Penalized regression splines in Mixture Density Networks Article Swipe
Quentin Edward Seifert
,
Anton Thielmann
,
Elisabeth Bergherr
,
Benjamin Säfken
,
Jakob Zierk
,
Manfred Rauh
,
Tobias Hepp
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.1515/ijb-2023-0134
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.1515/ijb-2023-0134
Mixture Density Networks (MDN) belong to a class of models that can be applied to data which cannot be sufficiently described by a single distribution since it originates from different components of the main unit and therefore needs to be described by a mixture of densities. In some situations, MDNs may have problems with the proper identification of the latent components. While these identification issues can to some extent be contained by using custom initialization strategies for the network weights, this solution is still less than ideal since it involves subjective opinions. We therefore suggest replacing the hidden layers between the model input and the output parameter vector of MDNs and estimating the respective distributional parameters with penalized cubic regression splines. Results on simulated data from both Gaussian and Gamma mixture distributions motivated by an application to indirect reference interval estimation drastically improved the identification performance with all splines reliably converging to their true parameter values.
Related Topics
Concepts
Initialization
Mathematics
Mixture model
Identification (biology)
Gaussian
Mixture distribution
Regression
Interval (graph theory)
Statistics
Density estimation
Applied mathematics
Computer science
Probability density function
Estimator
Biology
Physics
Botany
Combinatorics
Quantum mechanics
Programming language
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1515/ijb-2023-0134
- OA Status
- gold
- References
- 28
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4411041720
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4411041720Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1515/ijb-2023-0134Digital Object Identifier
- Title
-
Penalized regression splines in Mixture Density NetworksWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2025Year of publication
- Publication date
-
2025-05-01Full publication date if available
- Authors
-
Quentin Edward Seifert, Anton Thielmann, Elisabeth Bergherr, Benjamin Säfken, Jakob Zierk, Manfred Rauh, Tobias HeppList of authors in order
- Landing page
-
https://doi.org/10.1515/ijb-2023-0134Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
- OA URL
-
https://resolver.sub.uni-goettingen.de/purl?gro-2/150206Direct OA link when available
- Concepts
-
Initialization, Mathematics, Mixture model, Identification (biology), Gaussian, Mixture distribution, Regression, Interval (graph theory), Statistics, Density estimation, Applied mathematics, Computer science, Probability density function, Estimator, Biology, Physics, Botany, Combinatorics, Quantum mechanics, Programming languageTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- References (count)
-
28Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4411041720 |
|---|---|
| doi | https://doi.org/10.1515/ijb-2023-0134 |
| ids.doi | https://doi.org/10.1515/ijb-2023-0134 |
| ids.pmid | https://pubmed.ncbi.nlm.nih.gov/40462456 |
| ids.openalex | https://openalex.org/W4411041720 |
| fwci | 0.0 |
| mesh[0].qualifier_ui | |
| mesh[0].descriptor_ui | D015233 |
| mesh[0].is_major_topic | True |
| mesh[0].qualifier_name | |
| mesh[0].descriptor_name | Models, Statistical |
| mesh[1].qualifier_ui | |
| mesh[1].descriptor_ui | D006801 |
| mesh[1].is_major_topic | False |
| mesh[1].qualifier_name | |
| mesh[1].descriptor_name | Humans |
| mesh[2].qualifier_ui | |
| mesh[2].descriptor_ui | D012044 |
| mesh[2].is_major_topic | False |
| mesh[2].qualifier_name | |
| mesh[2].descriptor_name | Regression Analysis |
| mesh[3].qualifier_ui | |
| mesh[3].descriptor_ui | D003198 |
| mesh[3].is_major_topic | False |
| mesh[3].qualifier_name | |
| mesh[3].descriptor_name | Computer Simulation |
| mesh[4].qualifier_ui | |
| mesh[4].descriptor_ui | D016011 |
| mesh[4].is_major_topic | False |
| mesh[4].qualifier_name | |
| mesh[4].descriptor_name | Normal Distribution |
| type | article |
