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Generalization Error Analysis of Quantized Compressive Learning
Xiaoyun Li · Ping Li

Thu Dec 12 04:15 PM -- 04:20 PM (PST) @ West Ballroom C

Compressive learning is an effective method to deal with very high dimensional datasets by applying learning algorithms in a randomly projected lower dimensional space. In this paper, we consider the learning problem where the projected data is further compressed by scalar quantization, which is called quantized compressive learning. Generalization error bounds are derived for three models: nearest neighbor (NN) classifier, linear classifier and least squares regression. Besides studying finite sample setting, our asymptotic analysis shows that the inner product estimators have deep connection with NN and linear classification problem through the variance of their debiased counterparts. By analyzing the extra error term brought by quantization, our results provide useful implications to the choice of quantizers in applications involving different learning tasks. Empirical study is also conducted to validate our theoretical findings.

Author Information

Xiaoyun Li (Rutgers University)

Xiaoyun Li is a 4th year PhD student from the Department of Statistics at Rutgers University, supervised by Professor Ping Li. His research interests include statistical learning, hashing, randomized algorithms and optimization.

Ping Li (Baidu Research USA)

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