Directional quantile regression in R

Bocek, Pavel; Šiman, Miroslav

doi:10.14736/kyb-2017-3-0480

Cited by 3 publications

(6 citation statements)

References 17 publications

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“…One of the methods that addresses this problem is directional quantile regression (DQR) (Boček and Šiman, 2017;Kong and Mizera, 2012;Paindaveine and Šiman, 2011). The main idea is to estimate conditional quantiles in different directions, where each defines a half-space, and the quantile region is defined as the intersection of all half-spaces.…”

Section: Problem Formulationmentioning

confidence: 99%

“…The next approach, which we refer to as directional quantile regression (DQR) (Boček and Šiman, 2017;Kong and Mizera, 2012;Paindaveine and Šiman, 2011), is not restricted to produce rectangle-shaped quantile regions, in contrast to the naïve approach, and thus can improve the statistical efficiency. However, DQR is also limited as it can only produce convex quantile regions.…”

Section: Directional Quantile Regressionmentioning

confidence: 99%

“…As shown by Boček and Šiman (2017), the conditional quantile regions are closed, convex and nested, i.e., for any x ∈ X , R α1 (x) ⊆ R α2 (x) for α 1 ≥ α 2 . The convexity of the constructed regions is also illustrated in Figure 2.…”

Section: Directional Quantile Regressionmentioning

confidence: 99%

“…Before describing our contribution, we pause to extend the formulation of conditional directional quantiles as defined by Boček and Šiman (2017); Kong and Mizera (2012); Paindaveine and Šiman (2011) beyond linear models. This extension of DQR will be used as a subroutine in our main algorithm.…”

Section: Non-parametric Directional Quantile Regressionmentioning

confidence: 99%

See 3 more Smart Citations

Calibrated Multiple-Output Quantile Regression with Representation Learning

Feldman¹,

Bates²,

Romano³

2021

Preprint

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We develop a method to generate predictive regions that cover a multivariate response variable with a user-specified probability. Our work is composed of two components. First, we use a deep generative model to learn a representation of the response that has a unimodal distribution. Existing multiple-output quantile regression approaches are effective in such cases, so we apply them on the learned representation, and then transform the solution to the original space of the response. This process results in a flexible and informative region that can have an arbitrary shape, a property that existing methods lack. Second, we propose an extension of conformal prediction to the multivariate response setting that modifies any method to return sets with a pre-specified coverage level. The desired coverage is theoretically guaranteed in the finite-sample case for any distribution. Experiments conducted on both real and synthetic data show that our method constructs regions that are significantly smaller (sometimes by a factor of 100) compared to existing techniques.

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Section: Problem Formulationmentioning

confidence: 99%

Section: Directional Quantile Regressionmentioning

confidence: 99%

Section: Directional Quantile Regressionmentioning

confidence: 99%

Section: Non-parametric Directional Quantile Regressionmentioning

confidence: 99%

See 2 more Smart Citations

Calibrated Multiple-Output Quantile Regression with Representation Learning

Feldman¹,

Bates²,

Romano³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…We have reworked them, corrected them, improved them, simplified them, DOI: 10.14736/kyb-2016- annotated them, adjusted them to the latest versions of Octave and MATLAB, supplemented them with illustrative demo examples as well as with the tools for processing their output, and now we describe them and provide them here with a topical tutorial to answer the growing demand of our research community. Furthermore, we have already translated them to R ( [19]); see [2].…”

Section: Introductionmentioning

confidence: 99%

Directional quantile regression in Octave (and MATLAB)

Bocek¹,

Šiman²

2016

Kybernetika

Self Cite

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An application of directional quantiles to economic data with a multivariate response

Kalina¹

2020

Serb J Management

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Quantile regression represents a popular and useful methodology for modeling quantiles of a response variable based on one or more independent variables. Directional quantiles represent an available extension to the linear regression model with a multivariate response. However, we are not aware of any application of directional quantiles to real data in the literature. An illustration of directional quantiles to an economic dataset is presented in this paper, particularly a modeling of a two-dimensional response in the classical Engel's dataset on household consumption from the 19th century. The results reveal the directional quantiles to yield meaningful results. They order individual observations according to their depth, i.e. from the most central to the most outlying. We compare their result with those of a (more standard) outlier detection. On the whole, we perceive directional quantiles as a potentially useful tool for the analysis of data, if accompanied by a thorough analysis by standard tools.

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Directional quantile regression in R

Cited by 3 publications

References 17 publications

Calibrated Multiple-Output Quantile Regression with Representation Learning

Calibrated Multiple-Output Quantile Regression with Representation Learning

Directional quantile regression in Octave (and MATLAB)

An application of directional quantiles to economic data with a multivariate response

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