> "What if Bayes' rule was as simple as an if statement?"
As the article clearly showed, this is wishful thinking.
And there's one simple reason why:
- Bayesian inference is generally computationally intractable.
- "If" statements are quite tractable.
Any language in which you could perform Bayesian inference as easily as you perform "if" statements in would result in horrifyingly slow code and become useless.
You are thinking about languages that are targeting a single machine at a time. That's the way Microsoft thinks with their history in client-side software.
The implication of the quote is that Google attempts to implement the seemingly intractable algorithms by running them on huge clusters, and returning the results to a large audience that makes the computation worth it. If your language targets a data center then having a language support Bayesian inference might be useful.
As I pointed out elsewhere in this thread, Quantom computer languages literally do this.
Also, if you want to perform Bayseian inference, then it is equally as difficult computationally whether or not it can be expressed as simple 'if' statements. However, in terms of code simplicity, expressing it as simple if statements is easier.
Even if quantum computers do not exist, a theoretical model of them does exist, so we can discuss them the same way we discuss a turring machine. (Although we might need to clarify which model we are talking about).
However, that is irrelevant because quantum computers do exist. For example, in 2012, researcher's factored the number 21. [1].
However, even the existence of quantum computers is irrelevant, because programming languages designed for them still exist. [2] Not only that, but you can still run programs written in such languages on a classical computer.
Of course, you could also do the type of Bayesian programming in a language designed for that, instead of one designed for Quantom computation.
I think the original quotation simply used it as a rhetorical device to indicate difference in approach at a more abstract level than literally replacing conditionals with Bayes filters.
As the article clearly showed, this is wishful thinking.
And there's one simple reason why:
- Bayesian inference is generally computationally intractable.
- "If" statements are quite tractable.
Any language in which you could perform Bayesian inference as easily as you perform "if" statements in would result in horrifyingly slow code and become useless.