了不同模式下因子之间的每一种可能的（乘法）相互作用。然而，这也带来了过拟合的风险以及计算上的挑战，特别是在快速流数据的情况下。为了解决这些问题，我们开发了BASS - 塔克，一种贝叶斯流稀疏塔克分解方法。我们对核心张量元素设置了尖峰 - 平板先验，以自动选择有意义的因子相互作用，从而防止过拟合并进一步增强可解释性。为了实现高效的流分解，我们使用条件矩匹配和德尔塔方法，在接收到每个流批次时对潜在因子和核心张量进行一次性增量更新。因此，我们避免了像标准的假定密度滤波那样逐个处理数据点，因为标准方法需要为每个点更新核心张量，效率非常低。我们在运行的后验中明确引入并更新一个稀疏先验近似，以在流推理中实现有效的稀疏估计。我们在几个实际应用中展示了BASS - 塔克的优势。
Tucker decomposition is a classical tensor factorization model. Compared with the most widely used CP decomposition, Tucker model is much more flexible and interpretable in that it accounts for every possible (multiplicative) interaction be-tween the factors in different modes. However, this also brings in the risk of overfitting and computational challenges, especially in the case of fast streaming data. To address these issues, we develop BASS-Tucker, a BAyesian Streaming Sparse Tucker decomposition method. We place a spike-and-slab prior over the core tensor elements to automatically select meaningful factor interactions so as to prevent overfitting and to further enhance the interpretability. To enable efficient streaming factorization, we use conditional moment matching and delta method to develop one-shot incremental update of the latent factors and core tensor upon receiving each streaming batch. Thereby, we avoid processing the data points one by one as in the standard assumed density filtering, which needs to update the core tensor for each point and is quite inefficient. We explicitly introduce and up-date a sparse prior approximation in the running posterior to fulfill effective sparse estimation in the streaming inference. We show the advantage of BASS-Tucker in several real-world applications.