All of Nonparametric Statistics

By Stergios B. Fotopoulos. 2007

1,121 citations recorded by the source corpus.

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In Statistics and Probability

Citations in the corpus

Scaling Laws for Neural Language Models (2020, neutral): “Power-law scalings with model and dataset size in density estimation [Was06] and in random forest models [Bia12] may be connected with our results.”
A Neural Scaling Law from the Dimension of the Data Manifold (2020, methodology): “The theory of scaling we have advocated applies basic, ‘textbook’ [Was06] ideas from regression and density estimation.”
Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “In some applications such as testing for homogeneity from finite samples, representing the distribution P by µP bypasses an intermediate density estimation, which is known to be difficult in the high- 7 dimensional setting (Wasserman 2006; Section 6.5).”
Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential Families (2015, methodology): “More importantly, the method has been empirically observed to be relatively robust to increasing dimensionality – in sharp contrast to classical kernel density estimation [15, Sec.”
Kernel Mean Shrinkage Estimators (2014, background): “Thus, the algorithms become less susceptible to the curse of dimensionality (see, e.g. , Wasserman (2006, Section 6.5) and Sriperumbudur et al. (2012)).”
Density Estimation in Infinite Dimensional Exponential Families (2013, background): “This approach ignores the structure of P , however, and is known to perform poorly for moderate to large d [42, Section 6.5] (see also Section 6 of this paper).”
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.”
Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks (2017, methodology): “Despite various applications in low-dimensional spaces, unfortunately, these methods are known to be unreliable in high-dimensional space such as image space (Wasserman, 2006; Theis et al., 2015).”
Posterior calibration and exploratory analysis for natural language processing models (2015, methodology): “Since how to estimate conﬁdence bands for nonparametric regression is an unsolved problem (Wasserman, 2006), we resort to a simple method based on the binning.”
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)).”
Sparse Modeling for Image and Vision Processing (2014, neutral): “…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…”
Kernel ridge vs. principal component regression: Minimax bounds and the qualification of regularization operators (2017, methodology): “There is a vast literature on nonparametric regression, along with a huge variety of corresponding methods (e.g., Györfi et al., 2002; Wasserman, 2006).”
Nonparametric regression using deep neural networks with ReLU activation function (2017, methodology): “Various methods exist that allow to estimate the regression function nonparametri-cally, including kernel smoothing, series estimators/wavelets and splines; cf. [15, 50, 51].”
Breaking the Bandwidth Barrier: Geometrical Adaptive Entropy Estimation (2016, background): “samples is missing in the theoretical statistics literature (despite local log-likelihood methods for regression and density estimation being standard textbook fare [29, 14]).”
Converting High-Dimensional Regression to High-Dimensional Conditional Density Estimation (2017, methodology): “Smoothing using orthogonal functions is per se not a new concept [9, 56].”
Statistical guidelines for Apis mellifera research (2013, background): “The advantage of non-parametric statistics is that they do not assume a specific distribution of the data; the disadvantage is that the power (1-ß, see section 1.) is lower compared to their parametric counterparts (Wasserman, 2006), though the differences may not be great.”