| title | Penalized regression splines in Mixture Density Networks |
| awards[0].id | https://openalex.org/G7081482492 |
| awards[0].funder_id | https://openalex.org/F4320320882 |
| awards[0].display_name | |
| awards[0].funder_award_id | Bayesian Boosting – A new approach to data science |
| awards[0].funder_display_name | Volkswagen Foundation |
| awards[1].id | https://openalex.org/G1482220299 |
| awards[1].funder_id | https://openalex.org/F4320320879 |
| awards[1].display_name | |
| awards[1].funder_award_id | 517012999 |
| awards[1].funder_display_name | Deutsche Forschungsgemeinschaft |
| awards[2].id | https://openalex.org/G7829407014 |
| awards[2].funder_id | https://openalex.org/F4320320879 |
| awards[2].display_name | |
| awards[2].funder_award_id | 450330162 |
| awards[2].funder_display_name | Deutsche Forschungsgemeinschaft |
| biblio.issue | 1 |
| biblio.volume | 21 |
| biblio.last_page | 253 |
| biblio.first_page | 239 |
| topics[0].id | https://openalex.org/T11901 |
| topics[0].field.id | https://openalex.org/fields/17 |
| topics[0].field.display_name | Computer Science |
| topics[0].score | 0.9961000084877014 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/1702 |
| topics[0].subfield.display_name | Artificial Intelligence |
| topics[0].display_name | Bayesian Methods and Mixture Models |
| topics[1].id | https://openalex.org/T10136 |
| topics[1].field.id | https://openalex.org/fields/26 |
| topics[1].field.display_name | Mathematics |
| topics[1].score | 0.9858999848365784 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/2613 |
| topics[1].subfield.display_name | Statistics and Probability |
| topics[1].display_name | Statistical Methods and Inference |
| topics[2].id | https://openalex.org/T11871 |
| topics[2].field.id | https://openalex.org/fields/26 |
| topics[2].field.display_name | Mathematics |
| topics[2].score | 0.9858999848365784 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/2613 |
| topics[2].subfield.display_name | Statistics and Probability |
| topics[2].display_name | Advanced Statistical Methods and Models |
| funders[0].id | https://openalex.org/F4320320879 |
| funders[0].ror | https://ror.org/018mejw64 |
| funders[0].display_name | Deutsche Forschungsgemeinschaft |
| funders[1].id | https://openalex.org/F4320320882 |
| funders[1].ror | https://ror.org/03bsmfz84 |
| funders[1].display_name | Volkswagen Foundation |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| concepts[0].id | https://openalex.org/C114466953 |
| concepts[0].level | 2 |
| concepts[0].score | 0.696880578994751 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q6034165 |
| concepts[0].display_name | Initialization |
| concepts[1].id | https://openalex.org/C33923547 |
| concepts[1].level | 0 |
| concepts[1].score | 0.6352617740631104 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[1].display_name | Mathematics |
| concepts[2].id | https://openalex.org/C61224824 |
| concepts[2].level | 2 |
| concepts[2].score | 0.6215574741363525 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q2260434 |
| concepts[2].display_name | Mixture model |
| concepts[3].id | https://openalex.org/C116834253 |
| concepts[3].level | 2 |
| concepts[3].score | 0.5751725435256958 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q2039217 |
| concepts[3].display_name | Identification (biology) |
| concepts[4].id | https://openalex.org/C163716315 |
| concepts[4].level | 2 |
| concepts[4].score | 0.5057413578033447 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q901177 |
| concepts[4].display_name | Gaussian |
| concepts[5].id | https://openalex.org/C56672385 |
| concepts[5].level | 3 |
| concepts[5].score | 0.5006814002990723 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q17157111 |
| concepts[5].display_name | Mixture distribution |
| concepts[6].id | https://openalex.org/C83546350 |
| concepts[6].level | 2 |
| concepts[6].score | 0.48683232069015503 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q1139051 |
| concepts[6].display_name | Regression |
| concepts[7].id | https://openalex.org/C2778067643 |
| concepts[7].level | 2 |
| concepts[7].score | 0.4517979323863983 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q166507 |
| concepts[7].display_name | Interval (graph theory) |
