A Robust Notion of Simplicity in Machine Learning

In this article, we delve into the concept of complexity in machine learning and statistical learning theory. The author sheds light on how the idea of representational complexity, which was initially introduced by Mitchell (1997), has been further developed and refined over time. We learn that representational complexity is a measure of how simple or complex a hypothesis class is, based on the amount of language needed to describe it.
The author explains that there are two types of complexity: low representational complexity, where small classes of hypotheses are preferred, and robustness to capacity-based reasoning, which means that good generalization still applies even when the class size increases. However, the converse does not hold, as one can select small classes of complex hypotheses, and the same reasoning for good generalization still applies.
The author also touches on the notion of language dependence in measuring representational complexity, as different languages may require different levels of description length to convey the same meaning. The article emphasizes that this concept is crucial in machine learning, particularly in deep learning, where models are designed to be robust and generalize well across various tasks and datasets.
To help illustrate these complex concepts, the author uses engaging metaphors such as "a simplified picture of the approach" and "designing a different language." They also employ analogies like "a small box of crayons" to convey the idea that simple classes of hypotheses have fewer crayons (or parameters), making them easier to describe.
In summary, this article masterfully demystifies complex concepts in machine learning by using everyday language and engaging metaphors. It provides a comprehensive overview of the minimum description length principle, highlighting its importance in robustly measuring complexity for hypothesis classes. By striking a balance between simplicity and thoroughness, the author succinctly captures the essence of the article without oversimplifying it.