2 research outputs found
On sample complexity for computational pattern recognition
In statistical setting of the pattern recognition problem the number of
examples required to approximate an unknown labelling function is linear in the
VC dimension of the target learning class. In this work we consider the
question whether such bounds exist if we restrict our attention to computable
pattern recognition methods, assuming that the unknown labelling function is
also computable. We find that in this case the number of examples required for
a computable method to approximate the labelling function not only is not
linear, but grows faster (in the VC dimension of the class) than any computable
function. No time or space constraints are put on the predictors or target
functions; the only resource we consider is the training examples.
The task of pattern recognition is considered in conjunction with another
learning problem -- data compression. An impossibility result for the task of
data compression allows us to estimate the sample complexity for pattern
recognition