eprintid: 29234
rev_number: 17
eprint_status: archive
userid: 5607
dir: disk0/00/02/92/34
datestamp: 2020-12-18 07:33:16
lastmod: 2021-01-19 10:24:06
status_changed: 2020-12-18 07:33:16
type: doctoralThesis
metadata_visibility: show
creators_name: Petersen, Jens
title: Learning Distributions of Functions on a Continuous Time Domain
subjects: ddc-004
subjects: ddc-500
subjects: ddc-530
subjects: ddc-570
subjects: ddc-610
divisions: i-130001
adv_faculty: af-13
cterms_swd: Maschinelles Lernen
cterms_swd: Maschinelles Sehen
cterms_swd: Deep learning
abstract: This work presents several contributions on the topic of learning representations of function spaces, as well as on learning the dynamics of glioma growth as a particular instance thereof. We begin with two preparatory efforts, showing how expert knowledge can be leveraged efficiently in an interactive segmentation context, and presenting a proof of concept for inferring non-deterministic glioma growth patterns purely from data. The remainder of our work builds upon the framework of Neural Processes. We show how these models represent function spaces and discover that they can implicitly decompose the space into different frequency components, not unlike a Fourier transform. In this context we derive an upper bound on the maximum signal frequency Neural Processes can represent and show how to
control the learned representations to only contain certain frequencies. We continue with an improvement of a more recent addition to the Neural Process family called ConvCNP, which we combine with a Gaussian Process to make it non-deterministic and to improve generalization. Finally, we show how to perform segmentation in the Neural Process framework by extending a typical segmentation
architecture with spatio-temporal attention. The resulting model can interpolate complex spatial variations of segmentations over time and, applied to glioma growth, it is able to represent multiple temporally consistent growth trajectories, exhibiting realistic and diverse spatial
growth patterns.
date: 2020
id_scheme: DOI
id_number: 10.11588/heidok.00029234
ppn_swb: 1744104247
own_urn: urn:nbn:de:bsz:16-heidok-292346
date_accepted: 2020-12-09
advisor: HASH(0x561a6294c528)
language: eng
bibsort: PETERSENJELEARNINGDI2020
full_text_status: public
place_of_pub: Heidelberg
citation:   Petersen, Jens  (2020) Learning Distributions of Functions on a Continuous Time Domain.  [Dissertation]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/29234/1/Jens_Petersen-Learning_Distributions_of_Functions_on_a_Continuous_Time_Domain.pdf