Everybody who remembers how neural nets were going to save the world, raise your hands. Little higher. Make sure everybody sees.
Well, you were wrong, weren’t you. They’ve all but disappeared from cocktail party discussions. Turns out machine learning algorithms didn’t triumph, either.
Yet something has to come up on top. What will reign supreme? Topological data analysis, baby! Or so says the folks interviewed by Wired in their article “Scientific Data Has Become So Complex, We Have to Invent New Math to Deal With It.” Story of some guys who say we’re in the midst of the “big data equivalent of a Newtonian revolution, on par with the 17th century invention of calculus.”
But before we wax eloquently about our newest warrior against uncertainty, let’s cast our minds back to the 1990s, when we regularly came across things items like this.
Neural nets are universal function approximators! Any function you can think of, and even those you can’t, can be tossed in the trash. Who needs ’em? Just think. Some function out there explains the data you have, and since this function is probably too complicated to discover mathematically, all we have to do is feed these brain-like creatures the data and they’ll figure out the function for you.
The more data you give them, the more they learn. Pictures of brains, pictures of synapses, pictures of naked interwoven dendrites! It was so sexy.
Well, as said, we know how that turned out. The cycle has since been repeated with other Holy Grail methods, though it has never reached the same peak as neural nets.
You have to hand it to the computer algorithms set. They have the best marketing team in science. Who wants to “estimate” the “parameter” of a non-linear regression when you can “input” data into a “thinking” machine? Why not embrace fuzzy logic, which is hip and cool, and eschew dull probability? Hey, all these things are equivalent, but nobody will notice.
Or maybe they will. Don’t forget to read the Machine Learning, Big Data, Deep Learning, Data Mining, Statistics, Decision & Risk Analysis, Probability, Fuzzy Logic FAQ.
Back to topological data analysis. Idea is to take enormous data sets and twist and turn them as you would donuts into coffee cups (let him would readeth understand) and store only the pattern and not the details (dimension reduction). I like this approach, and surely there will be plenty of neat and nifty tricks discovered (see the article for some fun ones).
It’s not a new idea. Remember “grand tours” of data? These were big about fifteen years ago. Cute graphics routines which let you pick off a few dimensions at a time and spin them round and round until you saw (if there was anything to see) how a “random” scatter of points collapsed to something predictable looking.
Slick stuff, and useful. Wired gives the example of the Netflix prize, where the idea was to find algorithms that made better preference guesses because “even an incremental improvement in the predictive algorithm results in a substantial boost to the companyâ€™s bottom line.” And, lo, some group won with an algorithm that did find an incremental improvement.
That’s our lesson: incremental. Human behavior is so complicated that it’s doubtful—I’d even say almost certain—that no Hari Seldon will ever exist. No human being, or machine created by one, is going to discover an equation or set of equations which predict behavior at finer than the grossest levels and for time spans greater than (let us call them) moments.
The boost was incremental. Meaning it was a tweak and significant uncertainty remained. That’s what the neural net folks never figured on. Even if we knew (100% certainty) what the weights were between “synapses”, it did not mean, and it was not true, that we knew with certainty the thing modeled.
Statisticians forget this, too. Equivalently, even if we knew (100% certainty) the values of the parameters in some model, it does not mean, and it is not true, that we know with certainty the thing modeled. This is why I argue endlessly for a return to focus on the things themselves we’re modeling, and away from parameters.
That’s another reason to like machine “learning” and this new-ish idea of topographical data analysis. The focus is on the right thing.
A reader sent me this article, but I can’t recall who and I have lost the original email. I apologize for this. I hate not giving credit.