Bayesian Continuous-Time Tucker Decomposition
Bayesian Continuous-Time Tucker Decomposition
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发表时间：
2022
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通讯作者：
Shikai Fang;A. Narayan;Robert M. Kirby;Shandian Zhe
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作者：
Shikai Fang;A. Narayan;Robert M. Kirby;Shandian Zhe
张量分解是多路数据分析和预测的主要框架，尽管实际数据通常包含观察到的条目的时间戳，但现有的张量分解方法忽略了，或者使用这些有价值的临时信息。 Continuous-Time Tucker Decomposition (BCTT). We model the tensor-core of the classic Tucker decomposition as a time-varying function, and place a Gaussian process prior to flexibly estimate all kinds of temporary dynamics. In this way, our model maintains the interpretability while is flexi-ble enough to capture various complex temporary relationships between the tensor nodes. For ef-ficient and high-quality posterior inference, we use the stochastic differential equation (SDE) representation of temporary GPs to build an equal state-space prior, which avoids huge kernel matrix computation and sparse/low-rank approximations. We then use Kalman filtering, RTS smoothing, and conditional moment matching to develop a scalable message-passing inference al-gorithm. We show the advantage of our method in simulation and several real-world applications.
Tensor decomposition is a dominant framework for multiway data analysis and prediction. Although practical data often contains timestamps for the observed entries, existing tensor decomposition approaches overlook or under-use this valuable temporal information. They either drop the timestamps or bin them into crude steps and hence ignore the temporal dynamics within each step or use simple parametric time coefficients. To overcome these limitations, we propose Bayesian Continuous-Time Tucker Decomposition (BCTT). We model the tensor-core of the classical Tucker decomposition as a time-varying function, and place a Gaussian process prior to flexibly estimate all kinds of temporal dynamics. In this way, our model maintains the interpretability while is flexi-ble enough to capture various complex temporal relationships between the tensor nodes. For ef-ficient and high-quality posterior inference, we use the stochastic differential equation (SDE) representation of temporal GPs to build an equivalent state-space prior, which avoids huge kernel matrix computation and sparse/low-rank approximations. We then use Kalman filtering, RTS smoothing, and conditional moment matching to develop a scalable message-passing inference al-gorithm. We show the advantage of our method in simulation and several real-world applications.