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TENSOR DECOMPOSITIONS AND SPARSE LOG-LINEAR MODELS.

Publication ,  Journal Article
Johndrow, JE; Bhattacharya, A; Dunson, DB
Published in: Annals of statistics
January 2017

Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. We derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions.

Duke Scholars

Published In

Annals of statistics

DOI

EISSN

2168-8966

ISSN

0090-5364

Publication Date

January 2017

Volume

45

Issue

1

Start / End Page

1 / 38

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1403 Econometrics
  • 0104 Statistics
  • 0102 Applied Mathematics
 

Citation

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Chicago
ICMJE
MLA
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Johndrow, J. E., Bhattacharya, A., & Dunson, D. B. (2017). TENSOR DECOMPOSITIONS AND SPARSE LOG-LINEAR MODELS. Annals of Statistics, 45(1), 1–38. https://doi.org/10.1214/15-aos1414
Johndrow, James E., Anirban Bhattacharya, and David B. Dunson. “TENSOR DECOMPOSITIONS AND SPARSE LOG-LINEAR MODELS.Annals of Statistics 45, no. 1 (January 2017): 1–38. https://doi.org/10.1214/15-aos1414.
Johndrow JE, Bhattacharya A, Dunson DB. TENSOR DECOMPOSITIONS AND SPARSE LOG-LINEAR MODELS. Annals of statistics. 2017 Jan;45(1):1–38.
Johndrow, James E., et al. “TENSOR DECOMPOSITIONS AND SPARSE LOG-LINEAR MODELS.Annals of Statistics, vol. 45, no. 1, Jan. 2017, pp. 1–38. Epmc, doi:10.1214/15-aos1414.
Johndrow JE, Bhattacharya A, Dunson DB. TENSOR DECOMPOSITIONS AND SPARSE LOG-LINEAR MODELS. Annals of statistics. 2017 Jan;45(1):1–38.

Published In

Annals of statistics

DOI

EISSN

2168-8966

ISSN

0090-5364

Publication Date

January 2017

Volume

45

Issue

1

Start / End Page

1 / 38

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1403 Econometrics
  • 0104 Statistics
  • 0102 Applied Mathematics