That being said, the article otherwise seems like a great introduction. Not sure why they chose that title.
After all, if Black Swans were common enough to make prediction a fool's errand most of the time, the bird of that name would never have led to the book of that name, because everyone would be predicting their failure to predict things.
In the real world there are often no controls, and complex systems can be driven by an attractor for a very long time before one morning they are not, and every rule that you have is useless (often worse than useless).
Sources of error are not equal; "Black Swan Error" is unusual in that over time it may be that this source is more important than any other source of data in your domain - the strange attractor that drove the creation of your classifier over the last 20 years may never recapture your function and if that's the case your classifier will be literally the most wrong thing you could have!
However, it is not the only type. There is also the stock market, which demonstrates major unpredictability every few years, but which can also be approximated the same way between each of the Black Swans. (And they keep being Black Swans because the gap between them is large enough for people to convince themselves that "This time it's different, this time n̵o̵b̵o̵d̵y̵ ̵w̵i̵l̵l̵ ̵h̵a̵v̵e̵ ̵t̵o̵ ̵b̵e̵ ̵n̵a̵i̵l̵e̵d̵ ̵t̵o̵ ̵a̵n̵y̵t̵h̵i̵n̵g̵ growth will be eternal!")
Edit:
Point is, it generalises as how wrong you are in your predictions, and the closer your estimate of your error rate is to your actual error rate, the better your model is.
I have to say I rather prefer the black variety over the white.
Great point. We can't know that a machine learning algorithm used to make predictions won't be wrong if the future turns out to be significantly different from the past. A swan-classifier trained on images of white swans would fail hard if given pictures of black swans.
That said, people find it useful to use machine learning algorithms to predict the future, as the future tends to be similar to the past, at least in the limited domains to which machine learning is currently applied. As compute increases and we learn how to write machine learning architectures[0], we don't need to distinguish as much between 'machine learning' and plain old 'learning' and much of what philosophers have thought over the years about the problem of induction, and relevant domains of induction, becomes relevant to the topic.
[0] Or learn them. Jeff Dean mentions experimental success learning RNN architectures: https://www.youtube.com/watch?v=vzoe2G5g-w4
Any time you extend a statistical model temporally it immediately becomes mathematically invalid since probabilistic statistics are only valid for a fixed population at a fixed moment in time.
Unfortunately business and government is rife with people predicting the future based on statistical models that have no more mathematical validity than reading tea leaves.
Statistics as we know it "works" (can be derived) under the assumptions of controlled experimental data. As a thought experiment think about the weather - we know that if we build a classifier that predicts the weather in my garden tomorrow based on the history of the weather in my garden it will do very badly. Why - well because weather is very very very complex; the range of behavior is vast. But worse, it's unstable. The weather in my garden is driven by several complex systems; the ocean, the atmosphere, the earth's orbit and sol! Statistics can't predict the future of the weather in my garden.
Statistics also can't predict other things like the future of the financial markets (not least because if you find a statistical law about that they you will act on it and then screw it up)
It's important to me to bang on about this because there are loads of people who sit through their introductory courses and read the example of predicting a biased roulette wheel. Years later they end up running the company/country/community that I live in and they have a view that they can use the same principles to do it... and this thinking leads to nasty surprises for me.
Give me hourly readings of temperature, wind speed, wind direction, precipitation, cloud cover and barometric pressure for the last 10 years and I can give you a very accurate prediction of tomorrow's weather in your garden.
that aside you are missing a larger point. if you predict the future based on past data all you are saying is "the future will be the same as the past." you aren't predicting anything. you will be wrong every single time something novel occurs, which is pretty frequently in the real world.
I don't have the data handy but to the best of my recollection weather forecasting for high/low temperature and precipitation does pretty well for the range of 24-48 hours but declines steadily in accuracy, and is no better than random guess around 2 weeks out.
That said, you are not addressing my other point, which is that "weather prediction" is just saying "things are going to stay the same." You are always starting with a set of conditions and then looking at your records and seeing what happened in similar conditions and predicting that the same thing will happen again.
Predicting that things will stay the same may come out as better than random guess in many cases but it will still be 100% wrong in cases where something novel happens.
Many years ago I actually seriously tried to do what you describe above, I tried out all sorts of things around seasonal analysis and other features. What kills it is the chaotic nature of UK weather due to the jetstream and NAO.
Obviously, this is more or less feasible in practice, depending on the phenomenon under study. Calling markets unpredictable is not evidence against the existence of rigorous frameworks for statistical prediction.
Don't let bad experiences with inexperienced and overconfident practitioners blind you to established, uncontroversial, mathematical truths.