47 research outputs found
Kronecker Sum Decompositions of Space-Time Data
In this paper we consider the use of the space vs. time Kronecker product
decomposition in the estimation of covariance matrices for spatio-temporal
data. This decomposition imposes lower dimensional structure on the estimated
covariance matrix, thus reducing the number of samples required for estimation.
To allow a smooth tradeoff between the reduction in the number of parameters
(to reduce estimation variance) and the accuracy of the covariance
approximation (affecting estimation bias), we introduce a diagonally loaded
modification of the sum of kronecker products representation [1]. We derive a
Cramer-Rao bound (CRB) on the minimum attainable mean squared predictor
coefficient estimation error for unbiased estimators of Kronecker structured
covariance matrices. We illustrate the accuracy of the diagonally loaded
Kronecker sum decomposition by applying it to video data of human activity.Comment: 5 pages, 8 figures, accepted to CAMSAP 201
Learning Quasi-Kronecker Product Graphical Models
We consider the problem of learning graphical models where the support of the
concentration matrix can be decomposed as a Kronecker product. We propose a
method that uses the Bayesian hierarchical learning modeling approach. Thanks
to the particular structure of the graph, we use a the number of
hyperparameters which is small compared to the number of nodes in the graphical
model. In this way, we avoid overfitting in the estimation of the
hyperparameters. Finally, we test the effectiveness of the proposed method by a
numerical example.Comment: Updated version of the CDC paper (typos have been corrected