The purpose of this work is to provide both theoretical understanding of and practical algorithms for dynamic low-rank matrix recovery. Although the benefits of exploiting dynamics in low-rank matrix recovery have been observed in many applications, the theoretical understanding of and justification for these methods is limited. This dissertation concerns two widely-used dynamics models in the context of low-rank matrix recovery: random walk dynamics and measurement induced dynamics. For random walk dynamics, we propose a locally weighted matrix smoothing (LOWEMS) framework, establish its recovery guarantee and algorithmic convergence, and discuss two practical extensions for it. For measurement induced dynamics, we propose a general DynEmb framework and demonstrate its effectiveness for the knowledge tracing application. In the end, we conduct some initial theoretical analysis on a simplified measurement induced dynamic model.Ph.D
