On a Factorisation of Positive Definite Matrices

Majindar, Kulendra N.

doi:10.4153/cmb-1963-035-9

Search citation statements

Order By: Relevance

Paper Sections

Select...

Structured Penalization With the Hpp1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

1965

2017

Publication Types

Select...

Article4

Relationship

Self Cite0

Independent4

Authors

Journals

Cited by 4 publications

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore, since any positive definite matrix can be written as the Hadamard product of two other positive definite matrices (Majindar, 1963;Styan, 1973), Σ u and Σ v can always be chosen to yield a particular value of Cov[β/σ 2 ].…”

Section: Structured Penalization With the Hppmentioning

confidence: 99%

Lasso, fractional norm and structured sparse estimation using a Hadamard product parametrization

Hoff

2017

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

Using a multiplicative reparametrization, I show that a subclass of L q penalties with q ≤ 1 can be expressed as sums of L 2 penalties. It follows that the lasso and other norm-penalized regression estimates may be obtained using a very simple and intuitive alternating ridge regression algorithm. As compared to a similarly intuitive EM algorithm for L q optimization, the proposed algorithm avoids some numerical instability issues and is also competitive in terms of speed. Furthermore, the proposed algorithm can be extended to accommodate sparse highdimensional scenarios, generalized linear models, and can be used to create structured sparsity via penalties derived from covariance models for the parameters. Such model-based penalties may be useful for sparse estimation of spatially or temporally structured parameters.

show abstract

Section: Structured Penalization With the Hppmentioning

confidence: 99%