Specifically,becauseaQfunctionis defined with respect toaparticular policy,constructingPˆQ requires selection ofareference policy or distribution over policies.

In this paper,we consider the learning problem where the projected data isfurther compressed byscalarquantization, which iscalled quantized compressivelearning. Generalization error bounds are derived for three models: nearest neighbor (NN) classifier, linear classifier and least squares regression.

Theresults showthat(1)IRLS canhandle alargernumber ofoutliers thanother methods, (2) it is faster than competing methods at the same level of accuracy, (3) it restores a sparsely corrupted face image with satisfactory visual quality.

This paper identifies astructural property of data distributions that enables deep neural networks to learn hierarchically.