| concepts[8].id | https://openalex.org/C105795698 |
| concepts[8].level | 1 |
| concepts[8].score | 0.44081056118011475 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q12483 |
| concepts[8].display_name | Statistics |
| concepts[9].id | https://openalex.org/C189508267 |
| concepts[9].level | 3 |
| concepts[9].score | 0.43295592069625854 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q17088227 |
| concepts[9].display_name | Density estimation |
| concepts[10].id | https://openalex.org/C28826006 |
| concepts[10].level | 1 |
| concepts[10].score | 0.4320533275604248 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q33521 |
| concepts[10].display_name | Applied mathematics |
| concepts[11].id | https://openalex.org/C41008148 |
| concepts[11].level | 0 |
| concepts[11].score | 0.349712073802948 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q21198 |
| concepts[11].display_name | Computer science |
| concepts[12].id | https://openalex.org/C197055811 |
| concepts[12].level | 2 |
| concepts[12].score | 0.278286874294281 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q207522 |
| concepts[12].display_name | Probability density function |
| concepts[13].id | https://openalex.org/C185429906 |
| concepts[13].level | 2 |
| concepts[13].score | 0.22527149319648743 |
| concepts[13].wikidata | https://www.wikidata.org/wiki/Q1130160 |
| concepts[13].display_name | Estimator |
| concepts[14].id | https://openalex.org/C86803240 |
| concepts[14].level | 0 |
| concepts[14].score | 0.0 |
| concepts[14].wikidata | https://www.wikidata.org/wiki/Q420 |
| concepts[14].display_name | Biology |
| concepts[15].id | https://openalex.org/C121332964 |
| concepts[15].level | 0 |
| concepts[15].score | 0.0 |
| concepts[15].wikidata | https://www.wikidata.org/wiki/Q413 |
| concepts[15].display_name | Physics |
| concepts[16].id | https://openalex.org/C59822182 |
| concepts[16].level | 1 |
| concepts[16].score | 0.0 |
| concepts[16].wikidata | https://www.wikidata.org/wiki/Q441 |
| concepts[16].display_name | Botany |
| concepts[17].id | https://openalex.org/C114614502 |
| concepts[17].level | 1 |
| concepts[17].score | 0.0 |
| concepts[17].wikidata | https://www.wikidata.org/wiki/Q76592 |
| concepts[17].display_name | Combinatorics |
| concepts[18].id | https://openalex.org/C62520636 |
| concepts[18].level | 1 |
| concepts[18].score | 0.0 |
| concepts[18].wikidata | https://www.wikidata.org/wiki/Q944 |
| concepts[18].display_name | Quantum mechanics |
| concepts[19].id | https://openalex.org/C199360897 |
| concepts[19].level | 1 |
| concepts[19].score | 0.0 |
| concepts[19].wikidata | https://www.wikidata.org/wiki/Q9143 |
| concepts[19].display_name | Programming language |
| keywords[0].id | https://openalex.org/keywords/initialization |
| keywords[0].score | 0.696880578994751 |
| keywords[0].display_name | Initialization |
| keywords[1].id | https://openalex.org/keywords/mathematics |
| keywords[1].score | 0.6352617740631104 |
| keywords[1].display_name | Mathematics |
| keywords[2].id | https://openalex.org/keywords/mixture-model |
| keywords[2].score | 0.6215574741363525 |
| keywords[2].display_name | Mixture model |
| keywords[3].id | https://openalex.org/keywords/identification |
| keywords[3].score | 0.5751725435256958 |
| keywords[3].display_name | Identification (biology) |
| keywords[4].id | https://openalex.org/keywords/gaussian |
| keywords[4].score | 0.5057413578033447 |
| keywords[4].display_name | Gaussian |
| keywords[5].id | https://openalex.org/keywords/mixture-distribution |
| keywords[5].score | 0.5006814002990723 |
| keywords[5].display_name | Mixture distribution |
| keywords[6].id | https://openalex.org/keywords/regression |
| keywords[6].score | 0.48683232069015503 |
| keywords[6].display_name | Regression |
| keywords[7].id | https://openalex.org/keywords/interval |
| keywords[7].score | 0.4517979323863983 |
| keywords[7].display_name | Interval (graph theory) |
| keywords[8].id | https://openalex.org/keywords/statistics |
| keywords[8].score | 0.44081056118011475 |
| keywords[8].display_name | Statistics |
| keywords[9].id | https://openalex.org/keywords/density-estimation |
| keywords[9].score | 0.43295592069625854 |
