1 Trend Filtering

By Seung-Jean Kim, Kwangmoo Koh, Stephen P. Boyd, Dimitry M. Gorinevsky. 2009

658 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Computer Vision and Pattern Recognition

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Citations in the corpus

Additive models with trend filtering (2017, methodology): “In general, the efficiency of backfitting hinges on the efficiency of the univariate smoother employed; in practice, to implement Algorithm 1 we can use fast interior point methods (Kim et al. 2009) or fast operator splitting methods (Ramdas & Tibshirani 2016) for univariate trend filtering, both of”
Fused Lasso Additive Model (2014, methodology): “3.3 CONNECTIONS TO OTHER METHODS The fused lasso can be interpreted as 1 trend filtering with order k = 0 (Kim et al. 2009; Tibshirani 2014).”
Adaptive piecewise polynomial estimation via trend filtering (2013, methodology): “2 [Kim et al. (2009) focus mainly on linear trend ﬁltering, the case k = 1, but their arguments carry over to the general case as well.]”
Real-Time Convex Optimization in Signal Processing (2010, background): “The same ideas are applied to reconstructing signals with sparse derivative (or gradient, more generally) in total variation de-noising, and in signals with sparse second derivative (or Laplacian) [50].”
A Dynamic Programming Algorithm for the Fused Lasso and L0-Segmentation (2013, background): “( 2009 ) to solve the FLSA, and the running time is listed under the heading “QP”.”
The Hodrick-Prescott Filter A Special Case of Penalized Spline Smoothing (2010, methodology): “The origins of the method date back to, among others, Parker and Rice (1985), who comment on the use of smoothing with (penalized) splines as an alternative to smoothing splines.”
Detecting Changes in Slope With an L0 Penalty (2017, methodology): “The other approach we compare to is the trend-filtering algorithm (Kim et al. 2009).”
Fast and Flexible ADMM Algorithms for Trend Filtering (2014, methodology): “To simultaneously estimate a trend and detect outliers, we solve (ˆ β, ˆ z ) = argmin as in Kim et al. (2009), She & Owen (2011), where the nonzero components of ˆ z correspond to the adaptively detected outliers.”
The generalized lasso is reducible to a subspace constrained lasso (2013, neutral): “A range of interesting applications of this idea have already emerged including the fused lasso [14], trend filtering [15], wavelet smoothing [16].”
Trend Filtering Methods for Momentum Strategies (2011, methodology): “To find x̂, we may also use the quadratic programming algorithm, but Kim et al. (2009) suggest using the primal-dual interior point method in order to optimise the numerical computation speed.”