Parameter Identifiability of Discrete Bayesian Networks with Hidden Variables
Identifiability of parameters is an essential property for a statistical model to be useful in most settings. However, establishing parameter identifiability for Bayesian networks with hidden variables remains challenging. In the context of finite state spaces, we give algebraic arguments establishi...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2015-09-01
|
| Series: | Journal of Causal Inference |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/jci-2014-0021 |
| _version_ | 1818720506041335808 |
|---|---|
| author | Allman Elizabeth S. Rhodes John A. Stanghellini Elena Valtorta Marco |
| author_facet | Allman Elizabeth S. Rhodes John A. Stanghellini Elena Valtorta Marco |
| author_sort | Allman Elizabeth S. |
| collection | DOAJ |
| description | Identifiability of parameters is an essential property for a statistical model to be useful in most settings. However, establishing parameter identifiability for Bayesian networks with hidden variables remains challenging. In the context of finite state spaces, we give algebraic arguments establishing identifiability of some special models on small directed acyclic graphs (DAGs). We also establish that, for fixed state spaces, generic identifiability of parameters depends only on the Markov equivalence class of the DAG. To illustrate the use of these results, we investigate identifiability for all binary Bayesian networks with up to five variables, one of which is hidden and parental to all observable ones. Surprisingly, some of these models have parameterizations that are generically 4-to-one, and not 2-to-one as label swapping of the hidden states would suggest. This leads to interesting conflict in interpreting causal effects. |
| first_indexed | 2024-12-17T20:23:55Z |
| format | Article |
| id | doaj.art-679237fdea7b4d0abf7866d4f7fcc43d |
| institution | Directory Open Access Journal |
| issn | 2193-3677 2193-3685 |
| language | English |
| last_indexed | 2024-12-17T20:23:55Z |
| publishDate | 2015-09-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Journal of Causal Inference |
| spelling | doaj.art-679237fdea7b4d0abf7866d4f7fcc43d2022-12-21T21:33:51ZengDe GruyterJournal of Causal Inference2193-36772193-36852015-09-013218920510.1515/jci-2014-0021Parameter Identifiability of Discrete Bayesian Networks with Hidden VariablesAllman Elizabeth S.0Rhodes John A.1Stanghellini Elena2Valtorta Marco3Department of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, AK, USADepartment of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, AK, USADipartimento di Economia Finanza e Statistica, Universita di Perugia, Perugia, ItalyDepartment of Computer Science and Engineering, University of South Carolina, Columbia, SC, USAIdentifiability of parameters is an essential property for a statistical model to be useful in most settings. However, establishing parameter identifiability for Bayesian networks with hidden variables remains challenging. In the context of finite state spaces, we give algebraic arguments establishing identifiability of some special models on small directed acyclic graphs (DAGs). We also establish that, for fixed state spaces, generic identifiability of parameters depends only on the Markov equivalence class of the DAG. To illustrate the use of these results, we investigate identifiability for all binary Bayesian networks with up to five variables, one of which is hidden and parental to all observable ones. Surprisingly, some of these models have parameterizations that are generically 4-to-one, and not 2-to-one as label swapping of the hidden states would suggest. This leads to interesting conflict in interpreting causal effects.https://doi.org/10.1515/jci-2014-0021parameter identifiabilitydiscrete bayesian networkhidden variables |
| spellingShingle | Allman Elizabeth S. Rhodes John A. Stanghellini Elena Valtorta Marco Parameter Identifiability of Discrete Bayesian Networks with Hidden Variables Journal of Causal Inference parameter identifiability discrete bayesian network hidden variables |
| title | Parameter Identifiability of Discrete Bayesian Networks with Hidden Variables |
| title_full | Parameter Identifiability of Discrete Bayesian Networks with Hidden Variables |
| title_fullStr | Parameter Identifiability of Discrete Bayesian Networks with Hidden Variables |
| title_full_unstemmed | Parameter Identifiability of Discrete Bayesian Networks with Hidden Variables |
| title_short | Parameter Identifiability of Discrete Bayesian Networks with Hidden Variables |
| title_sort | parameter identifiability of discrete bayesian networks with hidden variables |
| topic | parameter identifiability discrete bayesian network hidden variables |
| url | https://doi.org/10.1515/jci-2014-0021 |
| work_keys_str_mv | AT allmanelizabeths parameteridentifiabilityofdiscretebayesiannetworkswithhiddenvariables AT rhodesjohna parameteridentifiabilityofdiscretebayesiannetworkswithhiddenvariables AT stanghellinielena parameteridentifiabilityofdiscretebayesiannetworkswithhiddenvariables AT valtortamarco parameteridentifiabilityofdiscretebayesiannetworkswithhiddenvariables |