Co-author: Oleg Burdakov and Anders Grimvall
Optimization methods for solving isotonic regression problems
In this talk, we present the results of a cooperation between the divisions of statistics and optimization in the area of a special type of non-parametric regression, known as the isotonic regression (IR).
The monotonic dependence is common in practically all types of systems. For instance, the rates of biogeochemical processes can be monotonic functions of factors like temperature and humidity, cancer rates can increase with age and exposure, etc. For such systems, it is an important problem to construct a monotonicity preserving model (or a response function) with a least-distance deviation from the observed responses.
This problem is based on solving the IR problem. We treat it as an
optimization problem, namely, as a quadratic programming problem with a
squared-distance-type objective function and linear monotonicity
preserving constraints. We will present our algorithms which allow us
to solve efficiently IR problems with very large data sets. Numerical
results will be presented for both test and applied problems.
Senast uppdaterad: 2014-10-14