Simultaneous Spline Quantile Regression Under Shape Constraints

Kitahara, Daichi; Ke, Leng; Tezuka, Yuji; Hirabayashi, Akira

doi:10.23919/eusipco47968.2020.9287462

Cited by 3 publications

(4 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the second step, we simultaneously estimate 𝑚 low 𝛼,𝑌 (𝑥) and 𝑚 up 𝛼,𝑌 (𝑥) with spline quantile regression similar to [42]. Specifically, we solve the following optimization problem minimize ¯𝑠, s∈…”

Section: Proposed Modal Interval Regression Methodsmentioning

confidence: 99%

“…In fact, it is very difficult to give a useful necessary and sufficient condition for each shape constraint. Instead, we derive a useful sufficient condition for each shape constraint in a manner similar to [42]. In [42], the second author of the current paper derived sufficient conditions for several shape (non-decreasing, non-increasing, convex and concave) constraints by extending the sufficient condition in [63]- [65] for the nonnegativity of the spline function 𝑠(𝑥) over 𝐼 𝑗 :…”

Section: Convex Optimization Problem On Coefficientsmentioning

confidence: 99%

“…To flexibly express the smooth modal intervals of various shapes, this paper proposes a modal interval regression method using spline regression models similar to [42]. The proposed modal interval regression consists of two steps.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modal Interval Regression Based on Spline Quantile Regression

YAO

Kitahara

Kuroda

et al. 2023

IEICE Trans. Fundamentals

Self Cite

View full text Add to dashboard Cite

The mean, median, and mode are usually calculated from univariate observations as the most basic representative values of a random variable. To measure the spread of the distribution, the standard deviation, interquartile range, and modal interval are also calculated. When we analyze continuous relations between a pair of random variables from bivariate observations, regression analysis is often used. By minimizing appropriate costs evaluating regression errors, we estimate the conditional mean, median, and mode. The conditional standard deviation can be estimated if the bivariate observations are obtained from a Gaussian process. Moreover, the conditional interquartile range can be calculated for various distributions by the quantile regression that estimates any conditional quantile (percentile). Meanwhile, the study of the modal interval regression is relatively new, and spline regression models, known as flexible models having the optimality on the smoothness for bivariate data, are not yet used. In this paper, we propose a modal interval regression method based on spline quantile regression. The proposed method consists of two steps. In the first step, we divide the bivariate observations into bins for one random variable, then detect the modal interval for the other random variable as the lower and upper quantiles in each bin. In the second step, we estimate the conditional modal interval by constructing both lower and upper quantile curves as spline functions. By using the spline quantile regression, the proposed method is widely applicable to various distributions and formulated as a convex optimization problem on the coefficient vectors of the lower and upper spline functions. Extensive experiments, including settings of the bin width, the smoothing parameter and weights in the cost function, show the effectiveness of the proposed modal interval regression in terms of accuracy and visual shape for synthetic data generated from various distributions. Experiments for real-world meteorological data also demonstrate a good performance of the proposed method.

show abstract

Section: Proposed Modal Interval Regression Methodsmentioning

confidence: 99%

Section: Convex Optimization Problem On Coefficientsmentioning

confidence: 99%

See 1 more Smart Citation

Modal Interval Regression Based on Spline Quantile Regression

YAO

Kitahara

Kuroda

et al. 2023

IEICE Trans. Fundamentals

Self Cite

View full text Add to dashboard Cite

show abstract

“…Quantile regression with splines has been investigated by He and Ng (1999). Noncrossing quantile regression has been explored by Kitahara et al (2021) and by Xu and Reich (2021) in a Bayesian setting.…”

Section: Splinesmentioning

confidence: 99%

A review of predictive uncertainty estimation with machine learning

Tyralis,

Papacharalampous

2024

Artif Intell Rev

View full text Add to dashboard Cite

Predictions and forecasts of machine learning models should take the form of probability distributions, aiming to increase the quantity of information communicated to end users. Although applications of probabilistic prediction and forecasting with machine learning models in academia and industry are becoming more frequent, related concepts and methods have not been formalized and structured under a holistic view of the entire field. Here, we review the topic of predictive uncertainty estimation with machine learning algorithms, as well as the related metrics (consistent scoring functions and proper scoring rules) for assessing probabilistic predictions. The review covers a time period spanning from the introduction of early statistical (linear regression and time series models, based on Bayesian statistics or quantile regression) to recent machine learning algorithms (including generalized additive models for location, scale and shape, random forests, boosting and deep learning algorithms) that are more flexible by nature. The review of the progress in the field, expedites our understanding on how to develop new algorithms tailored to users’ needs, since the latest advancements are based on some fundamental concepts applied to more complex algorithms. We conclude by classifying the material and discussing challenges that are becoming a hot topic of research.

show abstract

FPSeq2Q: Fully Parameterized Sequence to Quantile Regression for Net-Load Forecasting With Uncertainty Estimates

Faustine

Pereira²

2022

IEEE Trans. Smart Grid

View full text Add to dashboard Cite

Simultaneous Spline Quantile Regression Under Shape Constraints

Cited by 3 publications

References 35 publications

Modal Interval Regression Based on Spline Quantile Regression

Modal Interval Regression Based on Spline Quantile Regression

A review of predictive uncertainty estimation with machine learning

FPSeq2Q: Fully Parameterized Sequence to Quantile Regression for Net-Load Forecasting With Uncertainty Estimates

Contact Info

Product

Resources

About