Statistical regression is algorithm. I think I fail to get the sentiment of this comment though (as someone not in data-oriented profession)

I think it's too late, much like cryptographers lamenting the word "crypto", but I see where they're coming from. I have thought it is unfortunate that the popular conception of "the algorithm" is actually a remarkably bad example of an algorithm. I mean sure it's an algorithm - a computer is executing it - but when I think of an algorithm I think of a well defined sequence of steps solving a discrete problem. Whereas "the algorithm" / machine learning tends to attack a different kind of problem - "squishy" problems like recommendation systems where we don't really know how to explain how we come up with answers as a discrete list of instructions.

Ha! And can we please stop calling curve fitting a "statistical regression"?

A trained model is a set of rules to go from, for example, an image to a tag identifying the object it shows.

That's an algorithm. It is not "statistical regression", even if that is the method that was used in its creation.

The whole its-just-statistics-shtick is what's getting out of hand. People are just mindlessly repeating the point because it seemed smart when it was first made. Hint: it no longer does, especially if you use it wrong.

By that logic, most of mathematics are "algorithms" because they map one space to another. That is absolute nonsense. An algorithm is a sequence of steps, an implementation. A trained model is only an algorithm in the most generous interpretation of the term. You cannot discount the underlying mathematics of it, not matter how unscrutable it may be. A distribution implemented in Python doesn't magically become any less statistical just because it is executed on a CPU.

1. Multiply your input number by 7

2. Add three

3. Square the result

4. Take this result as your final number

There's an algorithm for f(x) = (7x + 3)^2. Similarly, any map from one space to another is an algorithm if it's describable on paper. Every mathematical proof is analogous to an algorithm in important ways. Math is not "equal to" algorithms, in the sense that two different algorithms can describe the same underlying math, but every description of any math essentially has to be an algorithm.

The only parts of math that would not fit would be anything non-constructible, but we know we are limited to exploring and describing only 0% of that world since our descriptions (algorithms) are countably infinite, and there are constructivists who believe non-constructible things don't exist in any meaningful sense. So, yes, most (or all) of the practice of mathematics is algorithms.

Why are we trying to gatekeep this word?

In addition natural numbers are algorithms, in that numbers are functions of no inputs, i.e. 3 is f()=3, similar to random()=[0,1]. And functions are a subset of algorithms.

My word for algorithms that aren't closed-form functions, my life's work, is "repetigrams" because they involve repetition in the form of iteration or recursion.

Math consists of proofs. Every proof corresponds to a computer program, by Curry-Howard Correspondence. Every program is an implementation of an algorithm.

Hence, math consists of things that correspond to implementations of algorithms.

Algorithms Considered Harmful