Abstract
Regularizing the least-squares criterion with the total number of coefficient changes, it is possible to estimate time-varying (TV) autoregressive (AR) models with piecewise-constant coefficients. Such models emerge in various applications including speech segmentation, biomedical signal processing, and geophysics. To cope with the inherent lack of continuity and the high computational burden when dealing with high-dimensional data sets, this article introduces a convex regularization approach enabling efficient and continuous estimation of TV-AR models. To this end, the problem is cast as a sparse regression one with grouped variables, and is solved by resorting to the group least-absolute shrinkage and selection operator (Lasso). The fresh look advocated here permeates benefits from advances in variable selection and compressive sampling to signal segmentation. An efficient block-coordinate descent algorithm is developed to implement the novel segmentation method. Issues regarding regularization and uniqueness of the solution are also discussed. Finally, an alternative segmentation technique is introduced to improve the detection of change instants. Numerical tests using synthetic and real data corroborate the merits of the developed segmentation techniques in identifying piecewise-constant TV-AR models.
Highlights
Autoregressive (AR) models have been the workhorse for parametric spectral estimation since they form a dense set in the class of continuous spectra and, in many cases, they approximate parsimoniously the spectrum of a given random process [1], Chap. 3]
The algorithm for change detection of piecewiseconstant AR models developed in this article belongs to the first class of methods, and its first novelty consists in developing a new regularization function which encourages piecewise-constant TV-AR coefficients while being convex and continuous; it can afford efficient convex optimization solvers
With the emphasis placed on large data sets, a candidate algorithm for implementing the developed change detector is a block-coordinate descent iteration, which is provably convergent to the group least-absolute shrinkage and selection operator (Lasso) solution
Summary
Autoregressive (AR) models have been the workhorse for parametric spectral estimation since they form a dense set in the class of continuous spectra and, in many cases, they approximate parsimoniously the spectrum of a given random process [1], Chap. 3]. The algorithm for change detection of piecewiseconstant AR models developed in this article belongs to the first class of methods, and its first novelty consists in developing a new regularization function which encourages piecewise-constant TV-AR coefficients while being convex and continuous; it can afford efficient convex optimization solvers. To this end, it is shown that the segmentation problem can be recast as a sparse regression problem. With the emphasis placed on large data sets, a candidate algorithm for implementing the developed change detector is a block-coordinate descent iteration, which is provably convergent to the group Lasso solution.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
