Subspace Change-Point Detection: A New Model and Solution

Moustakides

2018

Preprint

We consider the sequential changepoint detection problem of detecting changes that are characterized by a subspace structure which is manifested in the covariance matrix. In particular, the covariance structure changes from an identity matrix to an unknown spiked covariance model. We consider three sequential changepoint detection procedures: The exact cumulative sum (CUSUM) that assumes knowledge of all parameters, the largest eigenvalue procedure and a novel Subspace-CUSUM algorithm with the last two being used for the case when unknown parameters are present. By leveraging the extreme eigenvalue distribution from random matrix theory and modeling the non-negligible temporal correlation in the sequence of detection statistics due to the sliding window approach, we provide theoretical approximations to the average run length (ARL) and the expected detection delay (EDD) for the largest eigenvalue procedure. The three methods are compared to each other using simulations.

Section: A Related Workmentioning

confidence: 93%

“…Usually the subspace u and SNR ρ are unknown. In this case it is impossible to form the exact CUSUM statistic depicted in (8). One option is to estimate the unknown parameters and substitute them back into the likelihood function.…”

Section: Subspace-cusum Proceduresmentioning

confidence: 99%

Sequential Subspace Change-Point Detection

Moustakides

2018

Preprint

IEEE Trans. Knowl. Data Eng.

“…HRDD combines the information from both original data space and the label space to identify the most appropriate subspace for concept drift detection. Besides, many subspacebased change detection algorithms for time series data make particular assumptions on their data streams [31], [32]. For instance, in [32], the data stream is assumed to follow a Gaussian distribution.…”

Section: Learning Of a Lower-dimensional Subspacementioning

confidence: 99%

“…Besides, many subspacebased change detection algorithms for time series data make particular assumptions on their data streams [31], [32]. For instance, in [32], the data stream is assumed to follow a Gaussian distribution. HRDD does not make any assumptions on either the data stream or the underlying subspace.…”

Section: Learning Of a Lower-dimensional Subspacementioning

confidence: 99%

Hierarchical Reduced-space Drift Detection Framework for Multivariate Supervised Data Streams

Zhang¹,

Tiňo²,

Yao³

2021

In a streaming environment, the characteristics of the data themselves and their relationship with the labels may change over time. Most drift detection methods for supervised data streams are performance-based, that is, they detect changes only after the classification accuracy deteriorates. This may not be sufficient in many application areas where the reason behind a drift is also important. Another category of drift detectors are data distribution-based detectors. Although they can detect some drifts within the input space, changes affecting only the labelling mechanism cannot be identified. Furthermore, little work is available on drift detection for high-dimensional data streams. In this paper we propose an advanced Hierarchical Reduced-space Drift Detection (HRDD) framework for supervised data streams which captures drifts regardless of their effects on classification performance. This framework suggests monitoring both marginal and class-conditional distributions within a lower-dimensional space specifically relevant to the assigned classification task. Experimental comparisons have demonstrated that HRDD not only achieves high-quality performance on high-dimensional data streams, but also outperforms its competitors in terms of detection recall, precision and F-measure across a wide range of different concept drift types including subtle drifts.

“…The subspace-CUSUM procedure was developed in [232], in which the unknown subspace in the post-change spiked model is estimated sequentially and further used to obtain the log-likelihood ratio statistic. A CUSUM procedure for detecting switching subspace (from a known subspace to another target subspace) was studied in [86].…”

Section: F High-dimensional Streaming Datamentioning

confidence: 99%

Sequential (Quickest) Change Detection: Classical Results and New Directions

Zou

et al. 2021

Preprint

Online detection of changes in stochastic systems, referred to as sequential change detection or quickest change detection, is an important research topic in statistics, signal processing, and information theory, and has a wide range of applications. This survey starts with the basics of sequential change detection, and then moves on to generalizations and extensions of sequential change detection theory and methods. We also discuss some new dimensions that emerge at the intersection of sequential change detection with other areas, along with a selection of modern applications and remarks on open questions.