# Convolutional Analysis Operator Learning: Dependence on Training Data

## TL;DR

This paper investigates how the size of training data affects the quality of learned filters in convolutional analysis operator learning, providing theoretical bounds and empirical insights.

## Contribution

It offers the first deterministic and probabilistic bounds on filter errors in CAOL, linking dataset size to learning accuracy.

## Key findings

- Error bounds improve with more training data
- Empirical data supports theoretical bounds
- Using larger datasets benefits CAOL performance

## Abstract

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.