Unifying Divergence Minimization and Statistical Inference Via Convex Duality

By Yasemin Altun, Alex Smola. 2006

150 citations recorded by the source corpus.

Subfields: Computational Mechanics, Control and Systems Engineering, Statistical and Nonlinear Physics, Statistics and Probability, Mathematical Optimization

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Citations in the corpus

Learning Theory for Distribution Regression (2014, background): “The population limits are well-defined as being dot products between the embeddings of the generating distributions (Altun and Smola, 2006), and for characteristic kernels the distance between embeddings defines a metric on probability measures (Sriperumbudur et al., 2011; Gretton et al., 2012).”
Kernel Mean Shrinkage Estimators (2014, background): “ives a good estimate of µP in a way that does not depend on the dimension of the feature space, and, as sample size goes to inﬁnity, the estimation error vanishes (Shawe-Taylor and Cristianini, 2004; Altun and Smola, 2006). As a result, no need is felt to improve the kernel mean estimation. Many pra”
Continuous Doubly Constrained Batch Reinforcement Learning (2021, methodology): “This leaves us with the reverse KLdivergence and IPMs in Hilbert Space (Altun & Smola, 2006).”
A Kernel Method for the Two-Sample-Problem (2006, neutral): “e. a second set of observations drawn from the same distribution. While not the key focus of the present paper, such bounds can be used in the design of inference principles based on moment matching (Altun and Smola, 2006; Dud´ık and Schapire, 2006; Dud´ık et al., 2004). 4.2 Bound on the Unbiased St”
Semi-Supervised Learning via Generalized Maximum Entropy (2010, methodology): “…MaxEnt framework with non-differentiable penalty functions as outlined in (Dudík & Schapire, 2006) or with infinite dimensional spaces as (Altun & Smola, 2006) points out, a more general duality technique such as Fenchel's duality is required for a proper analysis of the primaldual space…”
Loss factorization, weakly supervised learning and label noise robustness (2016, methodology): “A similar statement may be derived for rkhs on top of [Bartlett and Mendelson, 2002, Altun and Smola, 2006].”
Two-stage sampled learning theory on distributions (2014, background): “The population limits are well-defined as being dot products between the embeddings of the generating distributions [25], and for characteristic kernels the distance between embeddings defines ametric on probability measures [26, 27].”
Kernel Exponential Family Estimation via Doubly Dual Embedding (2018, methodology): “whose dual problem will be reduced to the penalized MLE (2) with proper choice of ⌘ (Altun and Smola, 2006)[Lemma 6].”
Tailoring density estimation via reproducing kernel moment matching (2008, background): “A second class of density estimators employ exponential family models and are based on the duality between maximum entropy and maximum likelihood estimation (Barndorff-Nielsen, 1978; Dud´ık et al., 2004; Altun & Smola, 2006).”
Multitask Learning without Label Correspondences (2010, methodology): “By exploiting convex duality [5], we can solve the resulting optimization problem efficiently in the dual space using existing DC programming algorithms [6].”
A Kernel Two-Sample Test (2012, background): “While not the focus of the present paper, suchbounds can be used to perform inference based on moment matching (Altun and Smola, 2006; Dudı́k an Schapire, 2006; Dud́ık et al., 2004).”
A Hilbert Space Embedding for Distributions (2007, background): “In fact, [59, 17, 60] show that this may be achieved in the following fashion:”
A Minimax Approach to Supervised Learning (2016, methodology): “To that end, we use a similar technique as in the Fenchel’s duality theorem, also used at [11, 12, 13] to address divergence minimization problems.”
Approximate MaxEnt Inverse Optimal Control and Its Application for Mental Simulation of Human Interactions (2015, background): “which can be interpreted as a relaxation of the constraints in the primal as shown by (Dudı́k, Phillips, and Schapire 2004; Altun and Smola 2006).”
Estimating labels from label proportions (2008, methodology): “Our idea relies on uniform convergence properties of the expectation operator and of corresponding risk functionals (Altun and Smola, 2006; Dud´ık and Schapire, 2006).”
Causal reasoning by evaluating the complexity of conditional densities with kernel methods (2008, background): “The regularizer, the norm itself and not its square (as opposed to our complexity measure) is in agreement with the choice in [16].”
(Almost) No Label No Cry (2014, background): “It is not hard to show that Lemma 17 in Altun and Smola [23], and Corollary 9 in Quadrianto et al. [17] hold for LMM so that ‖θ̃∗ − θ∗‖22 ≤ (2λ)−1‖µ̃S − µS‖22.”