Nonparametric Quantile Estimation

By Ichiro Takeuchi, Quoc V. Le, Timothy D. Sears, Alex Smola. 2006

512 citations recorded by the source corpus.

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Citations in the corpus

Bayesian Learning of Kernel Embeddings (2016, background): “…are unclear (interestingly, it does not appear in the book that is most commonly cited as its source, Sch ¨ olkopf and Smola (2002)) but it may have been derived from Takeuchi et al. (2006) and has pre-cursors in classical work on bandwidth selection for kernel density estimation (Bowman, 1985).”
A Kernel Method for the Two-Sample-Problem (2006, methodology): “omes uniformly constant). We set σto be the median distance between points in the aggregate sample, as a compromise between these two extremes: this remains a heuristic, similar to those described in Takeuchi et al. (2006); Scho¨lkopf (1997), and the optimum choice of kernel size is an ongoing area ”
Quantile regression neural networks: Implementation in R and application to precipitation downscaling (2011, methodology): “In addition to the QRNN, other types of ﬂexible nonlinear regression models have been applied in a quantile regression context, for example quantile regression trees (Chaudhur and Loh, 2002), generalized additive models (Koenker, 2010), and kernel methods (Takeuchi et al., 2006).”
Efficient Benchmarking of Algorithm Configuration Procedures via Model-Based Surrogates (2017, methodology): “Instead, to obtain a general solution, we propose to use quantile regression (Koenker 2005; Takeuchi et al 2006).”
Single-Model Uncertainties for Deep Learning (2018, background): “However, these estimate a separate model per quantile level [77, 86], or require an a-priori finite”
Conditional Density Estimation via Least-Squares Density Ratio Estimation (2010, methodology): “Kernel quantile regression (KQR) allows one to predict the 100τ -percentile of conditional distributions for a given τ (∈ (0, 1)) when y is one-dimensional (Takeuchi et al., 2006; Li et al., 2007).”
Non‐crossing non‐parametric estimates of quantile curves (2008, methodology): “As pointed out by Takeuchi et al. (2006) the method can be modified to avoid quantile crossing, yielding a quadratic optimization procedure.”
Robust Optimization using Machine Learning for Uncertainty Sets (2014, methodology): “It can be shown [Koenker, 2005, Takeuchi et al., 2006] under some regularity conditions that the true conditional quantile function µ τ ( x ) is the minimizer of l τ ( β ) when minimized over all measurable functions.”
Mean Absolute Percentage Error for regression models (2016, methodology): “Then, the kernel quantile optimization problem, treated in [8, 9], is deﬁned by: min where λ > 0 handles the trade-oﬀ between the data ﬁtting term and the regularization term.”
Estimating conditional quantiles with the help of the pinball loss (2011, methodology): “Recall that [12, 20, 26] proposed an SVM that finds a solution fD,λ ∈H of argmin f∈H λ‖f‖(2)H +RL,D(f), (2)”
A Kernel Two-Sample Test (2012, methodology): “We setσ to be the median distance between points in the aggregate sample, as a compromise between these two extremes: this remains a heuristic, similar to those described in Takeuchi et al. (2006) and Scḧolkopf (1997), and the optimum choice of kernel size is an ongoing area of research.”
A scalable modular convex solver for regularized risk minimization (2007, background): “…(but essentially still solve (1)) include Support Vector regression [41], novelty detection [33], Huber’s robust regression, quantile regression [37], ordinal regression [21], ranking [15], maximization of multivariate performance measures [24], structured estimation [38, 40], Gaussian Process…”
Bundle Methods for Regularized Risk Minimization (2010, methodology): “…include Support Vector regression (Vapnik et al., 1997), novelty detection (Schölkopf et al., 2001), Huber’s robust regression, quantile regression (Takeuchi et al., 2006), ordinal regression (Herbrich et al., 2000), rank- Algorithm 5 ParallelBMRM 1: input: ε≥ 0, w0, data setD, number of slave…”
With Malice Towards None: Assessing Uncertainty via Equalized Coverage (2019, unknown): “(Quantile regression algorithms are not supported by finite sample coverage guarantees [32–36].”
On-line quantile regression in the RKHS (Reproducing Kernel Hilbert Space) for operational probabilistic forecasting of wind power (2016, methodology): “obtained by minimising the following regularised cost function evaluated over 16 N samples (xi, yi) (see [24], among others): 17”
Deep Learning-Based Multivariate Probabilistic Forecasting for Short-Term Scheduling in Power Markets (2019, methodology): “…the objective is to directly predict the speciﬁed quantiles q ϵ Q of the target distribution: t + k | y → t (10) In this framework, models are trained to minimize the quantile loss (or pinball loss) since it has been proved in [35] that minimizing this pinball loss E q yields the optimal quantiles.”
Kernel Methods in Finance (2008, methodology): “In a novel application (Christmann, 2005) and subsequently (Takeuchi et al., 2006) used SVMs to estimate these high quantiles.”
The Role of Vegetation in Mitigating Urban Land Surface Temperatures: A Case Study of Munich, Germany during the Warm Season (2015, background): “estimates that approximate the conditional mean of a response variable given certain values for predictor variables, quantile regression aims at estimating either the conditional median or other quantiles of the scale and shape of the distribution of the response variable [29].”