Ideal spatial adaptation by wavelet shrinkage

By David L. Donoho, Iain M. Johnstone. 1994

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In Statistics and Probability

Citations in the corpus

Regularization Paths for Generalized Linear Models via Coordinate Descent (2010, background): “Simple calculus shows (Donoho and Johnstone 1994) that the coordinate-wise update has the form where ˜ y i = ˜ β 0 + = j x ˜ β (cid:96) is the ﬁtted value excluding the contribution from x ij , and hence y i − ˜ y i the partial residual for ﬁtting β j .”
Nearly unbiased variable selection under minimax concave penalty (2010, background): “This minimax lower bound for the ℓq loss is an extension of the lower bound for the minimax ℓq risk in Donoho and Johnstone (1994a).”
Efficient Policy Learning (2017, background): “Further work on adaptive policy learning would complement a long existing literature on adaptive minimax estimation and inference (e.g., Armstrong and Kolesár, 2016; Birgé and Massart, 2001; Cai and Low, 2005; Donoho and Johnstone, 1994; Efron, 1983; Lepskii, 1991).”
PERFORMANCE GUARANTEES FOR INDIVIDUALIZED TREATMENT RULES (2011, methodology): “In example (4), X ∼ U [0,1] and we use a complex Q0, where Q0(X,1) and Q(X,−1) are similar to the blocks function used in Donoho and Johnstone [8].”
Deflecting Adversarial Attacks with Pixel Deflection (2018, methodology): “ soft-thresholding techniques. A brief overview of these shrinkage techniques are provided in Section7.2, for more thorough review on BayesShrink, VisuShrink and SUREShrink we refer the reader to [7] [13] and [12] respectively. VisuShrink is a faster technique as it uses a universal threshold but th”
Correlation-Based Adaptive Localization With Applications to Ensemble-Based 4D-Seismic History Matching (2018, methodology): “ntly reducing the data size, we lift the restriction such that thresholding can also be applied to the sub-band LLL n. In Luo et al. (2016), the threshold value is computed using the universal rule (Donoho and Johnstone, 1994) = p 2 ln(#do)˙; (15) with #d obeing the number of elements in d . In the ”
Approximation accuracy, gradient methods, and error bound for structured convex optimization (2010, methodology): “Keywords Convex optimization · Compressed sensing · 1-regularization · Nuclear/trace norm · Regression · Variable selection · Sensor network localization · Approximation accuracy · Proximal gradient method · Error bound · Linear convergence Mathematics Subject Classification (2000) 65K05 · 49M37”
Consistencies and rates of convergence of jump-penalized least squares estimators (2009, unknown): “Figure 1 shows the behavior of the Potts minimizer for the test signals of Donoho and Johnstone (1994) sampled at 2048 points and a choice of C = 2 .”
Least squares after model selection in high-dimensional sparse models (2009, background): “convergence of the oracle estimator p c2 s +σ2s/n becomes an ideal goal for the rate of convergence, and in general can be achieved only up to logarithmic terms in most cases (see Donoho and Jonstone [7] and Rigollet and Tsybakov [14]), except under very special circumstances, such as when it become”
Importance Sampled Learning Ensembles (2003, methodology): “The flrst term in (27) is the empirical risk on the learning data obtained by simply substituting ^ q(z) (21) for q(z) in ( 10 ).”