Covariance-engaged Classification of Sets via Linear Programming

Set classification aims to classify a set of observations as whole, opposed classifying individual separately. To formally understand the unfamiliar concept binary classification, we first investigate optimal decision rule under normal distribution, which utilizes empirical covariance be classified. We show that number in plays critical role bounding Bayes risk. Under this framework, further propose new methods classification. For case where only few parameters model drive difference between two classes, computationally-efficient approach parameter estimation using linear programming, leading Covariance-engaged LInear Programming (CLIPS) classifier. Its theoretical properties are investigated for both independent and various (short-range long-range dependent) time series structures among within each set. The convergence rates errors risk CLIPS classifier established having multiple leads faster rates, compared standard situation there is one observation applicable domains performs better than competitors highlighted comprehensive simulation study. Finally, illustrate usefulness proposed real image data histopathology.