  Proposed methods for prediction interval estimation so far focus on cases
where input variables are numerical. In datasets with solely nominal input
variables, we observe records with the exact same input $x^u$, but different
real valued outputs due to the inherent noise in the system. Existing
prediction interval estimation methods do not use representations that can
accurately model such inherent noise in the case of nominal inputs. We propose
a new prediction interval estimation method tailored for this type of data,
which is prevalent in biology and medicine. We call this method Distribution
Adaptive Prediction Interval Estimation given Nominal inputs (DAPIEN) and has
four main phases. First, we select a distribution function that can best
represent the inherent noise of the system for all unique inputs. Then we infer
the parameters $\theta_i$ (e.g. $\theta_i=[mean_i, variance_i]$) of the
selected distribution function for all unique input vectors $x^u_i$ and
generate a new corresponding training set using pairs of $x^u_i, \theta_i$.
III). Then, we train a model to predict $\theta$ given a new $x_u$. Finally, we
calculate the prediction interval for a new sample using the inverse of the
cumulative distribution function once the parameters $\theta$ is predicted by
the trained model. We compared DAPIEN to the commonly used Bootstrap method on
three synthetic datasets. Our results show that DAPIEN provides tighter
prediction intervals while preserving the requested coverage when compared to
Bootstrap. This work can facilitate broader usage of regression methods in
medicine and biology where it is necessary to provide tight prediction
intervals while preserving coverage when input variables are nominal.
