Efficient Volume Sampling for Row/Column Subset Selection

@article{Deshpande2010EfficientVS,
  title={Efficient Volume Sampling for Row/Column Subset Selection},
  author={Amit Deshpande and Luis Rademacher},
  journal={2010 IEEE 51st Annual Symposium on Foundations of Computer Science},
  year={2010},
  pages={329-338}
}
We give efficient algorithms for volume sampling, i.e., for picking $k$-subsets of the rows of any given matrix with probabilities proportional to the squared volumes of the simplices defined by them and the origin (or the squared volumes of the parallelepipeds defined by these subsets of rows). %In other words, we can efficiently sample $k$-subsets of $[m]$ with probabilities proportional to the corresponding $k$ by $k$ principal minors of any given $m$ by $m$ positive semi definite matrix… CONTINUE READING
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