On the optimality of conditional expectation as a Bregman predictor

By Arindam Banerjee, Xin Guo, Hui Wang. IEEE Transactions on Information Theory, 2005

308 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/56df317c39f685e75b340c8538b699088ffa918c

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Citations in the corpus

How Generative Adversarial Networks and Their Variants Work (2017, methodology): “It proposes a relaxed Wasserstein distance which is a combination of Bregman divergence [7] and the Wasserstein distance.”
Comparing Possibly Misspecified Forecasts (2020, background): “The class of loss functions that is consistent for the mean is known as the Bregman class (see, e.g., Savage 1971; Banerjee, Guo, and Wang 2005; Bregman 1967, and includes the squared-error loss function as a special case).”
Parametric Bayesian Estimation of Differential Entropy and Relative Entropy (2010, background): “[22]; we provide a proof in the appendix for completeness.”
(Almost) No Label No Cry (2014, background): “1 Proof of Lemma 1 For any SPSL F (S, h), we can write it as ([2], Lemma 1, [3]): F (S, h) = Fφ(S, h) .”
Learning to Filter with Predictive State Inference Machines (2015, background): “(4)Squared loss in an example Bregman divergence of which there are others that are optimized by the conditional expectation (Banerjee et al., 2005).”
How Generative Adversarial Networks and Its Variants Work : An Overview of GAN (2017, methodology): “It proposes a relaxed Wasserstein distance which is a combination of Bregman divergence [9] and the Wasserstein distance.”
Making and Evaluating Point Forecasts (2009, background): “Osband and Reichelstein (1985) assume that the scoring function is continuously differentiable with respect to its first argument, the point forecast; Banerjee et al. (2005) assume the existence of continuous second partial derivatives with respect to the observation. A challenging, nontrivial probl”
A generalized maximum entropy approach to bregman co-clustering and matrix approximation (2004, background): “In the context of exponential families, the sets S and Θ respectively correspond to the expectation parameter space and the natural parameter space where ψ is the cumulant function of the exponential family Banerjee et al. (2005b). Using the above notion of duality, we now define a class of reconstr”
Bregman Divergences and Surrogates for Learning (2009, background): “Using the general bijection between BLFs and the exponential families of distributions [15], [8], there exists through (10) a bijection between PCL and a subset of these exponential families whose members’ pdfs may be written: Pr ½yj ¼ exp D ðykr 1 ð Þ þ ðyÞ ðyÞÞ; where 2 IR denotes the natural para”
Theory and Use of the EM Algorithm (2011, background): “The posterior mean is the best estimate in the sense that it minimizes the expected posterior squared-error loss, and in fact minimizes the expectation of any of the Bregman divergences [3, 15].”
Information, Divergence and Risk for Binary Experiments (2009, background): “A concise summary of many of the properties of Bregman divergences is given by Banerjee et al. (2005b, Appendix A); see also Censor and Zenios (1997). In particular, Bregman divergences always satisfy Bφ(s,s0) ≥ 0 and Bφ(s0,s0) = 0 for all s,s0 ∈ S, regardless of the choice of φ.”
Clustering with Bregman Divergences (2005, background): “of the elements of the set to a fixed point for a distortion function F (x, y), then, under mild conditions, it can be shown that F (x, y) is a Bregman divergence [4].”