Mixing Strategies for Density Estimation

By Yuhong Yang. 2000

131 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/21cab7de1d7629918fddccfb35712885d0645fc6

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Citations in the corpus

Adapting to Unknown Smoothness by Aggregation of Thresholded Wavelet Estimators (2006, background): “The aggregation framework considered, among others, by [34], [54], [13],[46], [49], [5], [6] is the following: take F0 a finite subset of F , our aim is to mimic (up to an 6”
COMBINING FORECASTING PROCEDURES: SOME THEORETICAL RESULTS (2004, methodology): “Related theoretical results on linearly combining nonparametric regression procedures with independent errors are in Juditsky and Nemirovski (2000) and Yang (in press).”
Optimal rates and adaptation in the single-index model using aggregation (2007, methodology): “By the change of variable y = O x , we obtain where ˜ f ( y (1) where the inﬁmum is taken among all estimators R → R based on data from model (1.1) with d = 1 (univariate regression). order In to bound (5.5) from below, we use the following Theorem, from Tsybakov (2003a), which is a standard tool fo”
PAC-Bayesian Stochastic Model Selection (2003, methodology): “Catoni (To appear b) and Yang (2000b) prove somewhat different general theorems both of which have as a special case the statement that, independent of how g is selected, the expectation (over drawing a sample according to g) of the Kullback-Leibler Divergent D(gh) is bounded as follows.”
Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It (2014, methodology): “0averaged over the nposterior distributions obtained so far. Predicting based on Cesaro-averaged posteriors was introduced independently by several authors (Barron, 1987, Helmbold and Warmuth, 1992, Yang, 2000, Catoni, 1997) and has received a lot of attention in the machine learning literature in r”
Catching up faster by switching sooner: a predictive approach to adaptive estimation with an application to the AIC–BIC dilemma (2012, methodology): “By applying Jensen’s inequality as in proposition 15.2 of Grünwald (2007) (or the corresponding results in Yang (2000) or Yang and Barron (1999)) it follows that, for all pÅ ∈MÅ, r.pÅ, p̄, n/ n−1R.pÅ, p, n/, so that also rm.p̄, n/ 1 n Rm.p, n/: This implies that n rmm.n/ n rm.p̄, n/ Rm.p, n/ c3…”
Sparsity in penalized empirical risk minimization (2009, background): “Aggregation techniques, especially in the case of L2-regression, have been introduced in [23] and [28] and studied extensively in [4,5,9,26,29] among others.”
Model selection via testing: an alternative to (penalized) maximum likelihood estimators (2006, methodology): “Related points of view about the relationships between the minimax risk and the metric structure of the parameter space are to be found in Yatracos [73], Yang and Barron [72], Devroye and Lugosi [28] and Yang [69].”
Adaptive Regression by Mixing (2001, methodology): “…terms of the individualrisks of the original procedures using an idea from Bar-ron (1987) that originated in information theory [the idea also was used in Yang and Barron (1999) to derive minimax rates of convergence for a general function class and in Yang (2000a) to combine density estimators].”
Linear and convex aggregation of density estimators (2006, methodology): “The work on this subject is mainly devoted to the MS aggregation with the Kullback–Leibler divergence as the loss function ([6], [7], [29], [30]) and is based on information-theoretical ideas close to the earlier papers [1] and [13].”
Learning by mirror averaging (2005, methodology): “For two special cases [density estimation with the Kullback–Leibler (KL) loss, and regression model with squared loss] such bounds have been proved earlier in the works of Catoni [7, 8, 9] and Yang [29].”