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Abstract:
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I this talk, I will first introduce componentwise unbiased estimators for estimating covariance matrices in a subgaussian matrix-variate model and prove the concentration of measure bounds in the sense of guaranteeing the restricted eigenvalue conditions to hold on the unbiased estimator for spatial covariance B, when columns of data matrix are sampled with different rates. Equipped with such theory, we further develop multiple regression methods for estimating the inverse of B and show statistical rate of convergence. Our results provide insight for sparse recovery for relationships among entities (samples, locations, items) when features (variables, time points, user ratings) are present in the observed data matrix with heterogeneous rates. Our proof techniques can certainly be extended to other scenarios. We provide simulation evidence illuminating the theoretical predictions.
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