| keywords[9].display_name | Density estimation |
| keywords[10].id | https://openalex.org/keywords/applied-mathematics |
| keywords[10].score | 0.4320533275604248 |
| keywords[10].display_name | Applied mathematics |
| keywords[11].id | https://openalex.org/keywords/computer-science |
| keywords[11].score | 0.349712073802948 |
| keywords[11].display_name | Computer science |
| keywords[12].id | https://openalex.org/keywords/probability-density-function |
| keywords[12].score | 0.278286874294281 |
| keywords[12].display_name | Probability density function |
| keywords[13].id | https://openalex.org/keywords/estimator |
| keywords[13].score | 0.22527149319648743 |
| keywords[13].display_name | Estimator |
| language | en |
| locations[0].id | doi:10.1515/ijb-2023-0134 |
| locations[0].is_oa | False |
| locations[0].source.id | https://openalex.org/S96961628 |
| locations[0].source.issn | 1557-4679, 2194-573X |
| locations[0].source.type | journal |
| locations[0].source.is_oa | False |
| locations[0].source.issn_l | 1557-4679 |
| locations[0].source.is_core | True |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | The International Journal of Biostatistics |
| locations[0].source.host_organization | https://openalex.org/P4310313990 |
| locations[0].source.host_organization_name | De Gruyter |
| locations[0].source.host_organization_lineage | https://openalex.org/P4310313990 |
| locations[0].source.host_organization_lineage_names | De Gruyter |
| locations[0].license | |
| locations[0].pdf_url | |
| locations[0].version | publishedVersion |
| locations[0].raw_type | journal-article |
| locations[0].license_id | |
| locations[0].is_accepted | True |
| locations[0].is_published | True |
| locations[0].raw_source_name | The International Journal of Biostatistics |
| locations[0].landing_page_url | https://doi.org/10.1515/ijb-2023-0134 |
| locations[1].id | pmid:40462456 |
| locations[1].is_oa | False |
| locations[1].source.id | https://openalex.org/S4306525036 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | False |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | PubMed |
| locations[1].source.host_organization | https://openalex.org/I1299303238 |
| locations[1].source.host_organization_name | National Institutes of Health |
| locations[1].source.host_organization_lineage | https://openalex.org/I1299303238 |
| locations[1].license | |
| locations[1].pdf_url | |
| locations[1].version | publishedVersion |
| locations[1].raw_type | |
| locations[1].license_id | |
| locations[1].is_accepted | True |
| locations[1].is_published | True |
| locations[1].raw_source_name | The international journal of biostatistics |
| locations[1].landing_page_url | https://pubmed.ncbi.nlm.nih.gov/40462456 |
| locations[2].id | pmh:oai:publications.goettingen-research-online.de:2/150206 |
| locations[2].is_oa | True |
| locations[2].source | |
| locations[2].license | other-oa |
| locations[2].pdf_url | |
| locations[2].version | submittedVersion |
| locations[2].raw_type | yes |
| locations[2].license_id | https://openalex.org/licenses/other-oa |
| locations[2].is_accepted | False |
| locations[2].is_published | False |
| locations[2].raw_source_name | |
| locations[2].landing_page_url | https://resolver.sub.uni-goettingen.de/purl?gro-2/150206 |
| indexed_in | crossref, pubmed |
| authorships[0].author.id | https://openalex.org/A5083901528 |
| authorships[0].author.orcid | https://orcid.org/0000-0001-8674-1309 |
| authorships[0].author.display_name | Quentin Edward Seifert |
| authorships[0].countries | DE |
| authorships[0].affiliations[0].institution_ids | https://openalex.org/I74656192 |
| authorships[0].affiliations[0].raw_affiliation_string | Chair of Spatial Data Science and Statistical Learning, University of Göttingen , Göttingen , Germany |
| authorships[0].institutions[0].id | https://openalex.org/I74656192 |
| authorships[0].institutions[0].ror | https://ror.org/01y9bpm73 |
| authorships[0].institutions[0].type | education |
| authorships[0].institutions[0].lineage | https://openalex.org/I74656192 |
| authorships[0].institutions[0].country_code | DE |
| authorships[0].institutions[0].display_name | University of Göttingen |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Quentin Edward Seifert |
