Measuring with no tape

Project Manager: Søren Hauberg
PhD students in the project: Martin Jørgensen, Nicki Skafte Detlefsen
Funding: These concepts are funded by both the Villum Foundation and the European Research Council
Duration: 23.01.2017-01.12.2022

Society generates increasing amounts of data, which is both a resource and a challenge. The data reveal new insights that may potentially improve our livelihood, but their quantity renders such insights difficult to find. Machine learning techniques sift through the data looking for statistical patterns of interest to a given task. Due to an exponential growth in available data, these techniques enable us to automate difficult decisions, such as those needed for personalized medicine and self-driving cars.

This project note that machine learning techniques depend on a distance measure to determine which data points are similar and which are not. As this measure is difficult to choose, we develop methods for estimating an optimal distance measure directly from data. Empirical evidence suggest that the optimal distance measure in one region of data space need not coincide with the optimal measure in another region, i.e. that the distance measure should locally adapt to the data. We investigate mathematical descriptions of locally adaptive distance functions and derive algorithms for Bayesian modeling in spaces with locally adaptive distance functions.

The geometric nature of the developed methods ensure that attained models are interpretable by humans, which contrast current locally adaptive techniques. As society automate more decisions, interpretability is increasing important to ensure that the machine learning system can be trusted.


Søren Hauberg
DTU Compute
+45 45 25 38 99