In a meeting with Paul and me, Angie proposed an idea that she described as allowing us to be “cleverly brute force.”
I like that. In statistics we want everything to be brute force. Statistics is the science of defaults. A clever solution is a kind of cheat, and if we have a clever solution we want to figure out how it works, so we can make it brute force.
But . . . we can use cleverness to come up with a brute force solution. Hence, cleverly brute force.
Monte Carlo methods are all brute force, by definition. But the cleverness in the sampling method makes a lot of brute force effort come to answers in an acceptable period of time. Does a clever sampling method in a Monte Carlo problem count as cleverness or brute force?
Your use of the term “brute force” seems odd.
A brute force algorithm for determining a password, for example, is one that tries every possible combination of characters with equal weight. A clever approach would be to use information about the password’s creator, like DOB, pet’s name, etc., to predict combinations most likely to work. The latter strategy is clearly more akin to a statistical model.
Perhaps you mean “bespoke” and “systematic” rather than “clever” and “brute force”? Or maybe something key to the context is missing from your post?
Michael:
An example of a cleverly brute force solution is HMC/NUTS for Bayesian inference. HMC and NUTS are super-clever, but throwing them at a statistical problem is brute force. The cleverness enables the brute force to work.
Hm, are you using a highly technical version of the term that, as a non-Bayesian, non-Stan user, I don’t know? When you say, “In statistics we want everything to be brute force,” perhaps you mean something like “In Bayesian statistics, we want sampling algorithms to be what Stan users call ‘brute force'”? Outside of that (admittedly foreign) context, the only example I can think of in statistics where we prefer a brute force approach (when possible) is permutation statistics, which “brute forces” the probability rather than estimating it.
Okay, did some googling, looks like a brute force sampling algorithm is one that draws samples based on their being more probable. Or something. As Gilda Radner might say, Never mind!
I see “brute force” being used to refer not to the amount of force but to the care with which it is applied.
A normal approximation to a sampling distribution is typically “brute force” because even though it may not require much computational or mathematical effort, that effort is applied “brutishly”. It’s like how “just jiggle it” or “turn it off and turn it back on” are often pretty good solutions to many problems and don’t require any understanding of how or why they are appropriate.
Michael:
Taking a little measurement-error regression problem and throwing it into Stan is brute force; it’s nuking it, the equivalent to driving a Hummer to the corner store to pick up a quart of milk.
The phrase “cleverly brute force” was motivated by the quote “It appears to be a general principle that, whenever there is a randomized way of doing something, then there is a nonrandomized way that delivers better performance but requires more thought. – E.T.Jaynes.”
Think of PageRank and Monte Carlo sampling – they use randomness to handle uncertainty. Jaynes suggests we can do better with non-random solutions, if we think harder. The key question: is randomness just a stepping stone, or sometimes the best tool we have?
While random methods are like Swiss Army knives – working well enough broadly – we often discover non-random solutions that excel in restricted contexts. Challenge for researchers is to understand why these work and how far they extend. Though randomness might be optimal globally, finding the right problem restrictions often reveals better deterministic approaches.
The art lies in identifying meaningful restrictions of the problem space where patterns become computationally reducible. This allows systematic solutions to emerge from what would otherwise be computational chaos — what Wolfram might call “pockets of computational reducibility” in https://writings.stephenwolfram.com/2024/05/why-does-biological-evolution-work-a-minimal-model-for-biological-evolution-and-other-adaptive-processes/