Tensor-Structured Sketching for Constrained Least Squares

Constrained least squares problems arise in many applications. Their memory and computation costs are expensive practice involving high-dimensional input data. We employ the so-called "sketching" strategy to project problem onto a space of much lower "sketching dimension" via random sketching matrix. The key idea is reduce dimension as possible while maintaining approximation accuracy. Tensor structure often present data matrices squares, including linearized inverse tensor decompositions. In this work, we utilize general class row-wise tensorized sub-Gaussian constrained optimizations for design's compatibility with structures. provide theoretical guarantees on terms error criterion probability failure rate. context unconstrained linear regressions, obtain an optimal estimate dimension. For optimization constraint sets, show that depends statistical complexity characterizes geometry underlying problems. Our theories demonstrated few concrete examples, regression sparse recovery