Abstract
We propose a penalized likelihood method to fit the linear discriminant analysis model when the predictor is matrix valued. We simultaneously estimate the means and the precision matrix, which we assume has a Kronecker product decomposition. Our penalties encourage pairs of response category mean matrix estimators to have equal entries and also encourage zeros in the precision matrix estimator. To compute our estimators, we use a blockwise coordinate descent algorithm. To update the optimization variables corresponding to response category mean matrices, we use an alternating minimization algorithm that takes advantage of the Kronecker structure of the precision matrix. We show that our method can outperform relevant competitors in classification, even when our modeling assumptions are violated. We analyze three real datasets to demonstrate our method’s applicability. Supplementary materials, including an R package implementing our method, are available online.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 11-22 |
| Number of pages | 12 |
| Journal | Journal of Computational and Graphical Statistics |
| Volume | 28 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 2 2019 |
Fingerprint
Keywords
- Alternating minimization algorithm
- Classification
- Penalized likelihood
Cite this
A Penalized Likelihood Method for Classification With Matrix-Valued Predictors. / Molstad, Aaron J.; Rothman, Adam J.
In: Journal of Computational and Graphical Statistics, Vol. 28, No. 1, 02.01.2019, p. 11-22.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A Penalized Likelihood Method for Classification With Matrix-Valued Predictors
AU - Molstad, Aaron J.
AU - Rothman, Adam J
PY - 2019/1/2
Y1 - 2019/1/2
N2 - We propose a penalized likelihood method to fit the linear discriminant analysis model when the predictor is matrix valued. We simultaneously estimate the means and the precision matrix, which we assume has a Kronecker product decomposition. Our penalties encourage pairs of response category mean matrix estimators to have equal entries and also encourage zeros in the precision matrix estimator. To compute our estimators, we use a blockwise coordinate descent algorithm. To update the optimization variables corresponding to response category mean matrices, we use an alternating minimization algorithm that takes advantage of the Kronecker structure of the precision matrix. We show that our method can outperform relevant competitors in classification, even when our modeling assumptions are violated. We analyze three real datasets to demonstrate our method’s applicability. Supplementary materials, including an R package implementing our method, are available online.
AB - We propose a penalized likelihood method to fit the linear discriminant analysis model when the predictor is matrix valued. We simultaneously estimate the means and the precision matrix, which we assume has a Kronecker product decomposition. Our penalties encourage pairs of response category mean matrix estimators to have equal entries and also encourage zeros in the precision matrix estimator. To compute our estimators, we use a blockwise coordinate descent algorithm. To update the optimization variables corresponding to response category mean matrices, we use an alternating minimization algorithm that takes advantage of the Kronecker structure of the precision matrix. We show that our method can outperform relevant competitors in classification, even when our modeling assumptions are violated. We analyze three real datasets to demonstrate our method’s applicability. Supplementary materials, including an R package implementing our method, are available online.
KW - Alternating minimization algorithm
KW - Classification
KW - Penalized likelihood
UR - http://www.scopus.com/inward/record.url?scp=85052133610&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85052133610&partnerID=8YFLogxK
U2 - 10.1080/10618600.2018.1476249
DO - 10.1080/10618600.2018.1476249
M3 - Article
VL - 28
SP - 11
EP - 22
JO - Journal of Computational and Graphical Statistics
JF - Journal of Computational and Graphical Statistics
SN - 1061-8600
IS - 1
ER -