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Topological Summaries and Sufficient Statistics

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Topological Summaries and Sufficient Statistics
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Statistical modeling using topological summaries
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19
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CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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Abstract
I will discuss how topological summaries can be used to model various shapes as well as other high-dimensional data. I will talk about geometric and statistical properties of the space of summaries and how these summaries are the result of various filtrations. I will then discuss why multi-parameter persistence would be a very nice tool for these problems. The first half of the talk will be a review and I will focus on some of my research in the second half.