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High Dimensional Probability

Weekly Student Reading Group

Meeting - 6

CS@UIUC

Speaker: Chandni Nagda

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Recall: Norm of matrices with sub-gaussian entries

essentially

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Two-sided bound on sub-gaussian matrices

Improve this result in two ways

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  1. Sharper and two-sided bounds on the entire spectrum of A

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Approximate isometry when m >> n

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  1. Independence of entries → independence of rows

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Two-sided bound on sub-gaussian matrices

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Two-sided bound on sub-gaussian matrices

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Two-sided bound on sub-gaussian matrices

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Two-sided bound on sub-gaussian matrices

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Two-sided bound on sub-gaussian matrices

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Two-sided bound on sub-gaussian matrices

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Two-sided bound on sub-gaussian matrices

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Application: Covariance estimation

Need at least

suffices

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Application: Covariance estimation

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Application: Covariance estimation

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Application: Clustering of point sets

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Application: Clustering of point sets

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Application: Clustering of point sets

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Application: Clustering of point sets

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Application: Clustering of point sets

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References

  • Introduction to High Dimensional Probability, Roman Vershynin