A Distribution-Free Theory of Nonparametric Regression (Springer Series in Statistics)

By László Györfi, Michael Kohler, A. Kryzak, Harro Walk. 2002

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View Paper: https://www.semanticscholar.org/paper/77f4bb241c37644c124fb148fa646931d0357cc4

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Citations in the corpus

A data-driven statistical framework for post-grasp manipulation (2014, background): “It has been shown that the number of data points required to achieve the same accuracy for a GP grows exponentially with the state dimension (Györfi et al., 2002).”
Divide and Conquer Kernel Ridge Regression (2013, unknown): “The assumption f * ∈ H is, in any case, fairly standard (Gyorfi et al., 2002; Wasserman, 2006). where T 1 (d) = 2ρ 4 f * 2 H tr(K)β d λ , T 2 (d) = 4 f * 2 H + 2σ 2 /λ m µ d+1 + 3ρ 4 tr(K)β d λ , and T 3 (d) = Cb(n, d, k) ρ 2 γ(λ) + 1 √ n k f * 1 + 2σ 2 mλ + 4 f * 2 H m , and C denotes a universal…”
Efficient Algorithms for Outlier-Robust Regression (2018, background): “, let D be a distribution on ’d × [−1,1]. Let (x1, y1),...,(x n, y n) be i.i.d samples from D. Let ℓˆ argminℓ Í n i 1(y i − hℓ,x ii) 2, be the least-squares estimator. Then, (say, via Theorem 11.3 in [GKKW02]) errD(ℓˆ) 6 O(d) n +8 ·argminℓ errD(ℓ). In particular, in the realizable-case, i.e., when (”
Finite-Dimensional Projection for Classification and Statistical Learning (2008, unknown): “…conditions (a) and (b) above hold, and α 2 γ + , the right-hand side of inequality (15) is at least In can be checked easily that 2 α − 1 2 α +1 > − Of course, since we are only comparing upper bounds, the above result does not imply that the ﬁnite dimensional projection classiﬁer is necessarily…”
Divide and conquer kernel ridge regression: a distributed algorithm with minimax optimal rates (2013, background): “he conditional expectation f∗(x) = E[Y | X = x] is optimal. The problem of nonparametric regression is a classical one, and a researchers have studied a wide range of estimators (see, e.g., the books [11, 32, 30]). One class of methods, known as regularized M-estimators [30], are based on minimizing”
The Dependent Dirichlet Process and Related Models (2020, unknown): “See, for example, Györfi et al. (2002); Klemelä (2014); Faraway (2016) and references within.”
Boosted Fitted Q-Iteration (2017, methodology): “Then, ‖ k‖2µ ≤ 4 inf f∈F ‖f − %∗k‖ 2 µ + 4(1 + L) 2 k−1∑ i=0 L2i k−1∑ j=0 ‖ j‖2µ + 24 · 214B4k n ( log 42e+ 2 log(480eB2kn)VF+ ) where L = γCµ→∞, Bk = max(‖%̃k‖∞ , 1), and VF+ is the VC dimension ofF+ that is the class of all subgraphs of functions f ∈ F (see Chapter 9.4 of (Györfi et al., 2002)).”
Nonparametric regression using deep neural networks with ReLU activation function (2017, methodology): “: [0;1]d !R from the sample (X i;Y i) i:Various methods exist that allow to estimate the regression function nonparametrically, including kernel smoothing, series estimators/wavelets and splines, cf. [15,51,49]. In this work, we consider tting a multilayer feedforward articial neural network to the ”
Vector valued reproducing kernel Hilbert spaces and universality (2008, background): “ HK in L2(X,µ;Y). Since the probability measure µis unknown, we require that the above property holds for any choice of µ– compare with the deﬁnition of universal consistency for a learning algorithm [18]. Under the condition that the elements of HK are continuous functions vanishing at inﬁnity, we ”