Timezone: »
Poster
Lattice partition recovery with dyadic CART
OSCAR HERNAN MADRID PADILLA · Yi Yu · Alessandro Rinaldo
We study piece-wise constant signals corrupted by additive Gaussian noise over a $d$-dimensional lattice. Data of this form naturally arise in a host of applications, and the tasks of signal detection or testing, de-noising and estimation have been studied extensively in the statistical and signal processing literature. In this paper we consider instead the problem of partition recovery, i.e.~of estimating the partition of the lattice induced by the constancy regions of the unknown signal, using the computationally-efficient dyadic classification and regression tree (DCART) methodology proposed by \citep{donoho1997cart}. We prove that, under appropriate regularity conditions on the shape of the partition elements, a DCART-based procedure consistently estimates the underlying partition at a rate of order $\sigma^2 k^* \log (N)/\kappa^2$, where $k^*$ is the minimal number of rectangular sub-graphs obtained using recursive dyadic partitions supporting the signal partition, $\sigma^2$ is the noise variance, $\kappa$ is the minimal magnitude of the signal difference among contiguous elements of the partition and $N$ is the size of the lattice. Furthermore, under stronger assumptions, our method attains a sharper estimation error of order $\sigma^2\log(N)/\kappa^2$, independent of $k^*$, which we show to be minimax rate optimal. Our theoretical guarantees further extend to the partition estimator based on the optimal regression tree estimator (ORT) of \cite{chatterjee2019adaptive} and to the one obtained through an NP-hard exhaustive search method. We corroborate our theoretical findings and the effectiveness of DCART for partition recovery in simulations.
Author Information
OSCAR HERNAN MADRID PADILLA (University of California, Los Angeles)
Yi Yu (The university of Warwick)
Alessandro Rinaldo (CMU)
More from the Same Authors
-
2023 Poster: Change point detection and inference in multivariate non-parametric models under mixing conditions »
Carlos Misael Madrid Padilla · Haotian Xu · Daren Wang · OSCAR HERNAN MADRID PADILLA · Yi Yu -
2022 Spotlight: Lightning Talks 1B-4 »
Andrei Atanov · Shiqi Yang · Wanshan Li · Yongchang Hao · Ziquan Liu · Jiaxin Shi · Anton Plaksin · Jiaxiang Chen · Ziqi Pan · yaxing wang · Yuxin Liu · Stepan Martyanov · Alessandro Rinaldo · Yuhao Zhou · Li Niu · Qingyuan Yang · Andrei Filatov · Yi Xu · Liqing Zhang · Lili Mou · Ruomin Huang · Teresa Yeo · kai wang · Daren Wang · Jessica Hwang · Yuanhong Xu · Qi Qian · Hu Ding · Michalis Titsias · Shangling Jui · Ajay Sohmshetty · Lester Mackey · Joost van de Weijer · Hao Li · Amir Zamir · Xiangyang Ji · Antoni Chan · Rong Jin -
2022 Spotlight: Detecting Abrupt Changes in Sequential Pairwise Comparison Data »
Wanshan Li · Alessandro Rinaldo · Daren Wang -
2022 Poster: Detecting Abrupt Changes in Sequential Pairwise Comparison Data »
Wanshan Li · Alessandro Rinaldo · Daren Wang -
2022 Poster: Change-point Detection for Sparse and Dense Functional Data in General Dimensions »
Carlos Misael Madrid Padilla · Daren Wang · Zifeng Zhao · Yi Yu -
2022 Poster: Network change point localisation under local differential privacy »
Mengchu Li · Tom Berrett · Yi Yu -
2021 Poster: Locally private online change point detection »
Tom Berrett · Yi Yu -
2021 Poster: Adversarially Robust Change Point Detection »
Mengchu Li · Yi Yu -
2019 Poster: Statistical Analysis of Nearest Neighbor Methods for Anomaly Detection »
Xiaoyi Gu · Leman Akoglu · Alessandro Rinaldo -
2019 Poster: Are sample means in multi-armed bandits positively or negatively biased? »
Jaehyeok Shin · Aaditya Ramdas · Alessandro Rinaldo -
2019 Spotlight: Are sample means in multi-armed bandits positively or negatively biased? »
Jaehyeok Shin · Aaditya Ramdas · Alessandro Rinaldo -
2017 : Persistent homology of KDE filtration of Rips complexes »
Jaehyeok Shin · Alessandro Rinaldo -
2017 Poster: A Sharp Error Analysis for the Fused Lasso, with Application to Approximate Changepoint Screening »
Kevin Lin · James Sharpnack · Alessandro Rinaldo · Ryan Tibshirani -
2016 Poster: Statistical Inference for Cluster Trees »
Jisu KIM · Yen-Chi Chen · Sivaraman Balakrishnan · Alessandro Rinaldo · Larry Wasserman -
2013 Poster: Cluster Trees on Manifolds »
Sivaraman Balakrishnan · Srivatsan Narayanan · Alessandro Rinaldo · Aarti Singh · Larry Wasserman -
2012 Workshop: Algebraic Topology and Machine Learning »
Sivaraman Balakrishnan · Alessandro Rinaldo · Donald Sheehy · Aarti Singh · Larry Wasserman -
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