Some results on Tchebycheffian spline functions

By G. Kimeldorf, Grace Wahba. 1971

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Citations in the corpus

Learning kernel logistic regression in the presence of class label noise (2014, background): “By the representer theorem [19], the optimal f(x) has the form:”
Density Estimation in Infinite Dimensional Exponential Families (2013, background): “2), it is possible to see that the standard representer theorem (Kimeldorf and Wahba, 1971; Schölkopf et al., 2001) gives a similar, but slightly different linear system, and the solutions are the same if K is non-singular.”
Kernel methods in machine learning (2007, neutral): “Here we consider the more general case of minimizing a functional that includes a monotone function of the Hilbert space norm ‖f‖H as a stabilizer (Wahba [148]).”
Optimization with Sparsity-Inducing Penalties (2011, methodology): “When applied to the mapping φ : x 7→ K(x, ·), the third remark above yields a specific version of the representer theorem of Kimmeldorf and Wahba [75]12 stating that h⋆(·) = ∑ni=1 α⋆iK(xi, ·).”
Residual Weighted Learning for Estimating Individualized Treatment Rules (2015, background): “For a nonlinear decision rule, the decision function Due to the representer theorem (Kimeldorf and Wahba 1971), the nonlinear problem can be reduced to ﬁnding ﬁnite-dimensional coeﬃcients v i , and h ( x ) can be represented as =1 v j K ( x , x j ).”
Learning the Kernel Function via Regularization (2005, background): “Moreover, one can show that iff is a minimizer of the above functional it has the form f (x) = ∑ j∈INm c jK(x j ,x), x∈ X (2) for some real vectorc= (c j : j ∈ INm) of coefficients (see, for example, De Vito et al., 2005; Girosi, 1998; Kimeldorf and Wahba, 1971; Micchelli and Pontil, 2005; Schölkop”
Early stopping for non-parametric regression: An optimal data-dependent stopping rule (2011, methodology): “Using the representer theorem [15], any f that minimizes R̂(f) can be expressed as”
Convex Deep Learning via Normalized Kernels (2014, background): “Kernels [19] have had a significant impact in machine learning, partly because they offer flexible modeling capability without sacrificing convexity in common training scenarios [20].”
Decentralized Online Learning With Kernels (2017, methodology): “Multiple tools from distributed optimization may be used to do so; however, we note that the Representer Theorem [18] has not been established for general stochastic saddle point problems in RKHSs.”
Personalized handwriting recognition via biased regularization (2006, methodology): “Two neural network based methods were presented by Matić et al. (1993) and Platt and Matić (1997), although with limited experimental results.”
Heterogeneous feature machines for visual recognition (2009, unknown): “Though the function space F may be infinite dimensional, by the representer theorem [17], the solution of (1) takes the following finite dimensional form”