cdf

QRNN.cdf(x)

Approximate the posterior CDF for given inputs x.

Propagates the inputs in x forward through the network and approximates the posterior CDF by a piecewise linear function.

The piecewise linear function is given by its values at approximate quantiles $x_{\tau }‘$ for $\tau =\{0.0,{\tau }_1,\dots ,{\tau }_k,1.0\}$ where ${\tau }_k$ are the quantiles to be estimated by the network. The values for $x_{0.0}$ and $x_{1.0}$ are computed using

$$\begin{array}{r}\begin{array}{c}{x}_{0.0}=2.0x_{{\tau }_1}-x_{{\tau }_2}\\ x_{1.0}=2.0x_{{\tau }_k}-x_{{\tau }_{k-1}}\end{array}\end{array}$$

Parameters:

x (np.array) – Array of shape (n, m) containing n inputs for which to predict the conditional quantiles.

Returns:

Tuple (xs, fs) containing the $x$-values in xs and corresponding values of the posterior CDF $F(x)$ in fs.