arXiv subjects

Lynna Chu

Publications and source records attributed to Lynna Chu.

8 recordsLinked to original sources

arXiv2025

Graph-theoretic Inference for Random Effects in High-dimensional Studies

We study the problem of testing for the presence of random effects in mixed models with high-dimensional fixed effects. To this end, we propose a rank-based graph-theoretic approach to test whether a collection of random effects is zero. Our approach is non-parametric and model-free in the sense that we not require correct specification of the mixed model nor estimation of unknown parameters. Instead, the test statistic evaluates whether incorporating group-level correlation meaningfully improves the ability of a potentially high-dimensional covariate vector $X$ to predict a response variable $Y$. We establish the consistency of the proposed test and derive its asymptotic null distribution. Through simulation studies and a real data application, we demonstrate the practical effectiveness of the proposed test.

stat.ME↗

arXiv2025

Adaptive Block-Based Change-Point Detection for Sparse Spatially Clustered Data with Applications in Remote Sensing Imaging

We present a non-parametric change-point detection approach to detect potentially sparse changes in a time series of high-dimensional observations or non-Euclidean data objects. We target a change in distribution that occurs in a small, unknown subset of dimensions, where these dimensions may be correlated. Our work is motivated by a remote sensing application, where changes occur in small, spatially clustered regions over time. An adaptive block-based change-point detection framework is proposed that accounts for spatial dependencies across dimensions and leverages these dependencies to boost detection power and improve estimation accuracy. Through simulation studies, we demonstrate that our approach has superior performance in detecting sparse changes in datasets with spatial or local group structures. An application of the proposed method to detect activity, such as new construction, in remote sensing imagery of the Natanz Nuclear facility in Iran is presented to demonstrate the method's efficacy.

stat.ME↗

arXiv2024

DeepLocalization: Using change point detection for Temporal Action Localization

In this study, we introduce DeepLocalization, an innovative framework devised for the real-time localization of actions tailored explicitly for monitoring driver behavior. Utilizing the power of advanced deep learning methodologies, our objective is to tackle the critical issue of distracted driving-a significant factor contributing to road accidents. Our strategy employs a dual approach: leveraging Graph-Based Change-Point Detection for pinpointing actions in time alongside a Video Large Language Model (Video-LLM) for precisely categorizing activities. Through careful prompt engineering, we customize the Video-LLM to adeptly handle driving activities' nuances, ensuring its classification efficacy even with sparse data. Engineered to be lightweight, our framework is optimized for consumer-grade GPUs, making it vastly applicable in practical scenarios. We subjected our method to rigorous testing on the SynDD2 dataset, a complex benchmark for distracted driving behaviors, where it demonstrated commendable performance-achieving 57.5% accuracy in event classification and 51% in event detection. These outcomes underscore the substantial promise of DeepLocalization in accurately identifying diverse driver behaviors and their temporal occurrences, all within the bounds of limited computational resources.

cs.CV↗

arXiv2024

A Graph-based Approach to Estimating the Number of Clusters in High-dimensional Settings

We consider the problem of estimating the number of clusters (k) in a dataset. We propose a non-parametric approach to the problem that utilizes similarity graphs to construct a robust statistic that effectively captures similarity information among observations. This graph-based statistic is applicable to datasets of any dimension, is computationally efficient to obtain, and can be paired with any kind of clustering technique. Asymptotic theory is developed to establish the selection consistency of the proposed approach. Simulation studies demonstrate that the graph-based statistic outperforms existing methods for estimating k, especially in the high-dimensional setting. We illustrate its utility on an imaging dataset and an RNA-seq dataset.

stat.ME↗

arXiv2023

A Robust Framework for Graph-based Two-Sample Tests Using Weights

Graph-based tests are a class of non-parametric two-sample tests useful for analyzing high-dimensional data. The test statistics are constructed from similarity graphs (such as K-minimum spanning tree), and consequently, their performance is sensitive to the structure of the graph. When the graph has problematic structures (for example, hubs), as is common for high-dimensional data, this can result in low power and unstable performance among existing graph-based tests. We address this challenge by proposing new test statistics that are robust to problematic structures of the graph and can provide reliable inferences. We employ an edge-weighting strategy using intrinsic characteristics of the graph that are computationally simple and efficient to obtain. The limiting null distribution of the robust test statistics is derived and shown to work well for finite sample sizes. Simulation studies and data analysis of Chicago taxi-trip travel patterns demonstrate the new tests' improved performance across a range of settings.

stat.ME↗

arXiv2023

On the tightness of graph-based statistics

We establish tightness of graph-based stochastic processes in the space $D[0+\epsilon,1-\epsilon]$ with $\epsilon >0$ that allows for discontinuities of the first kind. The graph-based stochastic processes are based on statistics constructed from similarity graphs. In this setting, the classic characterization of tightness is intractable, making it difficult to obtain convergence of the limiting distributions for graph-based stochastic processes. We take an alternative approach and study the behavior of the higher moments of the graph-based test statistics. We show that, under mild conditions of the graph, tightness of the stochastic process can be established by obtaining upper bounds on the graph-based statistics' higher moments. Explicit analytical expressions for these moments are provided. The results are applicable to generic graphs, including dense graphs where the number of edges can be of higher order than the number of observations.

math.PR↗

arXiv2022

Sequential Change-point Detection for High-dimensional and non-Euclidean Data

In many applications, it is often of practical and scientific interest to detect anomaly events in a streaming sequence of high-dimensional or non-Euclidean observations. We study a non-parametric framework that utilizes nearest neighbor information among the observations to detect changes in an online setting. It can be applied to data in arbitrary dimension and non-Euclidean data as long as a similarity measure on the sample space can be defined. We consider new test statistics under this framework that can detect anomaly events more effectively than the existing test while keeping the false discovery rate controlled at a fixed level. Analytic formulas approximating the average run lengths of the new approaches are derived to make them fast applicable to modern datasets. Simulation studies are provided to support theoretical results. The proposed approach is illustrated with an analysis of the NYC taxi dataset.

stat.ME↗

arXiv2018

Asymptotic Distribution-Free Change-Point Detection for Multivariate and non-Euclidean Data

We consider the testing and estimation of change-points, locations where the distribution abruptly changes, in a sequence of multivariate or non-Euclidean observations. We study a nonparametric framework that utilizes similarity information among observations, which can be applied to various data types as long as an informative similarity measure on the sample space can be defined. The existing approach along this line has low power and/or biased estimates for change-points under some common scenarios. We address these problems by considering new tests based on similarity information. Simulation studies show that the new approaches exhibit substantial improvements in detecting and estimating change-points. In addition, under some mild conditions, the new test statistics are asymptotically distribution free under the null hypothesis of no change. Analytic p-value approximations to the significance of the new test statistics for the single change-point alternative and changed interval alternative are derived, making the new approaches easy off-the-shelf tools for large datasets. The new approaches are illustrated in an analysis of New York taxi data.

stat.ME↗