Core Concepts
Weighted least-squares approximation using determinantal point processes and volume sampling achieves quasi-optimality in expectation.
Abstract
The content discusses weighted least-squares approximation using determinantal point processes and volume sampling. It covers optimal sampling, quasi-optimality results, and stability of projections. Various distributions are explored, along with numerical experiments showcasing performance.
- Introduction to the problem of approximating functions.
- Weighted least-squares projection minimizes errors.
- Determinantal point processes introduce diversity in feature selection.
- Generalized volume sampling for quasi-optimality.
- Alternative strategies for reducing sample complexity.
- Preliminary results on weighted least-squares projections.
- Properties of projection determinantal point process and volume sampling.
- Stability analysis and error bounds for different distributions.
- Unbiased estimation and aggregation of projections.
Stats
n = O(m log(m))
λmin(Gw) ≥ 1 - δ