Smooth Operators

By Steffen Grünewälder, Arthur Gretton, John Shawe-Taylor. 2013

39 citations recorded by the source corpus.

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In Mathematical Optimization

Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, background): “Based on this interpretation, Harmeling et al. (2013) asserts that the Fraunhofer diffraction is in fact a special case of kernel mean embedding and that in theory an object p(ξ) with bounded support can be recovered completely from its diffraction-limited image, using an argument from the injectivi”
Kernel Mean Estimation via Spectral Filtering (2014, methodology): “To this end, we ﬁrst present a regularization interpretation that is different from the one in (3) which involves learning a smooth operator from H to H [22].”
Kernel Mean Shrinkage Estimators (2014, methodology): “As an interpretation, we are ﬁnding a smooth operator F that maps k ( x, · ) to itself (see Gr¨unew¨alder et al. (2013) for more details on this smooth operator framework).”
Kernel Mean Estimation and Stein's Effect (2013, positive): “Furthermore, the F-KMSE is of a similar form as the conditional mean embedding used in [23], which can be viewed more generally as a regression problem in RKHS with smooth operators [24].”
Kernel Bayes' rule: Bayesian inference with positive definite kernels (2013, methodology): “An alternative way of obtaining the regularized conditional mean embedding is as the solution to a vector-valued ridge regression problem, as proposed by Grünewälder et al. (2012) and Grünewälder et al. (2013).”
Bounding and Minimizing Counterfactual Error (2016, unknown): “Under Assumptions 9 and 10 about Y 0 , Y 1 , and Φ , we have that Y t (Ψ( r )) = Γ ∗ Φ f Yt , k r ( r, · ) H r , where Γ ∗ Φ is the adjoint operator of Γ Φ [17].”
Scatter Component Analysis: A Unified Framework for Domain Adaptation and Domain Generalization (2015, background): “Note that a general RKHS is not closed under the multiplication operator [72].”
Estimating individual treatment effect: generalization bounds and algorithms (2016, unknown): “Under Assumptions A4 and A6 about m 0 , m 1 , and Φ, we have that m t ( Ψ(r)) = Γ * Φ f Y t , k r (r, ·) Hr , where Γ * Φ is the adjoint operator of Γ Φ (Grunewalder et al., 2013).”