Minimal Penalties for Gaussian Model Selection

By Lucien Birgé, Pascal Massart. 2007

381 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a233d8da4bca83a507086c447000083c26486b4b

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In Control and Systems Engineering

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Citations in the corpus

Nonparametric drift estimation for i.i.d. paths of stochastic differential equations (2020, neutral): “p (3) t (x0, x) ≤ 1 2 √ 2πx0aβ exp [−( x 2β2 + a(2)x0 2β2 )] [ exp (a √ x0x/β (2)) + exp (−a √ x0x/β (2)) ] ≤ 1 2 √ 2πx0aβ [ exp [− ( √ x− ax0)2 2β2 + exp [− ( √ x+ a √ x0) 2 2β2 ] ] ≤ 1 √ 2πx0aβ ,”
Adaptive density estimation: a curse of support? ✩ (2009, methodology): “With the model selection approach proposed by Birg´e and Massart (2007), we can see that Theorem 1 implies i h i where C is a constant and M L represents all the possible sets m in Γ n such that ˆ f m has support in [ L , L ].”
Minimax risks for sparse regressions: Ultra-high-dimensional phenomenons (2010, neutral): “This upper bound (5.6) is a consequence of Birgé and Massart [11].”
Inferring Phylogenetic Networks with Maximum Pseudolikelihood under Incomplete Lineage Sorting (2015, methodology): “The network scores (negative log-pseudolikelihood) decreased sharply from h = 0 to h = 2 then slightly and somewhat linearly (see S1 Text), suggesting that h = 2 best ﬁts the ﬁsh data using a slope heuristic [46, 45].”
Adaptive Laguerre density estimation for mixed Poisson models (2015, methodology): “For Gaussian regression or white noise models, Birgé and Massart (2007) [6] prove that the method works for κ = 1+η, η > 0, and explodes for κ = 1−η.”
High-dimensional regression with unknown variance (2011, methodology): “(21) Following the work of Birgé and Massart [18], Lebarbier [50] considers the penalty pen(q) = (q + 1) (c1 log(n/(q + 1)) + c2) σ 2 and determines the constants c1 = 2, c2 = 5 by extensive numerical experiments (see also Comte and Rozenholc [25] for a similar approach in a more general ha l-0 06 ”
A survey of cross-validation procedures for model selection (2009, positive): “From the penalization point of view, Birg´e and Massart (2007) proved that when Card( n ) = e κn for some κ > 0, the minimal amount of penalty required so that an oracle inequality holds with O (1) is much larger than pen id ( m ). suitably In addition to the FPE α and GIC λ with chosen α, λ ,…”
Data-driven calibration of linear estimators with minimal penalties (2009, methodology): “Our estimator relies on the concept of minimal penalty, introduced by Birgé and Massart [6] and further studied in [7].”
changepoint: An R Package for Changepoint Analysis (2014, background): “The choice of appropriate penalty is still an open question and typically depends on many factors including the size of the changes and the length of segments, both of which are unknown prior to analysis (see Guyon and Yao (1999); Lavielle (2005); Birge and Massart (2007)).”
Optimal detection of changepoints with a linear computational cost (2011, background): “There is a growing body of research (see Guyon and Yao 1999; Picard et al. 2005; Birge and Massart 2007) that considers nonlinear penalty forms.”
Near optimal thresholding estimation of a Poisson intensity on the real line (2008, methodology): “This relationship characterizes the “slope heuristic” of Birgé and Massart [11].”
A survey of Bayesian predictive methods for model assessment, selection and comparison (2012, methodology): “For example, Birgé and Massart (2007) demonstrate this for a penalized least-squares criterion and Arlot and Celisse (2010) provide references in relation to (non-Bayesian) cross-validation methods.”