Algebraic Sparse Factor Analysis
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912146898550784 |
|---|---|
| author | Drton, Mathias Grosdos, Alexandros Portakal, Irem Sturma, Nils |
| author_facet | Drton, Mathias Grosdos, Alexandros Portakal, Irem Sturma, Nils |
| contents | Factor analysis is a statistical technique that explains correlations among observed random variables with the help of a smaller number of unobserved factors. In traditional full factor analysis, each observed variable is influenced by every factor. However, many applications exhibit interesting sparsity patterns, that is, each observed variable only depends on a subset of the factors. In this paper, we study such sparse factor analysis models from an algebro-geometric perspective. Under mild conditions on the sparsity pattern, we examine the dimension of the set of covariance matrices that corresponds to a given model. Moreover, we study algebraic relations among the covariances in sparse two-factor models. In particular, we identify cases in which a Gröbner basis for these relations can be derived via a 2-delightful term order and join of toric ideals of graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_14762 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Algebraic Sparse Factor Analysis Drton, Mathias Grosdos, Alexandros Portakal, Irem Sturma, Nils Statistics Theory Commutative Algebra 62H25, 62R01, 13F65, 14M25, 14N07 Factor analysis is a statistical technique that explains correlations among observed random variables with the help of a smaller number of unobserved factors. In traditional full factor analysis, each observed variable is influenced by every factor. However, many applications exhibit interesting sparsity patterns, that is, each observed variable only depends on a subset of the factors. In this paper, we study such sparse factor analysis models from an algebro-geometric perspective. Under mild conditions on the sparsity pattern, we examine the dimension of the set of covariance matrices that corresponds to a given model. Moreover, we study algebraic relations among the covariances in sparse two-factor models. In particular, we identify cases in which a Gröbner basis for these relations can be derived via a 2-delightful term order and join of toric ideals of graphs. |
| title | Algebraic Sparse Factor Analysis |
| topic | Statistics Theory Commutative Algebra 62H25, 62R01, 13F65, 14M25, 14N07 |
| url | https://arxiv.org/abs/2312.14762 |