This package implements the quantile regression neural network (QRNN) (Taylor, 2000; Cannon, 2011; Cannon, 2017), which is a flexible nonlinear form of quantile regression. The goal of quantile regression is to estimate conditional quantiles of a response variable that depend on covariates in some form of regression equation. The QRNN adopts the multi-layer perceptron neural network architecture. The QRNN implementation follows from previous work on the estimation of censored regression quantiles, thus allowing predictions for mixed discrete-continuous variables like precipitation (Friederichs and Hense, 2007). A differentiable approximation to the quantile regression cost function is adopted so that a simplified form of the finite smoothing algorithm (Chen, 2007) can be used to estimate model parameters. This approximation can also be used to force the model to solve a standard least squares regression problem or an expectile regression problem (Cannon, 2017).
An optional monotone constraint can be invoked, which guarantees monotonically
increasing behaviour of model outputs with respect to specified covariates
(Zhang, 1999). The input-hidden layer weight matrix can also be constrained
so that model relationships are strictly additive (see gam.style).
Borrowing strength by using a composite model for multiple regression
quantiles (Zou et al., 2008; Xu et al., 2017) is also possible
(see composite.stack). Applying the monotone constraint in
combination with the composite model allows one to simultaneously estimate
multiple non-crossing quantiles (Cannon, 2017); the resulting monotone composite
QRNN (MCQRNN) is demonstrated in mcqrnn.
QRNN models with a single layer of hidden nodes are trained using the
qrnn.fit function. Predictions from a fitted model are made using
the qrnn.predict function. Note: a single hidden layer
is usually sufficient for most modelling tasks. With added monotonicity
constraints, a second hidden layer may sometimes be beneficial
(Lang, 2005; Minin et al., 2010). QRNN models with two hidden layers are
available using the qrnn2.fit and
qrnn2.predict functions. If models for multiple quantiles
have been fitted, the (experimental) dquantile function and
its companion functions are available to approximate a probability density
function and related distribution functions. The function gam.style
can be used to visualize and investigate fitted covariate/response relationships
(Plate et al., 2000).
| Package: | qrnn |
| Type: | Package |
| License: | GPL-2 |
| LazyLoad: | yes |
Cannon, A.J., 2011. Quantile regression neural networks: implementation in R and application to precipitation downscaling. Computers & Geosciences, 37: 1277-1284. doi:10.1016/j.cageo.2010.07.005
Cannon, A.J., 2017. Non-crossing nonlinear regression quantiles by monotone composite quantile regression neural network, with application to rainfall extremes. EarthArXiv <https://eartharxiv.org/wg7sn>. doi:10.17605/OSF.IO/WG7SN
Chen, C., 2007. A finite smoothing algorithm for quantile regression. Journal of Computational and Graphical Statistics, 16: 136-164.
Friederichs, P. and A. Hense, 2007. Statistical downscaling of extreme precipitation events using censored quantile regression. Monthly Weather Review, 135: 2365-2378.
Lang, B., 2005. Monotonic multi-layer perceptron networks as universal approximators. International Conference on Artificial Neural Networks, Artificial Neural Networks: Formal Models and Their Applications-ICANN 2005, pp. 31-37.
Minin, A., M. Velikova, B. Lang, and H. Daniels, 2010. Comparison of universal approximators incorporating partial monotonicity by structure. Neural Networks, 23(4): 471-475.
Plate, T., J. Bert, J. Grace, and P. Band, 2000. Visualizing the function computed by a feedforward neural network. Neural Computation, 12(6): 1337-1354.
Taylor, J.W., 2000. A quantile regression neural network approach to estimating the conditional density of multiperiod returns. Journal of Forecasting, 19(4): 299-311.
Xu, Q., K. Deng, C. Jiang, F. Sun, and X. Huang, 2017. Composite quantile regression neural network with applications. Expert Systems with Applications, 76, 129-139.
Zhang, H. and Zhang, Z., 1999. Feedforward networks with monotone constraints. In: International Joint Conference on Neural Networks, vol. 3, p. 1820-1823. doi:10.1109/IJCNN.1999.832655
Xu, Q., K. Deng, C. Jiang, F. Sun, and X. Huang, 2017. Composite quantile regression neural network with applications. Expert Systems with Applications, 76, 129-139.
Zou, H. and M. Yuan, 2008. Composite quantile regression and the oracle model selection theory. The Annals of Statistics, 1108-1126.