Random Subspace

Random subspace methods address the computational challenges of high-dimensional data analysis by performing computations within randomly selected lower-dimensional subspaces. Current research focuses on developing and analyzing algorithms that leverage random subspaces for optimization problems (e.g., cubic regularized Newton methods, Gauss-Newton methods), causal inference, and generalization bound analysis in machine learning, often incorporating techniques like Krylov subspaces or Dirichlet process mixtures. These methods offer significant computational advantages, enabling the application of otherwise intractable algorithms to large datasets, while maintaining accuracy comparable to full-dimensional approaches in many cases. The resulting efficiency improvements have broad implications across various fields, including machine learning, statistics, and optimization.