Gaussian model selection

By Lucien Birgé, Pascal Massart. 2001

539 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/91f758bb644d1d1f93d75c33265582d27eccd33e

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Citations in the corpus

Nonparametric statistical inverse problems (2008, background): “In this case bk = 1 and (4) is the classical sequence space model in statistics [6].”
Aggregation for Gaussian regression (2007, background): “Lemma 4 in [10] (see also [22]) asserts that if M ≥ 6D there exists a subset Λ′ ⊂ ΛM,D such that, for some constant c̃ > 0 independent of M and D,”
Prediction error of cross-validated Lasso (2015, methodology): “p Lasso [51], the adaptive Lasso [54] and the square-root Lasso [4]. Penalized regression is not the only approach; for example, methods of model selection by testing hypotheses have been proposed in [1, 2, 7, 6]. Most of these methods involve some sort of a tuning parameter, which is often chosen u”
Model selection via testing: an alternative to (penalized) maximum likelihood estimators (2006, methodology): “Let us observe that the result given in the second part of this corollary completely parallels, and actually generalizes, since we are not restricted to considering linear models "Sm, the results of Theorem 2 of [17] for penalized projection estimators on linear models.”
Near-ideal model selection by ℓ1 minimization (2008, methodology): “It is known that these methods perform well both empirically and theoretically (see [14] and [2, 4] and the many references therein).”
ADAPTIVE ESTIMATION OF A QUADRATIC FUNCTIONAL BY MODEL SELECTION (2001, methodology): “This method has been successfully developed to estimate adaptively a function s in various contexts [see Birg´e and Massart (1997), Barron, Birg´e and Massart (1999), Baraud (1997) or Birge and Massart (2000b)].”
Inference for single and multiple change‐points in time series (2013, methodology): “On the basis of some numerical computations of Birgé and Massart (2001), Lavielle (2005) suggested that the constant c in (51) be c=2.”
Adaptive estimation of the intensity of inhomogeneous Poisson processes via concentration inequalities (2003, methodology): “Proof. We use a lemma which is due to L. Birg´ e and P. Massart [ 9 ].”
Risk hull method and regularization by projections of ill-posed inverse problems (2006, unknown): “The Annals of Statistics 2006, Vol. 34, No. 4, 1653–1677 DOI: 10.1214/009053606000000542 © Institute of Mathematical Statistics, 2006”
Detection of multiple change-points in multivariate time series (2006, unknown): “In a non asymptotic context, Birgé and Massart [3] have shown that a penalty function of the form”
A Modified Bayes Information Criterion with Applications to the Analysis of Comparative Genomic Hybridization Data (2007, methodology): “In comparison to the classical BIC and penalized likelihood methods (e.g., Tibshirani, 1996; Birgé and Massart, 2001; Gu and Wang, 2003; Lavielle, 2005), the modified BIC differs in the penalty term.”
Using penalized contrasts for the change-point problem (2005, background): “(13) In a non-asymptotic context, Birgé and Massart [8] have shown that a penalty function of the form penðsÞ 1⁄4 KðsÞ 1þ c log n KðsÞ ; b 1⁄4 2s 2 n (14)”