| authorships[0].is_corresponding | False |
| authorships[0].raw_affiliation_strings | Chair of Spatial Data Science and Statistical Learning, University of Göttingen , Göttingen , Germany |
| authorships[1].author.id | https://openalex.org/A5063790800 |
| authorships[1].author.orcid | https://orcid.org/0000-0002-6768-8992 |
| authorships[1].author.display_name | Anton Thielmann |
| authorships[1].countries | DE |
| authorships[1].affiliations[0].institution_ids | https://openalex.org/I43980791 |
| authorships[1].affiliations[0].raw_affiliation_string | Chair of Data Science and Applied Statistics, TU Clausthal , Clausthal , Germany |
| authorships[1].institutions[0].id | https://openalex.org/I43980791 |
| authorships[1].institutions[0].ror | https://ror.org/04qb8nc58 |
| authorships[1].institutions[0].type | education |
| authorships[1].institutions[0].lineage | https://openalex.org/I43980791 |
| authorships[1].institutions[0].country_code | DE |
| authorships[1].institutions[0].display_name | Clausthal University of Technology |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Anton Thielmann |
| authorships[1].is_corresponding | False |
| authorships[1].raw_affiliation_strings | Chair of Data Science and Applied Statistics, TU Clausthal , Clausthal , Germany |
| authorships[2].author.id | https://openalex.org/A5043960694 |
| authorships[2].author.orcid | https://orcid.org/0000-0003-3983-9957 |
| authorships[2].author.display_name | Elisabeth Bergherr |
| authorships[2].countries | DE |
| authorships[2].affiliations[0].institution_ids | https://openalex.org/I74656192 |
| authorships[2].affiliations[0].raw_affiliation_string | Chair of Spatial Data Science and Statistical Learning, University of Göttingen , Göttingen , Germany |
| authorships[2].institutions[0].id | https://openalex.org/I74656192 |
| authorships[2].institutions[0].ror | https://ror.org/01y9bpm73 |
| authorships[2].institutions[0].type | education |
| authorships[2].institutions[0].lineage | https://openalex.org/I74656192 |
| authorships[2].institutions[0].country_code | DE |
| authorships[2].institutions[0].display_name | University of Göttingen |
| authorships[2].author_position | middle |
| authorships[2].raw_author_name | Elisabeth Bergherr |
| authorships[2].is_corresponding | False |
| authorships[2].raw_affiliation_strings | Chair of Spatial Data Science and Statistical Learning, University of Göttingen , Göttingen , Germany |
| authorships[3].author.id | https://openalex.org/A5016630281 |
| authorships[3].author.orcid | https://orcid.org/0000-0003-4702-3333 |
| authorships[3].author.display_name | Benjamin Säfken |
| authorships[3].countries | DE |
| authorships[3].affiliations[0].institution_ids | https://openalex.org/I43980791 |
| authorships[3].affiliations[0].raw_affiliation_string | Chair of Data Science and Applied Statistics, TU Clausthal , Clausthal , Germany |
| authorships[3].institutions[0].id | https://openalex.org/I43980791 |
| authorships[3].institutions[0].ror | https://ror.org/04qb8nc58 |
| authorships[3].institutions[0].type | education |
| authorships[3].institutions[0].lineage | https://openalex.org/I43980791 |
| authorships[3].institutions[0].country_code | DE |
| authorships[3].institutions[0].display_name | Clausthal University of Technology |
| authorships[3].author_position | middle |
| authorships[3].raw_author_name | Benjamin Säfken |
| authorships[3].is_corresponding | False |
| authorships[3].raw_affiliation_strings | Chair of Data Science and Applied Statistics, TU Clausthal , Clausthal , Germany |
| authorships[4].author.id | https://openalex.org/A5006902289 |
| authorships[4].author.orcid | https://orcid.org/0000-0002-9054-9544 |
| authorships[4].author.display_name | Jakob Zierk |
| authorships[4].countries | DE |
| authorships[4].affiliations[0].institution_ids | https://openalex.org/I4210088053 |
| authorships[4].affiliations[0].raw_affiliation_string | Department of Paediatrics and Adolescent Medicine , University Hospital Erlangen , Erlangen , Germany |
| authorships[4].institutions[0].id | https://openalex.org/I4210088053 |
| authorships[4].institutions[0].ror | https://ror.org/0030f2a11 |
| authorships[4].institutions[0].type | healthcare |
