# SPQR: An R Package for Semi-Parametric Density and Quantile Regression

arXiv: https://arxiv.org/abs/2210.14482 · HTML: https://mlsanity.com/paper/2210.14482/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 37 references that are in the map.
- First posted on arXiv 26 Oct 2022.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Visualizing the Effects of Predictor Variables in Black Box Supervised Learning Models](https://mlsanity.com/paper/1612.08468/) (2016)
- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [Bayesian Neural Network Priors Revisited](https://mlsanity.com/paper/2102.06571/) (2021)
- [Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC](https://mlsanity.com/paper/1507.04544/) (2015)
- [A Simple and Effective Model-Based Variable Importance Measure](https://mlsanity.com/paper/1805.04755/) (2018)
- [qgam: Bayesian non-parametric quantile regression modelling in R](https://mlsanity.com/paper/2007.03303/) (2020)
- [Bayesian Non-parametric Quantile Process Regression and Estimation of Marginal Quantile Effects](https://mlsanity.com/paper/2102.11309/) (2021)

## Abstract (arXiv)

We develop an R package SPQR that implements the semi-parametric quantile regression (SPQR) method in Xu and Reich (2021). The method begins by fitting a flexible density regression model using monotonic splines whose weights are modeled as data-dependent functions using artificial neural networks. Subsequently, estimates of conditional density and quantile process can all be obtained. Unlike many approaches to quantile regression that assume a linear model, SPQR allows for virtually any relationship between the covariates and the response distribution including non-linear effects and different effects on different quantile levels. To increase the interpretability and transparency of SPQR, model-agnostic statistics developed by Apley and Zhu (2020) are used to estimate and visualize the covariate effects and their relative importance on the quantile function. In this article, we detail how this framework is implemented in SPQR and illustrate how this package should be used in practice through simulated and real data examples.