On the Complexity of the Weighted Fused Lasso

Bento, José; Furmaniak, Ralph; Ray, Surjyendu

doi:10.1109/lsp.2018.2867800

Cited by 8 publications

(5 citation statements)

References 25 publications

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“…Second, note that in one-dimensional case the time complexities of path solution algorithms for the nearlyisotonic regression and the fusion approximator are equal to O(n log(n)), cf. ; Hoefling (2010); Bento et al (2018) with the references therein. Therefore, if we have λ F fixed, then using the result of Theorem 5 we can get the solution path with respect to λ N I with the time complexity O(n log(n)).…”

Section: Degrees Of Freedommentioning

confidence: 99%

Fused lasso nearly-isotonic signal approximation in general dimensions

Pastukhov

2024

Stat Comput

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In this paper, we introduce and study fused lasso nearly-isotonic signal approximation, which is a combination of fused lasso and generalized nearly-isotonic regression. We show how these three estimators relate to each other and derive solution to a general problem. Our estimator is computationally feasible and provides a trade-off between monotonicity, block sparsity, and goodness-of-fit. Next, we prove that fusion and near-isotonisation in a one-dimensional case can be applied interchangably, and this step-wise procedure gives the solution to the original optimization problem. This property of the estimator is very important, because it provides a direct way to construct a path solution when one of the penalization parameters is fixed. Also, we derive an unbiased estimator of degrees of freedom of the estimator.

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Section: Degrees Of Freedommentioning

confidence: 99%

Fused lasso nearly-isotonic signal approximation in general dimensions

Pastukhov

2024

Stat Comput

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“…Second, note that in one-dimensional case the time complexities of path solution algorithms for nearly-isotonic regression and fusion approximator are equal to O(n log(n)), cf. [11,17,26] with the references therein. Therefore, if we have λ F fixed, then using the result of Theorem 5 we can get the solution path with respect to λ N I with the time complexity O(n log(n)).…”

Section: Computational Aspects Simulation Study and Application To A ...mentioning

confidence: 99%

Fused Lasso Nearly-Isotonic Signal Approximation in General Dimensions

Pastukhov

2023

Preprint

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In this paper we introduce and study fused lasso nearly-isotonic signal approximation, which is a combination of fused lasso and generalized nearly-isotonic regression. We show how these three estimators relate to each other and derive solution to a general problem. Our estimator is computationally feasible and provides a trade-off between monotonicity, block sparsity and goodness-of-fit. Next, we prove that fusion and near-isotonisation in one dimensional case can be applied interchangably, and this step-wise procedure gives the solution to the original optimization problem. This property of the estimator is very important, because it provides a direct way to construct path solution when one of the penalization parameters is fixed. Also, we derive unbiased estimator of degrees of freedom of the estimator.

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“…The CCDC is like BFAST Monitor with the aim of detecting changes in near-real-time; however, CCDC uses a robust regression technique, called the Least Absolute Shrinkage and Selection Operator (LASSO) [73]. Unlike OLS used in BFAST and BFAST Monitor, LASSO is used in CCDC to fit the season-trend model to the history period, which minimizes over-fitting by limiting the total absolute value of the coefficients [74,75]. The Root Mean Square Error (RMSE) of the fitted history model and residuals of incoming observations are used to detect a change, so if the new residuals deviate from the fitted model about six times in a row, the breakpoint location and magnitude will be identified.…”

Section: Continuous Change Detection and Classification (Ccdc)mentioning

confidence: 99%

A Survey on Change Detection and Time Series Analysis with Applications

2021

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With the advent of the digital computer, time series analysis has gained wide attention and is being applied to many fields of science. This paper reviews many traditional and recent techniques for time series analysis and change detection, including spectral and wavelet analyses with their advantages and weaknesses. First, Fourier and least-squares-based spectral analysis methods and spectral leakage attenuation methods are reviewed. Second, several time-frequency decomposition methods are described in detail. Third, several change or breakpoints detection methods are briefly reviewed. Finally, some of the applications of the methods in various fields, such as geodesy, geophysics, remote sensing, astronomy, hydrology, finance, and medicine, are listed in a table. The main focus of this paper is reviewing the most recent methods for analyzing non-stationary time series that may not be sampled at equally spaced time intervals without the need for any interpolation prior to the analysis. Understanding the methods presented herein is worthwhile to further develop and apply them for unraveling our universe.

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On the Complexity of the Weighted Fused Lasso

Cited by 8 publications

References 25 publications

Fused lasso nearly-isotonic signal approximation in general dimensions

Fused lasso nearly-isotonic signal approximation in general dimensions

Fused Lasso Nearly-Isotonic Signal Approximation in General Dimensions

A Survey on Change Detection and Time Series Analysis with Applications

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