Non-conservative screening rule for sparse tensor regression

Sparse tensor regression, as an extension to higher dimensions, maintains the inherent tensor structure to mitigate the curse of dimensionality, and can adeptly capture intricate nonlinear data relationships. Nonetheless, effectively minimizing computational complexity and reducing time costs remains a significant challenge. To address this limitation, this paper integrates the "screening" concept into tensor regression by introducing a novel non-conservative screening rule, i.e., fast Unit-Tensor Screening based on Working Set and Second-Order (TSWSSO). This method leverages second-order information from the primal problem to formulate screening tests while employs working set strategy along with precise warm starts to demonstrate its superior screening efficacy. Karush-Kuhn-Tucker (KKT) Checking is exploited to guarantee the safety of screening rule both theoretically and practically. Our proposed rules surpass seven alternative solutions studied on synthetic and real datasets by significantly enhancing solution speed without sacrificing accuracy. Furthermore, the foundational concept of this screening rule extends effectively to other tensor regression models, showcasing strong generalization capabilities.