Hail should support *ordinal regression*. Ordinal regression deals with a dependent variable whose values are finite, discrete and ordered. This differs from a categorical variable where each value can be represented by a binary variable. As I understand it, ordinal regression of a dependent variable `y`

is phrased in two steps: mapping from the independent variable `x`

to a threshold-space, then mapping from threshold-space to the dependent variable `y`

. For example:

\theta = x * w + \varepsilon \\
y = \begin{cases}
y_1 & \theta < \theta_1 \\
y_2 & \theta_1 \leq \theta \lt \theta_2 \\
y_3 & \theta_2 \leq \theta
\end{cases}

The choices of \theta_i and w are fit according to some loss function. I do not fully understand the power of the intermediate threshold space. At the very least, it involves projecting the x vector onto a line which is then partitioned.