| authorships[4].institutions[0].lineage | https://openalex.org/I4210088053 |
| authorships[4].institutions[0].country_code | DE |
| authorships[4].institutions[0].display_name | Universitätsklinikum Erlangen |
| authorships[4].author_position | middle |
| authorships[4].raw_author_name | Jakob Zierk |
| authorships[4].is_corresponding | False |
| authorships[4].raw_affiliation_strings | Department of Paediatrics and Adolescent Medicine , University Hospital Erlangen , Erlangen , Germany |
| authorships[5].author.id | https://openalex.org/A5015914687 |
| authorships[5].author.orcid | https://orcid.org/0000-0002-4852-7157 |
| authorships[5].author.display_name | Manfred Rauh |
| authorships[5].countries | DE |
| authorships[5].affiliations[0].institution_ids | https://openalex.org/I4210088053 |
| authorships[5].affiliations[0].raw_affiliation_string | Department of Paediatrics and Adolescent Medicine , University Hospital Erlangen , Erlangen , Germany |
| authorships[5].institutions[0].id | https://openalex.org/I4210088053 |
| authorships[5].institutions[0].ror | https://ror.org/0030f2a11 |
| authorships[5].institutions[0].type | healthcare |
| authorships[5].institutions[0].lineage | https://openalex.org/I4210088053 |
| authorships[5].institutions[0].country_code | DE |
| authorships[5].institutions[0].display_name | Universitätsklinikum Erlangen |
| authorships[5].author_position | middle |
| authorships[5].raw_author_name | Manfred Rauh |
| authorships[5].is_corresponding | False |
| authorships[5].raw_affiliation_strings | Department of Paediatrics and Adolescent Medicine , University Hospital Erlangen , Erlangen , Germany |
| authorships[6].author.id | https://openalex.org/A5022688021 |
| authorships[6].author.orcid | https://orcid.org/0000-0003-3105-8128 |
| authorships[6].author.display_name | Tobias Hepp |
| authorships[6].countries | DE |
| authorships[6].affiliations[0].institution_ids | https://openalex.org/I74656192 |
| authorships[6].affiliations[0].raw_affiliation_string | Chair of Spatial Data Science and Statistical Learning, University of Göttingen , Göttingen , Germany |
| authorships[6].affiliations[1].institution_ids | https://openalex.org/I181369854 |
| authorships[6].affiliations[1].raw_affiliation_string | Department of Medical Informatics, Biometry and Epidemiology , Friedrich-Alexander University Erlangen-Nuremberg , Erlangen , Germany |
| authorships[6].institutions[0].id | https://openalex.org/I181369854 |
| authorships[6].institutions[0].ror | https://ror.org/00f7hpc57 |
| authorships[6].institutions[0].type | education |
| authorships[6].institutions[0].lineage | https://openalex.org/I181369854 |
| authorships[6].institutions[0].country_code | DE |
| authorships[6].institutions[0].display_name | Friedrich-Alexander-Universität Erlangen-Nürnberg |
| authorships[6].institutions[1].id | https://openalex.org/I74656192 |
| authorships[6].institutions[1].ror | https://ror.org/01y9bpm73 |
| authorships[6].institutions[1].type | education |
| authorships[6].institutions[1].lineage | https://openalex.org/I74656192 |
| authorships[6].institutions[1].country_code | DE |
| authorships[6].institutions[1].display_name | University of Göttingen |
| authorships[6].author_position | last |
| authorships[6].raw_author_name | Tobias Hepp |
| authorships[6].is_corresponding | False |
| authorships[6].raw_affiliation_strings | Chair of Spatial Data Science and Statistical Learning, University of Göttingen , Göttingen , Germany, Department of Medical Informatics, Biometry and Epidemiology , Friedrich-Alexander University Erlangen-Nuremberg , Erlangen , Germany |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://resolver.sub.uni-goettingen.de/purl?gro-2/150206 |
| open_access.oa_status | gold |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Penalized regression splines in Mixture Density Networks |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-12-13T23:11:00.310470 |
| primary_topic.id | https://openalex.org/T11901 |
| primary_topic.field.id | https://openalex.org/fields/17 |
| primary_topic.field.display_name | Computer Science |
| primary_topic.score | 0.9961000084877014 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/1702 |
| primary_topic.subfield.display_name | Artificial Intelligence |
