High dimensional change point estimation via sparse projection

Multivariate Time Series Change-Point Detection with a Novel Pearson-like Scaled Bregman Divergence

Change-point detection is a challenging problem that has a number of applications across various real-world domains. The primary objective of CPD is to identify specific time points where the underlying system undergoes transitions between different states, each characterized by its distinct data distribution. Precise identification of change points in time series omics data can provide insights into the dynamic and temporal characteristics inherent to complex biological systems. Many change-point detection methods have traditionally focused on the direct estimation of data distributions. However, these approaches become unrealistic in high-dimensional data analysis. Density ratio methods have emerged as promising approaches for change-point detection since estimating density ratios is easier than directly estimating individual densities. Nevertheless, the divergence measures used in these methods may suffer from numerical instability during computation. Additionally, the most popular α -relative Pearson divergence cannot measure the dissimilarity between two distributions of data but a mixture of distributions. To overcome the limitations of existing density ratio-based methods, we propose a novel approach called the Pearson-like scaled-Bregman divergence-based (PLsBD) density ratio estimation method for change-point detection. Our theoretical studies derive an analytical expression for the Pearson-like scaled Bregman divergence using a mixture measure. We integrate the PLsBD with a kernel regression model and apply a random sampling strategy to identify change points in both synthetic data and real-world high-dimensional genomics data of Drosophila. Our PLsBD method demonstrates superior performance compared to many other change-point detection methods.

Change point detection for high dimensional data via kernel measure with application to human aging brain data

Identifying the existence and locations of change points has been a broadly encountered task in many statistical application areas. The existing change point detection methods may produce unsatisfactory results for high-dimensional data since certain distributional assumptions are made on data, which are hard to verify in practice. Moreover, some parameters (such as the number of change points) need to be estimated beforehand for some methods, making their powers sensitive to these values. Here, we propose a kernel-basedU $$ U $$ -statistic to identify change points (KUCP) for high dimensional data, which is free of distributional assumptions and sup-parameter estimations. Specifically, we employ a kernel function to describe similarities among the subjects and construct aU $$ U $$ -statistic to test the existence of change point for a given location. The asymptotic properties of theU $$ U $$ -statistic are deduced. We also develop a procedure to locate the change points sequentially via a dichotomy algorithm. Extensive simulations demonstrate that KUCP has higher sensitivity in identifying existence of change points and higher accuracy in locating these change points than its counterparts. We further illustrate its practical utility by analyzing a gene expression data of human brain to detect the time point when gene expression profiles begin to change, which has been reported to be closely related with aging brain.

Efficient multiple change point detection for high-dimensional generalized linear models

Change point detection for high-dimensional data is an important yet challenging problem for many applications. In this paper, we consider multiple change point detection in the context of high-dimensional generalized linear models, allowing the covariate dimension p to grow exponentially with the sample size n. The model considered is general and flexible in the sense that it covers various specific models as special cases. It can automatically account for the underlying data generation mechanism without specifying any prior knowledge about the number of change points. Based on dynamic programming and binary segmentation techniques, two algorithms are proposed to detect multiple change points, allowing the number of change points to grow with n. To further improve the computational efficiency, a more efficient algorithm designed for the case of a single change point is proposed. We present theoretical properties of our proposed algorithms, including estimation consistency for the number and locations of change points as well as consistency and asymptotic distributions for the underlying regression coefficients. Finally, extensive simulation studies and application to the Alzheimer's Disease Neuroimaging Initiative data further demonstrate the competitive performance of our proposed methods.

Inference in High-Dimensional Online Changepoint Detection

We introduce and study two new inferential challenges associated with the sequential detection of change in a high-dimensional mean vector. First, we seek a confidence interval for the changepoint, and second, we estimate the set of indices of coordinates in which the mean changes. We propose an online algorithm that produces an interval with guaranteed nominal coverage, and whose length is, with high probability, of the same order as the average detection delay, up to a logarithmic factor. The corresponding support estimate enjoys control of both false negatives and false positives. Simulations confirm the effectiveness of our methodology, and we also illustrate its applicability on the U.S. excess deaths data from 2017 to 2020. The supplementary material, which contains the proofs of our theoretical results, is available online.

A New Class of Weighted CUSUM Statistics

A change point is a location or time at which observations or data obey two different models: before and after. In real problems, we may know some prior information about the location of the change point, say at the right or left tail of the sequence. How does one incorporate the prior information into the current cumulative sum (CUSUM) statistics? We propose a new class of weighted CUSUM statistics with three different types of quadratic weights accounting for different prior positions of the change points. One interpretation of the weights is the mean duration in a random walk. Under the normal model with known variance, the exact distributions of these statistics are explicitly expressed in terms of eigenvalues. Theoretical results about the explicit difference of the distributions are valuable. The expansions of asymptotic distributions are compared with the expansion of the limit distributions of the Cramér-von Mises statistic and the Anderson and Darling statistic. We provide some extensions from independent normal responses to more interesting models, such as graphical models, the mixture of normals, Poisson, and weakly dependent models. Simulations suggest that the proposed test statistics have better power than the graph-based statistics. We illustrate their application to a detection problem with video data.

