Term	Definition
$x$	The “input” which we can predict with.
$y$	The “output” which we want to predict.
$\left(x,y\right)$	An “example” or “sample” which is an <input,output> pair
$S$	A set of samples.
$m$	The number of samples.
$m_{\text{test}}$	The number of samples in the testing set.
$m_{\text{train}}$	The number of samples in the training set.
$h$	A hypothesis = a function from $x$ to $y$
$D$	An (unknown) distribution over $\left(x,y\right)$ pairs.
$\text{Bin}\left(m,k,p\right)$	The probability that a Binomial with $m$ coins and bias $p$ has $k$ or fewer heads.
$\bar{e}\left(m,k,\delta \right)$	An upper bound on $\text{Bin}\left(m,k,p\right)$.
$p\left(h\right)$	A distribution over hypotheses not dependent on the training set.
$q\left(h\right)$	A distribution over hypotheses dependent on the training set.
${\widehat{e}}_S\left(h\right)$	Error rate on the sample set $S$
$e_D\left(h\right)$	${Pr}_{\left(x,y\right)\sim D}\left(h\left(x\right)\ne y\right)$ = true error rate = future error rate
${\widehat{e}}_{\text{test}}\left(h\right)$	Error rate on a test set
$\delta$	The probability that a bound fails. Typically small.