62 citations · 268 across the 38 of their papers we have counts for
6 papers · 1 filter
Random Walks on Simplicial Complexes and Harmonics
Sayan Mukherjee, John Steenbergen
In this paper, we introduce random walks with absorbing states on simplicial complexes. Given a simplicial complex of dimension , a random walk with an absorbing state is define…
The Information Geometry of Mirror Descent
Garvesh Raskutti, Sayan Mukherjee
Information geometry applies concepts in differential geometry to probability and statistics and is especially useful for parameter estimation in exponential families where paramet…
Persistent Homology Transform for Modeling Shapes and Surfaces
Katharine Turner, Sayan Mukherjee, Doug M Boyer
In this paper we introduce a statistic, the persistent homology transform (PHT), to model surfaces in and shapes in . This statistic is a collection of…
Probabilistic Fréchet Means for Time Varying Persistence Diagrams
Elizabeth Munch, Katharine Turner, Paul Bendich +3
In order to use persistence diagrams as a true statistical tool, it would be very useful to have a good notion of mean and variance for a set of diagrams. In 2011, Mileyko and his…
The Topology of Probability Distributions on Manifolds
Omer Bobrowski, Sayan Mukherjee
Let be a set of random points in , generated from a probability measure on a -dimensional manifold . In this paper we study the homology of …
Consistency of maximum likelihood estimation for some dynamical systems
Kevin McGoff, Sayan Mukherjee, Andrew Nobel +1
We consider the asymptotic consistency of maximum likelihood parameter estimation for dynamical systems observed with noise. Under suitable conditions on the dynamical systems and…