All of Nonparametric Statistics

By Larry A. Wasserman. 2005

516 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability, Evaluation & Benchmarks

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Citations in the corpus

Scaling Laws for Neural Language Models (2020, neutral): “e meaningful even if it occurs after the leveling off. 7 Related Work Power laws can arise from a wide variety of sources [THK18]. Power-law scalings with model and dataset size in density estimation [Was06] and in random forest models [Bia12] may be connected with our results. These models suggest ”
Reconciling modern machine-learning practice and the classical bias–variance trade-off (2018, background): “tures and hence ﬁxed ﬁtting capacity. Richer families of function classes are typically used in the context of non-parametric statistics, where smoothing and regularization are almost always employed [25]. Regularization, of all forms, can both prevent interpolation and change the effective capacity”
Learning Theory for Distribution Regression (2014, positive): “parable Hilbert space valued outputs, in contrast to the real-valued output considered by Po´czos et al. (2013). Third, density estimates in high dimensional spaces suﬀer from slow convergence rates (Wasserman, 2006, Section 6.5). Our approach mitigates this problem, as it works directly on distribu”
Control functionals for Monte Carlo integration (2014, background): “te Eqn. 46 as f(x) = + X1 k=1 b kcos(2ˇkx)(47) for b k= ka k, and the a k’s chosen so that ˚(x) = 0 in Eqn. 46. This leads to a direct connection with non-linear regression using orthogonal bases (Wasserman, 2006, Chap. 8). Note however the non-standard nature our regression problem: In non-linear ”
Kernel Mean Shrinkage Estimators (2014, methodology): “, no intermediate density estimation is required, for example, when testing for homogeneity from ﬁnite samples. Thus, the algorithms become less susceptible to the curse of dimensionality; see, e.g., Wasserman (2006, Section 6.5) and Sriperumbudur et al. (2012). The aforementioned properties make Hi”
Proportion of non‐zero normal means: universal oracle equivalences and uniformly consistent estimators (2008, unknown): “Observe that for any x > 1, ∫ x 0 1 k ∑k k=1(1−cos(ujt))dt = x− 1 k ∑k j=1 sin(ujx) uj ≥ x−1, so max{0≤t≤x}{ 1k ∑k k=1(1− cos(ujt))} ≥ (1− 1x ), and the claim follows directly by letting x→∞.”
Identification of and Correction for Publication Bias (2017, unknown): “(2015), as well as additional trials identified by Welch et al. (2017). They then extract estimates as described in Croke et al.”
How Well Can Generative Adversarial Networks (GAN) Learn Densities: A Nonparametric View (2017, background): “terative optimization approach of solving the minimax problem approximate the optimal solution? Density estimation hasbeen acentral topic in nonparametricstatistics [Nemirovski, 2000, Tsybakov, 2009, Wassermann, 2006]. The minimax optimal rate of convergence has been understood fairly well, for a wi”
Functional additive regression (2015, methodology): “tion 1(A), imposed for the linear FAR theory. It is a common smoothness requirement in nonparametric regression, when the orthogonal basis approach is used, as discussed, for example, in Chapter 8 in [37]. Condition 3(B) is imposed for identiﬁability. 26 Y. FAN, G. M. JAMES AND P. RADCHENKO Conditio”
Transformation Autoregressive Networks (2018, background): “); (15) which is obtained by substituting (2) into (14) with h ias deﬁned in (4). 3. Related Works Nonparametric density estimation has been a well studied problem in statistics and machine learning (Wasserman, 2007). Unfortunately, nonparametric approaches like kernel density estimation suffer grea”