StoTAM: Stochastic Alternating Minimization for Tucker-Structured Tensor Sensing
This work addresses efficient tensor recovery for signal processing and machine learning applications, but it appears incremental as it builds on existing factorized formulations with stochastic updates.
The paper tackles the problem of low-rank tensor sensing for high-dimensional data by proposing a stochastic alternating minimization algorithm that operates on Tucker-structured factors, avoiding expensive tensor projections and enabling efficient mini-batch updates. Numerical experiments show favorable convergence behavior in wall-clock time compared to existing stochastic baselines.
Low-rank tensor sensing is a fundamental problem with broad applications in signal processing and machine learning. Among various tensor models, low-Tucker-rank tensors are particularly attractive for capturing multi-mode subspace structures in high-dimensional data. Existing recovery methods either operate on the full tensor variable with expensive tensor projections, or adopt factorized formulations that still rely on full-gradient computations, while most stochastic factorized approaches are restricted to tensor decomposition settings. In this work, we propose a stochastic alternating minimization algorithm that operates directly on the core tensor and factor matrices under a Tucker factorization. The proposed method avoids repeated tensor projections and enables efficient mini-batch updates on low-dimensional tensor factors. Numerical experiments on synthetic tensor sensing demonstrate that the proposed algorithm exhibits favorable convergence behavior in wall-clock time compared with representative stochastic tensor recovery baselines.