High Dimensional Change Point Inference: Recent Developments and Extensions

Change point analysis aims to detect structural changes in a data sequence. It has always been an active research area since it was introduced in the 1950s. In modern statistical applications, however, high-throughput data with increasing dimensions are ubiquitous in fields ranging from economics, finance to genetics and engineering. For those problems, the earlier works are typically no longer applicable. As a result, the problem of testing a change point for high dimensional data sequences has been an important yet challenging task. In this paper, we first focus on models for at most one change point, and review recent state-of-art techniques for change point testing of high dimensional mean vectors and compare their theoretical properties. Based on that, we provide a survey of some extensions to general high dimensional parameters beyond mean vectors as well as strategies for testing multiple change points in high dimensions. Finally, we discuss some open problems for possible future research directions.

Identification of community structure-based brain states and transitions using functional MRI

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Community-based detection of discrete brain states using stochastic latent block model.

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Bayesian change-point detection and model selection via posterior predictive discrepancy.

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Markov chain Monte Carlo methods for estimation of community memberships.

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Distinctive brain states for varying task demands in working memory task fMRI.

Brain function relies on a precisely coordinated and dynamic balance between the functional integration and segregation of distinct networks. Characterizing the way in which brain regions reconfigure their interactions to give rise to distinct but hidden brain states remains an open challenge. In this paper, we propose a Bayesian method for characterizing community structure-based latent brain states and showcase a novel strategy based on posterior predictive discrepancy using the latent block model to detect transitions between community structures in blood oxygen level-dependent (BOLD) time series. The set of estimated parameters in the model includes a latent label vector that assigns network nodes to communities, and also block model parameters that reflect the weighted connectivity within and between communities. Besides extensive in-silico model evaluation, we also provide empirical validation (and replication) using the Human Connectome Project (HCP) dataset of 100 healthy adults. Our results obtained through an analysis of task-fMRI data during working memory performance show appropriate lags between external task demands and change-points between brain states, with distinctive community patterns distinguishing fixation, low-demand and high-demand task conditions.

Asymptotic distribution-free change-point detection for data with repeated observations

In the regime of change-point detection, a nonparametric framework based on scan statistics utilizing graphs representing similarities among observations is gaining attention due to its flexibility and good performances for high-dimensional and non-Euclidean data sequences, which are ubiquitous in this big data era. However, this graph-based framework encounters problems when there are repeated observations in the sequence, which often happens for discrete data, such as network data. In this work, we extend the graph-based framework to solve this problem by averaging or taking union of all possible optimal graphs resulted from repeated observations. We consider both the single change-point alternative and the changed-interval alternative, and derive analytic formulas to control the Type I error for the new methods, making them fast applicable to large datasets. The extended methods are illustrated on an application in detecting changes in a sequence of dynamic networks over time. All proposed methods are implemented in an R package gSeg available on CRAN.

Identifying complex gene-gene interactions: a mixed kernel omnibus testing approach

Genes do not function independently; rather, they interact with each other to fulfill their joint tasks. Identification of gene-gene interactions has been critically important in elucidating the molecular mechanisms responsible for the variation of a phenotype. Regression models are commonly used to model the interaction between two genes with a linear product term. The interaction effect of two genes can be linear or nonlinear, depending on the true nature of the data. When nonlinear interactions exist, the linear interaction model may not be able to detect such interactions; hence, it suffers from substantial power loss. While the true interaction mechanism (linear or nonlinear) is generally unknown in practice, it is critical to develop statistical methods that can be flexible to capture the underlying interaction mechanism without assuming a specific model assumption. In this study, we develop a mixed kernel function which combines both linear and Gaussian kernels with different weights to capture the linear or nonlinear interaction of two genes. Instead of optimizing the weight function, we propose a grid search strategy and use a Cauchy transformation of the P-values obtained under different weights to aggregate the P-values. We further extend the two-gene interaction model to a high-dimensional setup using a de-biased LASSO algorithm. Extensive simulation studies are conducted to verify the performance of the proposed method. Application to two case studies further demonstrates the utility of the model. Our method provides a flexible and computationally efficient tool for disentangling complex gene-gene interactions associated with complex traits.

Ensemble binary segmentation for irregularly spaced data with change-points

We propose a new technique for consistent estimation of the number and locations of the change-points in the structure of an irregularly spaced time series. The core of the segmentation procedure is the ensemble binary segmentation method (EBS), a technique in which a large number of multiple change-point detection tasks using the binary segmentation method are applied on sub-samples of the data of differing lengths, and then the results are combined to create an overall answer. We do not restrict the total number of change-points a time series can have, therefore, our proposed method works well when the spacings between change-points are short. Our main change-point detection statistic is the time-varying autoregressive conditional duration model on which we apply a transformation process in order to decorrelate it. To examine the performance of EBS we provide a simulation study for various types of scenarios. A proof of consistency is also provided. Our methodology is implemented in the R package , available to download from CRAN.