4 papers
Topological Regularization via Persistence-Sensitive Optimization
Arnur Nigmetov, Aditi S. Krishnapriyan, Nicole Sanderson +1
Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to en…
Efficient Approximation of the Matching Distance for 2-parameter persistence
Michael Kerber, Arnur Nigmetov
The matching distance is a computationally tractable topological measure to compare multi-filtered simplicial complexes. We design efficient algorithms for approximating the matchi…
Metric Spaces with Expensive Distances
Michael Kerber, Arnur Nigmetov
In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in te…
Geometry Helps to Compare Persistence Diagrams
Michael Kerber, Dmitriy Morozov, Arnur Nigmetov
Exploiting geometric structure to improve the asymptotic complexity of discrete assignment problems is a well-studied subject. In contrast, the practical advantages of using geomet…