Timezone: »
We propose a novel class of dynamic nonparanormal graphical models, which allows us to model high dimensional heavy-tailed systems and the evolution of their latent network structures. Under this model we develop statistical tests for presence of edges both locally at a fixed index value and globally over a range of values. The tests are developed for a high-dimensional regime, are robust to model selection mistakes and do not require commonly assumed minimum signal strength. The testing procedures are based on a high dimensional, debiasing-free moment estimator, which uses a novel kernel smoothed Kendall's tau correlation matrix as an input statistic. The estimator consistently estimates the latent inverse Pearson correlation matrix uniformly in both index variable and kernel bandwidth. Its rate of convergence is shown to be minimax optimal. Thorough numerical simulations and an application to a neural imaging dataset support the usefulness of our method.
Joint work with Junwei Lu and Han Liu.
Author Information
Mladen Kolar (U Chicago)
More from the Same Authors
-
2022 : Adaptive Inexact Sequential Quadratic Programming via Iterative Randomized Sketching »
Ilgee Hong · Sen Na · Mladen Kolar -
2022 Poster: A Nonconvex Framework for Structured Dynamic Covariance Recovery »
Katherine Tsai · Mladen Kolar · Sanmi Koyejo -
2017 Workshop: Advances in Modeling and Learning Interactions from Complex Data »
Gautam Dasarathy · Mladen Kolar · Richard Baraniuk -
2017 Poster: The Expxorcist: Nonparametric Graphical Models Via Conditional Exponential Densities »
Arun Suggala · Mladen Kolar · Pradeep Ravikumar -
2016 Poster: Statistical Inference for Pairwise Graphical Models Using Score Matching »
Ming Yu · Mladen Kolar · Varun Gupta -
2014 Workshop: Modern Nonparametrics 3: Automating the Learning Pipeline »
Eric Xing · Mladen Kolar · Arthur Gretton · Samory Kpotufe · Han Liu · Zoltán Szabó · Alan Yuille · Andrew G Wilson · Ryan Tibshirani · Sasha Rakhlin · Damian Kozbur · Bharath Sriperumbudur · David Lopez-Paz · Kirthevasan Kandasamy · Francesco Orabona · Andreas Damianou · Wacha Bounliphone · Yanshuai Cao · Arijit Das · Yingzhen Yang · Giulia DeSalvo · Dmitry Storcheus · Roberto Valerio -
2013 Workshop: Modern Nonparametric Methods in Machine Learning »
Arthur Gretton · Mladen Kolar · Samory Kpotufe · John Lafferty · Han Liu · Bernhard Schölkopf · Alexander Smola · Rob Nowak · Mikhail Belkin · Lorenzo Rosasco · peter bickel · Yue Zhao -
2012 Workshop: Modern Nonparametric Methods in Machine Learning »
Sivaraman Balakrishnan · Arthur Gretton · Mladen Kolar · John Lafferty · Han Liu · Tong Zhang -
2011 Poster: Minimax Localization of Structural Information in Large Noisy Matrices »
Mladen Kolar · Sivaraman Balakrishnan · Alessandro Rinaldo · Aarti Singh -
2011 Spotlight: Minimax Localization of Structural Information in Large Noisy Matrices »
Mladen Kolar · Sivaraman Balakrishnan · Alessandro Rinaldo · Aarti Singh -
2009 Poster: Time-Varying Dynamic Bayesian Networks »
Le Song · Mladen Kolar · Eric Xing -
2009 Spotlight: Time-Varying Dynamic Bayesian Networks »
Le Song · Mladen Kolar · Eric Xing -
2009 Poster: Sparsistent Learning of Varying-coefficient Models with Structural Changes »
Mladen Kolar · Le Song · Eric Xing -
2009 Spotlight: Sparsistent Learning of Varying-coefficient Models with Structural Changes »
Mladen Kolar · Le Song · Eric Xing