Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userWeighted-Graph-Based Change Point Detection
255
0
0.0
(
0
)
Added by
Lizhen Nie
Publication date
2021
fields
Mathematical Statistics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We consider the detection and localization of change points in the distribution of an offline sequence of observations. Based on a nonparametric framework that uses a similarity graph among observations, we propose new test statistics when at most one change point occurs and generalize them to multiple change points settings. The proposed statistics leverage edge weight information in the graphs, exhibiting substantial improvements in testing power and localization accuracy in simulations. We derive the null limiting distribution, provide accurate analytic approximations to control type I error, and establish theoretical guarantees on the power consistency under contiguous alternatives for the one change point setting, as well as the minimax localization rate. In the multiple change points setting, the asymptotic correctness of the number and location of change points are also guaranteed. The methods are illustrated on the MIT proximity network data.
rate research
Read More
Structural breaks have been commonly seen in applications. Specifically for detection of change points in time, research gap still remains on the setting in ultra high dimension, where the covariates may bear spurious correlations. In this paper, we propose a two-stage approach to detect change points in ultra high dimension, by firstly proposing the dynamic titled current correlation screening method to reduce the input dimension, and then detecting possible change points in the framework of group variable selection. Not only the spurious correlation between ultra-high dimensional covariates is taken into consideration in variable screening, but non-convex penalties are studied in change point detection in the ultra high dimension. Asymptotic properties are derived to guarantee the asymptotic consistency of the selection procedure, and the numerical investigations show the promising performance of the proposed approach.
Without imposing prior distributional knowledge underlying multivariate time series of interest, we propose a nonparametric change-point detection approach to estimate the number of change points and their locations along the temporal axis. We develop a structural subsampling procedure such that the observations are encoded into multiple sequences of Bernoulli variables. A maximum likelihood approach in conjunction with a newly developed searching algorithm is implemented to detect change points on each Bernoulli process separately. Then, aggregation statistics are proposed to collectively synthesize change-point results from all individual univariate time series into consistent and stable location estimations. We also study a weighting strategy to measure the degree of relevance for different subsampled groups. Simulation studies are conducted and shown that the proposed change-point methodology for multivariate time series has favorable performance comparing with currently popular nonparametric methods under various settings with different degrees of complexity. Real data analyses are finally performed on categorical, ordinal, and continuous time series taken from fields of genetics, climate, and finance.
Changepoint detection is the problem of finding abrupt or gradual changes in time series data when the distribution of the time series changes significantly. There are many sophisticated statistical algorithms for solving changepoint detection problem, although there is not much work devoted towards gradual changepoints as compared to abrupt ones. Here we present a new approach to solve changepoint detection problem using fuzzy rough set theory which is able to detect such gradual changepoints. An expression for the rough-fuzzy estimate of changepoints is derived along with its mathematical properties concerning fast computation. In a statistical hypothesis testing framework, asymptotic distribution of the proposed statistic on both single and multiple changepoints is derived under null hypothesis enabling multiple changepoint detection. Extensive simulation studies have been performed to investigate how simple crude statistical measures of disparity can be subjected to improve their efficiency in estimation of gradual changepoints. Also, the said rough-fuzzy estimate is robust to signal-to-noise ratio, high degree of fuzziness in true changepoints and also to hyper parameter values. Simulation studies reveal that the proposed method beats other fuzzy methods and also popular crisp methods like WBS, PELT and BOCD in detecting gradual changepoints. The applicability of the estimate is demonstrated using multiple real-life datasets including Covid-19. We have developed the python package roufcp for broader dissemination of the methods.
Topological Data Analysis (TDA) is a rapidly growing field, which studies methods for learning underlying topological structures present in complex data representations. TDA methods have found recent success in extracting useful geometric structures for a wide range of applications, including protein classification, neuroscience, and time-series analysis. However, in many such applications, one is also interested in sequentially detecting changes in this topological structure. We propose a new method called Persistence Diagram based Change-Point (PD-CP), which tackles this problem by integrating the widely-used persistence diagrams in TDA with recent developments in nonparametric change-point detection. The key novelty in PD-CP is that it leverages the distribution of points on persistence diagrams for online detection of topological changes. We demonstrate the effectiveness of PD-CP in an application to solar flare monitoring.
Vector Auto-Regressive (VAR) models capture lead-lag temporal dynamics of multivariate time series data. They have been widely used in macroeconomics, financial econometrics, neuroscience and functional genomics. In many applications, the data exhibit structural changes in their autoregressive dynamics, which correspond to changes in the transition matrices of the VAR model that specify such dynamics. We present the R package VARDetect that implements two classes of algorithms to detect multiple change points in piecewise stationary VAR models. The first exhibits sublinear computational complexity in the number of time points and is best suited for structured sparse models, while the second exhibits linear time complexity and is designed for models whose transition matrices are assumed to have a low rank plus sparse decomposition. The package also has functions to generate data from the various variants of VAR models discussed, which is useful in simulation studies, as well as to visualize the results through network layouts.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
