All of Nonparametric Statistics (Springer Texts in Statistics)

By Larry A. Wasserman. 2006

273 citations recorded by the source corpus.

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Citations in the corpus

Learning Theory for Distribution Regression (2014, background): “Third, density estimates in high dimensional spaces suffer from slow convergence rates (Wasserman, 2006, Section 6.5).”
Modelling transition dynamics in MDPs with RKHS embeddings (2012, background): “Unlike density estimates, however, distribution embedding estimates do not scale poorly with the dimension d of the underlying space: the risk of a kernel density estimate increases as O(m−4/(4+d)) when the optimal bandwidth is used (Wasserman, 2006)[Sec.”
Divide and conquer kernel ridge regression: a distributed algorithm with minimax optimal rates (2013, background): “The problem of non-parametric regression is a classical one, and a researchers have studied a wide range of estimators (see, for example, the books of Gyorﬁ et al. (2002), Wasserman (2006), or van de Geer (2000)).”
Regularization in reinforcement learning (2011, methodology): “An alternative is the family of nonparametric approaches, which has been successful Nonparametric Models in the statistics and the supervised learning communities for a long time [Györfi et al., 2002; Hastie et al., 2001; Bishop, 2006; Wasserman, 2007].”
Cognitive Models of Test-Item Effects in Human Category Learning (2010, methodology): “A human cat- egory learning model needs to be able to explain all such Test-Item Effects.”
Convergence Rates for Differentially Private Statistical Estimation (2012, background): “It is a well-established result in theoretical statistics (see, e.g, Wasserman, 2006) that if T is Hadamarddifferentiable, and if Ex∼F [IF(x, T, F )2] is bounded, then T (Fn) converges to T (F ) as n→∞.”
Multiattention Network for Semantic Segmentation of Fine-Resolution Remote Sensing Images (2020, background): “Given that kernel learning [55] processes all inputs simultaneously and order independently by computing the similarity between the inputs, attention could be interpreted as a kernel smoother [56] applied over the inputs in a sequence, where the kernel evaluates the similarity between different inpu”
Least squares after model selection in high-dimensional sparse models (2009, background): “ from above. The lemma allows for many standard bounded dictionaries that arise in the nonparametric estimation, for example, regression splines, orthogonal polynomials, and trigonometric series (see [10, 20, 21, 25]). Similar results are known to hold for standard Gaussian regressors as well [26]. ”
Kernel Bayes' rule: Bayesian inference with positive definite kernels (2013, background): “Kernel density estimates converges more slowly in L 2 as the dimension d of the space increases, however: for an optimal bandwidth choice, this error drops as O(n −4(4+d) ) (Wasserman, 2006, Section 6.5).”
Exact minimax risk for linear least squares, and the lower tail of sample covariance matrices (2019, result): “setting, where the covariates X1,...,Xnare treated as deterministic and the risk is evaluated within-sample; in this case, the expected excess risk of the OLS estimator is bounded by σ2d/n(see, e.g., [Was06]). In the random design setting considered here, a classical result ([GKKW02], Theorem 11.3) ”
Sparse Modeling for Image and Vision Processing (2014, unknown): “…applied to image denoising with natural image patches before; it is usually called Nadaraya-Watson estimator [see Nadaraya, 1964, Watson, 1964, Wasserman, 2006].10 9This idea has in fact appeared in the literature in various guises and under different equivalent interpretations, e.g., kernel…”
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 ”
A Practical and Conceptual Framework for Learning in Control (2010, methodology): “Usually, this means using statistical models that are infinite-dimensional (Wasserman, 2006).”