| primary_topic.display_name | Bayesian Methods and Mixture Models |
| related_works | https://openalex.org/W2198732287, https://openalex.org/W4287816759, https://openalex.org/W2044981176, https://openalex.org/W2598185551, https://openalex.org/W2919740138, https://openalex.org/W2017090935, https://openalex.org/W2116212858, https://openalex.org/W2032556230, https://openalex.org/W2372918136, https://openalex.org/W2889431959 |
| cited_by_count | 0 |
| locations_count | 3 |
| best_oa_location.id | pmh:oai:publications.goettingen-research-online.de:2/150206 |
| best_oa_location.is_oa | True |
| best_oa_location.source | |
| best_oa_location.license | other-oa |
| best_oa_location.pdf_url | |
| best_oa_location.version | submittedVersion |
| best_oa_location.raw_type | yes |
| best_oa_location.license_id | https://openalex.org/licenses/other-oa |
| best_oa_location.is_accepted | False |
| best_oa_location.is_published | False |
| best_oa_location.raw_source_name | |
| best_oa_location.landing_page_url | https://resolver.sub.uni-goettingen.de/purl?gro-2/150206 |
| primary_location.id | doi:10.1515/ijb-2023-0134 |
| primary_location.is_oa | False |
| primary_location.source.id | https://openalex.org/S96961628 |
| primary_location.source.issn | 1557-4679, 2194-573X |
| primary_location.source.type | journal |
| primary_location.source.is_oa | False |
| primary_location.source.issn_l | 1557-4679 |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | The International Journal of Biostatistics |
| primary_location.source.host_organization | https://openalex.org/P4310313990 |
| primary_location.source.host_organization_name | De Gruyter |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310313990 |
| primary_location.source.host_organization_lineage_names | De Gruyter |
| primary_location.license | |
| primary_location.pdf_url | |
| primary_location.version | publishedVersion |
| primary_location.raw_type | journal-article |
| primary_location.license_id | |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | The International Journal of Biostatistics |
| primary_location.landing_page_url | https://doi.org/10.1515/ijb-2023-0134 |
| publication_date | 2025-05-01 |
| publication_year | 2025 |
| referenced_works | https://openalex.org/W2124186730, https://openalex.org/W2119063824, https://openalex.org/W4288705518, https://openalex.org/W6634817459, https://openalex.org/W2154065358, https://openalex.org/W2016548223, https://openalex.org/W2090268867, https://openalex.org/W3022120663, https://openalex.org/W2553595002, https://openalex.org/W4313446488, https://openalex.org/W2142899013, https://openalex.org/W4306702035, https://openalex.org/W2526050071, https://openalex.org/W2163605009, https://openalex.org/W2950642167, https://openalex.org/W1990420052, https://openalex.org/W2140308441, https://openalex.org/W3013713234, https://openalex.org/W6678400365, https://openalex.org/W4231665431, https://openalex.org/W3112717819, https://openalex.org/W6991341863, https://openalex.org/W4229930971, https://openalex.org/W1968578768, https://openalex.org/W4239041730, https://openalex.org/W1965179593, https://openalex.org/W4241468802, https://openalex.org/W3103713301 |
| referenced_works_count | 28 |
| abstract_inverted_index.a | 7, 23, 43 |
| abstract_inverted_index.In | 47 |
| abstract_inverted_index.We | 93 |
| abstract_inverted_index.an | 135 |
| abstract_inverted_index.be | 13, 19, 40, 70 |
| abstract_inverted_index.by | 22, 42, 72, 134 |
| abstract_inverted_index.is | 83 |
| abstract_inverted_index.it | 27, 89 |
| abstract_inverted_index.of | 9, 32, 45, 58, 109 |
| abstract_inverted_index.on | 123 |
| abstract_inverted_index.to | 6, 15, 39, 67, 137, 152 |
| abstract_inverted_index.all | 148 |
| abstract_inverted_index.and | 36, 104, 111, 129 |
| abstract_inverted_index.can | 12, 66 |
| abstract_inverted_index.for | 77 |
| abstract_inverted_index.may | 51 |
| abstract_inverted_index.the | 33, 55, 59, 78, 97, 101, 105, 113, 144 |
| abstract_inverted_index.MDNs | 50, 110 |
| abstract_inverted_index.both | 127 |
| abstract_inverted_index.data | 16, 125 |
| abstract_inverted_index.from | 29, 126 |
| abstract_inverted_index.have | 52 |
| abstract_inverted_index.less | 85 |
| abstract_inverted_index.main | 34 |
