4 papers · 1 filter
A Two-Sample Test on Weighted Persistence Intensity Functions in Topological Data Analysis
Yeongung Han, Ilmun Kim, Jisu Kim
The intensity function, defined as the Lebesgue density of the expected measure of a persistence diagram, is a fundamental summary of the probability distribution of persistence di…
Locally minimax optimal confidence sets for the best model
Ilmun Kim, Aaditya Ramdas
This paper tackles a fundamental inference problem: given observations from a distribution over with unknown mean , we must form a confidence…
Dimension-agnostic inference using cross U-statistics
Ilmun Kim, Aaditya Ramdas
Classical asymptotic theory for statistical inference usually involves calibrating a statistic by fixing the dimension while letting the sample size increase to infinity. R…
The Projected Covariance Measure for assumption-lean variable significance testing
Anton Rask Lundborg, Ilmun Kim, Rajen D. Shah +1
Testing the significance of a variable or group of variables for predicting a response , given additional covariates , is a ubiquitous task in statistics. A simple but co…