Mathematical Data Science Seminar Series
Date: Monday, November 3
Time: 2:30 p.m.–3:30 p.m.
Location: via Zoom
Estimation of 1d structures from empirical data – Andrew Warren
Given a data distribution which is concentrated around a one-dimensional structure, can we infer that structure? We consider versions of this problem where the distribution resides in a metric space and the 1d structure is assumed to either be the range of an absolutely continuous curve, or is a connected set of finite 1d Hausdorff measure. In each of these cases, we relate the inference task to solving a variational problem where there is a tradeoff between data fidelity and simplicity of the inferred structure; the variational problems we consider are closely related to the so-called “principal curve” problem of Hastie and Steutzle as well as the “average-distance problem” of Buttazzo, Oudet, and Stepanov. For each of the variational problems under consideration, we establish: existence of minimizers, stability with respect to the data distribution, and consistency of a discretization scheme which is amenable to Lloyd-type numerical methods. Lastly, we consider applications to estimation of stochastic processes from partial observation, as well as the lineage tracing problem from mathematical biology.
This talk includes joint work with Anton Afanassiev, Young-Heon Kim, Forest Kobayashi, and Geoff Schiebinger.
Zoom Meeting ID： 927 8056 1489
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