(with Elchanan Solomon and Paul Bendich) [arXiv preprint] We use our notion of distributed persistence and local geometry to define a new dimensionality-reduction algorithm called DIPOLE. paper, code
(with Elchanan Solomon and Paul Bendich) [Symposium on Computational Geometry] We introduce a distributed version of persistent homology that provably characterizes a metric space in a Lipschitz way. paper
(with Elchanan Solomon and Paul Bendich) [4th International Conference on Artificial Intelligence and Statistics (AISTATS)] We introduce a new framework for optimizing topological functionals that is faster and produces more robust optima than prior methods. paper, code
(with Stan Uryasev) [2019 Winter Simulation Conference] We prove equivalences of portfolio optimization problems with negative expectile, a risk measure generalizing expected value, and omega ratio. We also derive subgradients for negative expectile. paper, code
[Proceedings of the American Mathematical Society] We prove persistence diagrams with the p-Wasserstein metric do not admit a coarse embedding into a Hilbert space when p > 2. paper, talk
(with Peter Bubenik) [Journal of Applied and Computational Topology] We show that persistence diagrams with the bottleneck distance do not admit a coarse embedding into a Hilbert space. paper, talk
(with Paul Bendich and Peter Bubenik) [Journal of Applied and Computational Topology] We propose a general technique for extracting a larger set of stable information from persistent homology computations than is currently done. paper, code
