SPADES AND MIXTURE MODELS

By Florentina Bunea, Alexandre B. Tsybakov, Marten H. Wegkamp, Adrian Barbu. 2009

65 citations recorded by the source corpus.

This paper studies sparse density estimation via l1 penalization (SPADES). We focus on estimation in high-dimensional mixture models and nonparametric adaptive den- sity estimation. We show, respectively, that SPADES can recover, with high probability, the unknown components of a mixture of probability densities and that it yields minimax adaptive density estimates. These results are based on a general sparsity oracle inequality that the SPADES estimates satisfy. MSC2000 Subject classification: Primary 62G08, Secondary 62C20, 62G05, 62G20

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/bb5b14e68c47fede9656617cdcced210860be376

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Citations in the corpus

ROBUST EMPIRICAL MEAN ESTIMATORS (2011, methodology): “The following assumptions were used in [11] to state the results.”
High-dimensional additive hazards models and the Lasso (2011, background): “While non-asymptotic results, like sparse oracle inequalities for instance, are now well-known for regression or density estimation (see for instance [7, 5, 4], among many others), such results are not yet available for survival data.”
Non-negative least squares for high-dimensional linear models: consistency and sparse recovery without regularization (2012, background): “1, recovery of the support of β∗ fails in the presence of noise, because the {φj}’s are placed too densely relative to the number of sampling points; see [11] for a similar discussion concerning the recovery of mixture components in sparse mixture density estimation.”