BQNet

BQNet.jl is a Julia package for distributional regression using Bernstein quantile networks (BQN). That is,

the conditional distribution is specified by its quantile function and assumed to be a Bernstein polynomial of a certain degree
its distribution parameters, the coefficients of the Bernstein polynomial, are linked to the input variables/covariates by a neural network
the model parameters, the weights and biases of the network, are estimated by optimising a composite quantile loss function.

The package is based on Flux.

Installation

BQNet can be installed by

using Pkg
Pkg.add(url = "https://github.com/jbbremnes/BQNet.jl")

or by entering REPL's package environment by pressing ] and then

add "https://github.com/jbbremnes/BQNet.jl"

In the following examples the BQN is applied to various data

...

Bremnes, J. B. (2020). Ensemble Postprocessing Using Quantile Function Regression Based on Neural Networks and Bernstein Polynomials. Monthly Weather Review 148, 1, 403-414. R code.
Schulz, B. and Lerch, S. (2022). Machine learning methods for postprocessing ensemble forecasts of wind gusts: A systematic comparison. Monthly Weather Review, 150 (1), 235-257. doi:10.1175/MWR-D-21-0150.1
Gneiting, T., Lerch, S. and Schulz, B. (2023). Probabilistic solar forecasting: Benchmarks, post-processing, verification. Solar Energy, 252 (1), 72-80. doi:10.1016/j.solener.2022.12.054
Höhlein, K., B. Schulz, R. Westermann, and S. Lerch (2024). Postprocessing of Ensemble Weather Forecasts Using Permutation-Invariant Neural Networks. Artif. Intell. Earth Syst., 3, doi:10.1175/AIES-D-23-0070.1.