Generalization Error Bounds for Bayesian Mixture Algorithms

By R. Meir, Tong Zhang. 2003

157 citations recorded by the source corpus.

Subfields: Probabilistic & Bayesian Methods, Statistical Learning Theory

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Citations in the corpus

PAC-Bayesian Theory Meets Bayesian Inference (2016, neutral): “[26], Meir and Zhang [35], Ng and Jordan [36], Rousseau [40] for other studies drawing links between frequentist statistics and Bayesian inference, but outside the PAC-Bayesian framework.”
Wireless Network Intelligence at the Edge (2018, background): “This missing block can be addressed by the Bayesian learning theory [125] and the probably approximately correct (PAC) framework [126].”
Error asymmetry in causal and anticausal regression (2016, background): “However, the classical learning theories, such as [16,17,18,19,20], are mainly focused on the general nature of statistical algorithms or data dependent properties, but do not consider a connection between the causality in the generation process of data and the corresponding implications for the pre”
Information-theoretic upper and lower bounds for statistical estimation (2006, methodology): “The key ingredient in our proof of the information exponential inequality is a well-known convex duality, which employs KL-complexity, and has already been used in some recent machine learning papers to study sample complexity bounds [2], [4], [5], [11], [12].”
Rademacher Chaos Complexities for Learning the Kernel Problem (2010, methodology): “Applying the contraction property of Rademacher averages (theorem 7 of Meir & Zhang, 2003 ) implies that, with probability <inline-graphic xlink:href="NECO_a_00028inline135.”
From ɛ-entropy to KL-entropy: Analysis of minimum information complexity density estimation (2006, methodology): “For example, see (Meir & Zhang, 2003; Seeger, 2002).”
Boosting with early stopping: Convergence and consistency (2005, methodology): “Now the one-sided Rademacher process comparison result in [32], Theorem 7, which is essentially a slightly refined result (with better constant) of the two-sided version in [24], Theorem 4.”
A Vector-Contraction Inequality for Rademacher Complexities (2016, background): “Meir and Zhang [15] gave a nice and simple proof of the scalar contraction inequality as stated above.”
User-friendly introduction to PAC-Bayes bounds (2021, background): “Many aggregates share a formal similarity with the EWA of online learning and with the Gibbs posterior of the PAC-Bayes approach, we refer the reader to [144, 106, 202, 139, 203, 42, 206, 119, 116, 64, 40, 183, 65, 60, 63, 59, 62, 126, 61].”
Relative deviation learning bounds and generalization with unbounded loss functions (2013, methodology): “…in the hypothesis set (Dudley, 1984; Pollard, 1984; Dudley, 1987; Pollard, 1989; Haussler, 1992), an alternative assumption similar to Hoeffding’s inequality based on the expectation of a hyperbolic function, a quantity similar to the moment-generating function, is used by Meir and Zhang (2003).”
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning) (2005, unknown): “Recent work by Meir and Zhang [2003] provides some PAC bounds directly for Bayesian algorithms (like the predictive classifier) whose predictions are made on the basis of a data-dependent posterior distribution.”
On the generalization ability of on-line learning algorithms (2001, background): “…(2) Prominent examples of this kind are the bounds for linear-threshold classifiers, where depends on the margin of [11]–[14], and the bounds for Bayesian mixtures, where depends on the Kullback–Leibler divergence between the data-dependent mixture coefficients and the a priori coefficients [15].”
Collaborative Filtering with the Trace Norm: Learning, Bounding, and Transducing (2011, methodology): “Lemma 9 Let Y be a random matrix defined as in Eq.”
On the Complexity of Linear Prediction: Risk Bounds, Margin Bounds, and Regularization (2008, methodology): “Like Meir and Zhang [2003] (see Section 5 therein), we begin by using conjugate duality to bound the Rademacher complexity.”
Sparse multinomial logistic regression: fast algorithms and generalization bounds (2005, methodology): “Third, in Section 4, we derive generalization bounds for our methods based on recently published learning-theoretic results [26], [33].”