Minimum-Width Confidence Bands via Constraint Optimization

VCLA hosted a talk by Emilia Oikarinen

ABSTRACT

Confidence intervals are a popular way to visualize and analyze data distributions.

Unlike p-values, they can convey information both about statistical significance as well as effect size. However, only little work exists on applying confidence intervals to multivariate data. In this talk we define confidence intervals for multivariate data, in terms of minimum-width confidence band problem (MWCB), that extend the one-dimensional definition in a natural way and discuss drawbacks of earlier formalizations. Furthermore, we show that the problem of finding multivariate confidence intervals is NP-hard.

The use of constraint optimization has recently proven to be a  successful approach to providing solutions to various NP-hard search and optimization problems in data analysis. Here we extend the use of constraint optimization systems further to the MWCB problem. We present constraint models for the MWCB problem in terms of mixed integer programming and maximum satisfiability, as well as a greedy heuristic approach. Furthermore, we empirically evaluate the scalability of the constraint optimization approaches and solution quality compared to the greedy approach on real-world datasets.

Joint work with Jeremias Berg, Matti Järvisalo, Jussi Korpela, Kai Puolamäki, and Antti Ukkonen.

Emilia Oikarinen, Finnish Institute of Occupational Health