| abstract_inverted_index.some | 48, 68 |
| abstract_inverted_index.than | 86 |
| abstract_inverted_index.that | 11 |
| abstract_inverted_index.this | 81 |
| abstract_inverted_index.true | 154 |
| abstract_inverted_index.unit | 35 |
| abstract_inverted_index.with | 54, 117, 147 |
| abstract_inverted_index.(MDN) | 4 |
| abstract_inverted_index.Gamma | 130 |
| abstract_inverted_index.While | 62 |
| abstract_inverted_index.class | 8 |
| abstract_inverted_index.cubic | 119 |
| abstract_inverted_index.ideal | 87 |
| abstract_inverted_index.input | 103 |
| abstract_inverted_index.model | 102 |
| abstract_inverted_index.needs | 38 |
| abstract_inverted_index.since | 26, 88 |
| abstract_inverted_index.still | 84 |
| abstract_inverted_index.their | 153 |
| abstract_inverted_index.these | 63 |
| abstract_inverted_index.using | 73 |
| abstract_inverted_index.which | 17 |
| abstract_inverted_index.belong | 5 |
| abstract_inverted_index.cannot | 18 |
| abstract_inverted_index.custom | 74 |
| abstract_inverted_index.extent | 69 |
| abstract_inverted_index.hidden | 98 |
| abstract_inverted_index.issues | 65 |
| abstract_inverted_index.latent | 60 |
| abstract_inverted_index.layers | 99 |
| abstract_inverted_index.models | 10 |
| abstract_inverted_index.output | 106 |
| abstract_inverted_index.proper | 56 |
| abstract_inverted_index.single | 24 |
| abstract_inverted_index.vector | 108 |
| abstract_inverted_index.Density | 2 |
| abstract_inverted_index.Mixture | 1 |
| abstract_inverted_index.Results | 122 |
| abstract_inverted_index.applied | 14 |
| abstract_inverted_index.between | 100 |
| abstract_inverted_index.mixture | 44, 131 |
| abstract_inverted_index.network | 79 |
| abstract_inverted_index.splines | 149 |
| abstract_inverted_index.suggest | 95 |
| abstract_inverted_index.values. | 156 |
| abstract_inverted_index.Abstract | 0 |
| abstract_inverted_index.Gaussian | 128 |
| abstract_inverted_index.Networks | 3 |
| abstract_inverted_index.improved | 143 |
| abstract_inverted_index.indirect | 138 |
| abstract_inverted_index.interval | 140 |
| abstract_inverted_index.involves | 90 |
| abstract_inverted_index.problems | 53 |
| abstract_inverted_index.reliably | 150 |
| abstract_inverted_index.solution | 82 |
| abstract_inverted_index.splines. | 121 |
| abstract_inverted_index.weights, | 80 |
| abstract_inverted_index.contained | 71 |
| abstract_inverted_index.described | 21, 41 |
| abstract_inverted_index.different | 30 |
| abstract_inverted_index.motivated | 133 |
| abstract_inverted_index.opinions. | 92 |
| abstract_inverted_index.parameter | 107, 155 |
| abstract_inverted_index.penalized | 118 |
| abstract_inverted_index.reference | 139 |
| abstract_inverted_index.replacing | 96 |
| abstract_inverted_index.simulated | 124 |
| abstract_inverted_index.therefore | 37, 94 |
| abstract_inverted_index.components | 31 |
| abstract_inverted_index.converging | 151 |
| abstract_inverted_index.densities. | 46 |
| abstract_inverted_index.estimating | 112 |
| abstract_inverted_index.estimation | 141 |
| abstract_inverted_index.originates | 28 |
| abstract_inverted_index.parameters | 116 |
| abstract_inverted_index.regression | 120 |
| abstract_inverted_index.respective | 114 |
| abstract_inverted_index.strategies | 76 |
| abstract_inverted_index.subjective | 91 |
| abstract_inverted_index.application | 136 |
| abstract_inverted_index.components. | 61 |
| abstract_inverted_index.drastically | 142 |
| abstract_inverted_index.performance | 146 |
| abstract_inverted_index.situations, | 49 |
| abstract_inverted_index.distribution | 25 |
| abstract_inverted_index.sufficiently | 20 |
| abstract_inverted_index.distributions | 132 |
| abstract_inverted_index.distributional | 115 |
| abstract_inverted_index.identification | 57, 64, 145 |
| abstract_inverted_index.initialization | 75 |
| cited_by_percentile_year | |
| countries_distinct_count | 1 |
| institutions_distinct_count | 7 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/16 |
| sustainable_development_goals[0].score | 0.47999998927116394 |
| sustainable_development_goals[0].display_name | Peace, Justice and strong institutions |
| citation_normalized_percentile.value | 0.08724274 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |