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The necessary and sufficient condition for BLUEs of estimable functions of parameters in a linear fixed effect model being un-altered by a change in error covariance structure is due to Rao [18]. Structural insight into Rao’s condition can be gained by writing the quadratic form that is permitted to be added to the original covariance in block diagonal form. When the original full linear model is made smaller by reducing the number of regressors (which may include interactions of any order), block diagonal or diagonal matrices also provide insight into conditions for the entire set of full, small, and intermediate models each to retain their own BLUEs. The paper outlines the role that such changes in error covariance structure can play in data confidentiality and data encryption, especially when the covariance of the BLUEs is also retained. Extensions to linear mixed models and BLUPs are outlined in principle. ....
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Service recommendation is key to improving users’ online experience. The development of the Internet has accelerated the creation of many services, and whether users can obtain good experiences among the massive number of services mainly depends on the quality of service recommendation. It is commonly believed that deep learning has excellent nonlinear fitting ability in capturing the complex interactions between users and items. The advantage in learning intricacy relationships enables deep learning to become an important technology for present service recommendation. Recently, it is noticed that linear models can perform almost as well as the state-of-the-art deep learning models, suggesting that capturing linear relationships between users and items is also very important for recommender systems. Therefore, numerous deep learning systems combined with linear models have been proposed. However, existing models are incapable of considering the size of the embedding. When the embeddi ....