noise and simplicity are opposites (information entropy), thus if we dislike noise we should like simplicity. Does this seem like a reasonable perspective?
Not quite. Noise and simplicity are not opposites. I would say that the amount of noise in the data (along with the amount of data) imposes a limit, an upper bound, on the complexity that you can credibly detect.
Basically, if your data is noisy you are forced to consider only low-complexity models.
Can you elaborate on why you think it's a boundary, not an opposite? I still feel like it's an opposite. My impression, from self-study, is that randomness in information means the best way to describe eg a sequence of coin flips is to copy the sequence exactly, there is no algorithm or heuristic that allows you to describe the random information more efficiently, like "all heads" or "heads, tails, heads, tails, etc." That sort of efficient description of information seems identical to simplicity to me. If randomness is defined as the a...
This essay claims to refute a popularized understanding of Occam's Razor that I myself adhere to. It is confusing me, since I hold this belief at a very deep level that it's difficult for me to examine. Does anyone see any problems in its argument, or does it seem compelling? I specifically feel as though it might be summarizing the relevant Machine Learning research badly, but I'm not very familiar with the field. It also might be failing to give any credit to simplicity as a general heuristic when simplicity succeeds in a specific field, and it's unclear whether such credit would be justified. Finally, my intuition is that situations in nature where there is a steady bias towards growing complexity are more common than the author claims, and that such tendencies are stronger for longer. However, for all of this, I have no clear evidence to back up the ideas in my head, just vague notions that are difficult to examine. I'd appreciate someone else's perspective on this, as mine seems to be distorted.
Essay: http://bruce.edmonds.name/sinti/