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It's analogous to the problem of induction (Hume). Without assumptions, it's impossible to connect past observations to predictions about the future. Observing
by bonoboTP 3y ago
It's analogous to the problem of induction (Hume). Without assumptions, it's impossible to connect past observations to predictions about the future. Observing that the sun rises a thousand mornings does not automatically make it any more or less likely that it will rise tomorrow, unless we make some assumptions, for example that events tend to be similar over time. And those assumptions can't be extracted from the data. Maybe things tended to be similar over time in the past, but that says nothing about the future. The pattern might break tomorrow and to say that it likely won't, is simply an assumption on a higher level.
But it seems like science is "doing fine" despite this problem. Similarly machine learning chugs along fine, because people use their experience and prior knowledge when designing the algorithms. These assumptions are also called inductive biases. They are biasing the learning towards certain patterns (like "things tend to be similar locally").
- ithinkso 3y agoOne just assumes Occam's razor and you're good to go in a vast majority of cases
- bonoboTP 3y agoIf you formalize Occam's "simplicity" as description length, then that depends on encoding. By assuming an encoding, you implicitly assume a distribution (according to entropy coding, eg Huffman coding) and hence inject an inductive bias. I'm not saying that it's bad to assume one. The point is that it is an assumption. My bigger point is that the no free lunch theorem should only bother you as much as the induction problem bothers you. Which in practice means not at all.