  A common assumption in machine learning is that samples are independently and
identically distributed (i.i.d). However, the contributions of different
samples are not identical in training. Some samples are difficult to learn and
some samples are noisy. The unequal contributions of samples has a considerable
effect on training performances. Studies focusing on unequal sample
contributions (e.g., easy, hard, noisy) in learning usually refer to these
contributions as robust machine learning (RML). Weighing and regularization are
two common techniques in RML. Numerous learning algorithms have been proposed
but the strategies for dealing with easy/hard/noisy samples differ or even
contradict with different learning algorithms. For example, some strategies
take the hard samples first, whereas some strategies take easy first.
Conducting a clear comparison for existing RML algorithms in dealing with
different samples is difficult due to lack of a unified theoretical framework
for RML. This study attempts to construct a mathematical foundation for RML
based on the bias-variance trade-off theory. A series of definitions and
properties are presented and proved. Several classical learning algorithms are
also explained and compared. Improvements of existing methods are obtained
based on the comparison. A unified method that combines two classical learning
strategies is proposed.
