Deep Continuous Quantile Regression

This package explores different approaches to learning the uncertainty, and, more generally, the conditional distribution of the target variable.

This is particularily importent when

• the mean of the target variable is not sufficient for the use case
• the errors are heteroscedastic, i.e. vary depending on input features
• the errors are skewed, making a single descriptor such as variance inadequate.

We explore two main approches:

1. fitting a mixture density model
2. learning the location of conditional qunatiles, q, of the distribution.

Our mixture density network exploits an implementation trick to achieve negative-log-likelihood minimisation in keras.

Same trick is useed to optimize the "pinball" loss in quantile regression networks.

Within the quantile-based approach, we further explore: a. fitting a separate model to predict each quantile b. fitting a multi-output network to predict multiple quantiles simultaneously c. learning a regression on X and q simultanesously, thus effectively learning the complete (conditional) cumulative density function.

Installation

Install package from source:

pip install git+https://github.com/ig248/deepquantiles

Or from PyPi:

pip install deepquantiles

Content

• deepqunatiles.regressors: implementation of core algorithms
• deepquantiles.presets: a collection of pre-configured estimators and settings used in experiments
• deepquantiles.datasets: functions used for generating test data
• deepquantiles.nb_utils: helper functions used in notebooks
• notebooks: Jupyter notebooks with examples and experiments

Tests

Run

make dev-install
make lint
make test

References