Learning from Binary Multiway Data: Probabilistic Tensor Decomposition and its Statistical Optimality.
Learning from Binary Multiway Data: Probabilistic Tensor Decomposition and its Statistical Optimality.
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发表时间：
2020-07
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通讯作者：
Li L
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作者：
Wang M;Li L
我们考虑用二进制项分解高阶张量的问题。这类数据问题经常出现在神经成像、推荐系统、主题建模和传感器网络定位等应用中。我们提出了一个多线性Bernoulli模型，发展了一种基于秩约束似然估计的方法，并得到了理论上的精度保证。与连续值问题相比，二元张量问题根据信噪比表现出有趣的相变现象。建立了参数张量估计的误差界，并证明了在所考虑的模型下，所得到的估计是极小极大最优的。此外，我们还提出了一种保证收敛的交替优化算法。通过对多个数据集的张量补全和聚类任务的仿真和分析，证明了该方法的有效性。
We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a multilinear Bernoulli model, develop a rank-constrained likelihood-based estimation method, and obtain the theoretical accuracy guarantees. In contrast to continuous-valued problems, the binary tensor problem exhibits an interesting phase transition phenomenon according to the signal-to-noise ratio. The error bound for the parameter tensor estimation is established, and we show that the obtained rate is minimax optimal under the considered model. Furthermore, we develop an alternating optimization algorithm with convergence guarantees. The efficacy of our approach is demonstrated through both simulations and analyses of multiple data sets on the tasks of tensor completion and clustering.