abstract:
Learning patterns in data requires to extract interesting, statistically significant regularities in (large) data sets,
e.g. detection of cancer cells in tissue microarrays and estimating
their staining or role mining in security permission
management. Admissible solutions or hypotheses specify the context of
pattern analysis problems which have to cope with model mismatch and
noise in data. An information theoretic approach is developed which
estimates the precision of inferred solution sets and regularizes
solutions in a noise adapted way. The tradeoff between
'informativeness' and 'robustness' is mirrored by the balance between
high information content and identifiability of solution sets, thereby
giving rise to a new notion of context sensitive information. Cost
function to rank solutions and, more abstractly, algorithms are
considered as noisy channels with an approximation capacity. The
effectiveness of this concept is demonstrated by model validation for
spectral clustering based on different variants of graph cuts. The
concept also enables us to measure how many bit are extracted by
sorting algorithms when the input and thereby the pairwise comparisons
are subject to fluctuations. |