Yanfang Mo

Yanfang Mo, Wei Chen, Sei Zhen Khong et al.

Efficient resource allocation is one of the main driving forces of human civilizations. Of the many existing approaches to resource allocation, matrix completion is one that is frequently applied. In this paper, we investigate a special type of matrix completion problem concerning the class of $(0,1)$-matrices with given row/column sums and certain zeros prespecified. We provide a necessary and sufficient condition under which such a class is nonempty. The condition is stated in the form of the nonnegativity of a structure tensor constructed from the information regarding the given row/column sums and fixed zeros. Moreover, we show that a more general matrix completion problem can be studied in a similar manner, namely that involving the class of nonnegative integer matrices with prescribed row/column sums, predetermined zeros, and different bounds across the rows. To illustrate the utility of our results, we apply them to demand response applications in smart grids. Specifically, we address two adequacy problems in differentiated energy services, namely, the problems of supply/demand matching and minimum purchase profile.

Yanfang Mo, S. Joe Qin

In this paper, we propose a probabilistic reduced-dimensional vector autoregressive (PredVAR) model to extract low-dimensional dynamics from high-dimensional noisy data. The model utilizes an oblique projection to partition the measurement space into a subspace that accommodates the reduced-dimensional dynamics and a complementary static subspace. An optimal oblique decomposition is derived for the best predictability regarding prediction error covariance. Building on this, we develop an iterative PredVAR algorithm using maximum likelihood and the expectation-maximization (EM) framework. This algorithm alternately updates the estimates of the latent dynamics and optimal oblique projection, yielding dynamic latent variables with rank-ordered predictability and an explicit latent VAR model that is consistent with the outer projection model. The superior performance and efficiency of the proposed approach are demonstrated using data sets from a synthesized Lorenz system and an industrial process from Eastman Chemical.