Convergence rate of Bayesian tensor estimator: Optimal rate without restricted strong convexity
This provides a theoretical foundation for tensor-based methods in applications like collaborative filtering and multi-task learning, though it appears incremental as it extends existing convergence analysis.
The paper tackles the problem of estimating the convergence rate of a Bayesian low-rank tensor estimator for regression, showing that it achieves a near-optimal rate in predictive accuracy without requiring strong convexity and adapts to unknown tensor rank.
In this paper, we investigate the statistical convergence rate of a Bayesian low-rank tensor estimator. Our problem setting is the regression problem where a tensor structure underlying the data is estimated. This problem setting occurs in many practical applications, such as collaborative filtering, multi-task learning, and spatio-temporal data analysis. The convergence rate is analyzed in terms of both in-sample and out-of-sample predictive accuracies. It is shown that a near optimal rate is achieved without any strong convexity of the observation. Moreover, we show that the method has adaptivity to the unknown rank of the true tensor, that is, the near optimal rate depending on the true rank is achieved even if it is not known a priori.