  Convolutional analysis operator learning (CAOL) enables the unsupervised
training of (hierarchical) convolutional sparsifying operators or autoencoders
from large datasets. One can use many training images for CAOL, but a precise
understanding of the impact of doing so has remained an open question. This
paper presents a series of results that lend insight into the impact of dataset
size on the filter update in CAOL. The first result is a general deterministic
bound on errors in the estimated filters, and is followed by a bound on the
expected errors as the number of training samples increases. The second result
provides a high probability analogue. The bounds depend on properties of the
training data, and we investigate their empirical values with real data. Taken
together, these results provide evidence for the potential benefit of using
more training data in CAOL.
