Learning Theory: An Approximation Theory Viewpoint: Index

By Felipe Cucker, Ding-Xuan Zhou. 2007

452 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/94b8f6ec39deaf334abd91280d5e5aa8a7efd29a

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In Artificial Intelligence

Citations in the corpus

Vector valued reproducing kernel Hilbert spaces and universality (2008, methodology): “In learning theory, reproducing kernel Hilbert spaces (RKHS) are an important tool for designing learning algorithms, see for example [8, 29, 31] and the book [9].”
Generalization bounds for learning the kernel (2009, methodology): “First, we show that the generalization analysis of the kernel learning algorithms reduces to investigation of the suprema of the Rademacher chaos process of order two over candidate kernels, which we refer to as Rademacher chaos complexity.”
The Balancing Act in Causal Inference (2021, background): “…to some constraints, the model M in Equation 20 is the unit ball {m(x) : ‖m‖M ≤ 1} of an RKHS, and furthermore, the unit ball of every RKHS can be described like this (see, e.g., Cucker & Zhou, 2007, Chapters 2 and 4).5 One of the most common ways to characterize functions is their smoothness.”
Convergence of Value Aggregation for Imitation Learning (2018, unknown): “(Cucker and Zhou, 2007, Lemma 7.2) Let c1, c2, . . . , cl > 0 and s > q1 > q2 > · · · > ql−1 > 0.”
Generalization Properties of Learning with Random Features (2016, background): “It is always true in the limit case Q = κ, γ = 1, sometimes referred to as the capacity independent setting [14].”
A note on application of integral operator in learning theory (2009, methodology): “[5,12]).”
Estimating conditional quantiles with the help of the pinball loss (2011, unknown): “We refer to [10], Chapter 5, and [24], Theorem 6.”
Kernel-Based Methods for Hypothesis Testing: A Unified View (2013, methodology): “Indeed, kernel-based methods hinge upon the Hilbertian structure of the so-called RKHS, the natural function space associated with these nonparametric approaches [25], [26].”
Echo state networks are universal (2018, methodology): “In the language of learning theory, this is equivalent to the possibility of making approximation errors arbitrarily small [Cuck 02, Smal 03, Cuck 07].”