Local Extremes, Runs, Strings and Multiresolution

By P. Davies, Arne Kovac. 2001

308 citations recorded by the source corpus.

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In Statistics and Probability

Citations in the corpus

Convex-constrained Sparse Additive Modeling and Its Extensions (2017, background): “Fortunately, this can be achieved through the following characterization of DC functions of one variable: Theorem 3 ((Roberts & Varberg, 1973, §14)).”
Additive models for quantile regression: Model selection and confidence bandaids (2010, methodology): “Total variation penalties also underlie the taut-string methods of Davies and Kovac (2001), and the fused LASSO methods”
Penalized triograms: total variation regularization for bivariate smoothing (2004, background): “Total variation penalties applied on the function itself have been recently considered also in the statistical literature, by Nicholls (1998) and Davies and Kovac (2001).”
Fast and Flexible ADMM Algorithms for Trend Filtering (2014, methodology): “These speciﬁc parameter values are the defaults suggested by Boyd & Vandenberghe (2004) for interior point methods, and are very close to the defaults in the original PDIP linear trend ﬁltering code from Kim et al. (2009).”
Unbalanced Haar Technique for Nonparametric Function Estimation (2007, methodology): “KEY WORDS: Adaptive smooting; Binary segmentation; CART; Matching pursuit; Piecewise constant estimators; Wavelets.”
Piecewise linear regularized solution paths (2007, methodology): “dependent penalties [ 1 ], or multiple penalties [18].”
Estimating time-varying networks (2008, methodology): “The total variation penalty has been successfully applied in detecting sharp transitions in signal processing, image denoising and nonparametric estimation, e.g Rudin et al. (1992); Mammen and Geer (1997); Davies and Kovac (2001).”
Properties and refinements of the fused lasso (2008, methodology): “…that, in the nonparametric function estimation settings, one can obtain μ̂F as a piecewise-constant variable-knot spline function on [0,1] [see Mammen and van de Geer (1997), Proposition 8] and that the taut-string algorithm of Davies and Kovac (2001a) solves the constrained version of (2.2).”
Total Variation Blind Deconvolution: The Devil Is in the Details (2014, methodology): “The proof exploits recent work of Condat [5], Strong and Chan [20] and the taut string algorithm of Davies and Kovacs [6].”
On the Bernstein–von Mises phenomenon for nonparametric Bayes procedures (2013, background): “e abstract and dictated by the applications we have in mind. They are, however, closely connected to the frequentist literature on nonparametric multiscale inference, as developed in the papers [11], [9], [12], [10], [29], where also many further references can be found. This connection gives a furt”
Splines in Higher Order TV Regularization (2006, unknown): “This completes the proof.”
Robust Estimators are Hard to Compute (2006, unknown): “[2].”
Semantic Pooling for Complex Event Analysis in Untrimmed Videos (2016, background): “We have not speciﬁed the proximal map of the total variation norm P h = 2 k(cid:6)k tv , however, it has a well-known linear time exact algorithm, see e.g., [68].”