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Many real time series datasets exhibit structural changes over time. A popular model for capturing their temporal dependence is that of vector autoregressions (VAR), which can accommodate structural changes through time evolving transition matrices. The problem then becomes to both estimate the (unknown) number of structural break points, together with the VAR model parameters. An additional challenge emerges in the presence of very large datasets, namely on how to accomplish these two objectives in a computational efficient manner. In this article, we propose a novel procedure which leverages a block segmentation scheme (BSS) that reduces the number of model parameters to be estimated through a regularized least-square criterion. Specifically, BSS examines appropriately defined blocks of the available data, which when combined with a fused lasso-based estimation criterion, leads to significant computational gains without compromising on the statistical accuracy in identifying the number and location of the structural breaks. This procedure is further coupled with new local and exhaustive search steps to consistently estimate the number and relative location of the break points. The procedure is scalable to big high-dimensional time series datasets with a computational complexity that can achieve O(n), where n is the length of the time series (sample size), compared to an exhaustive procedure that requires steps. Extensive numerical work on synthetic data supports the theoretical findings and illustrates the attractive properties of the procedure. Finally, an application to a neuroscience dataset exhibits its usefulness in applications. Supplementary files for this article are available online.
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Interpolating discriminant functions in high-dimensional Gaussian latent mixtures
Abstract This paper considers binary classification of high-dimensional features under a postulated model with a low-dimensional latent Gaussian mixture structure and nonvanishing noise. A generalized least-squares estimator is used to estimate the direction of the optimal separating hyperplane. The estimated hyperplane is shown to interpolate on the training data. While the direction vector can be consistently estimated, as could be expected from recent results in linear regression, a naive plug-in estimate fails to consistently estimate the intercept. A simple correction, which requires an independent hold-out sample, renders the procedure minimax optimal in many scenarios. The interpolation property of the latter procedure can be retained, but surprisingly depends on the way the labels are encoded.
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- Award ID(s):
- 2210557
- PAR ID:
- 10490549
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrika
- Volume:
- 111
- Issue:
- 1
- ISSN:
- 0006-3444
- Format(s):
- Medium: X Size: p. 291-308
- Size(s):
- p. 291-308
- Sponsoring Org:
- National Science Foundation
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