In the sense I think you're using it, "statistics" are really methods for dimensionality reduction - we take means, and medians and standard deviations with the hopes that they will capture the parts of the data we care about. This is important for two reasons - for one, for anything even moderately high dimension we'll never have enough data to be able to forego some means of aggregation due to the "curse of dimensionality". Secondly, the human-machine interaction information bandwidth is annoyingly low, so we need some way to compress any information for human consumption. "Statistics" are one way we do so.
"Statistics" is also a field of study based around understanding how multiple data points relate to each other - that is of course critical to machine learning, and I think the terminology collision is why you're getting downvoted.
Statistics, as a field, already used general-purpose optimization algorithms before modern ML techniques came about, so in that sense, ML just fits into an existing position in the statistical toolbox (like replacing a chisel with a 3D printer). In the other direction, statistical techniques like cross-validation are necessary for you to get your ML correct.
I would like to think that statistics comes more from a pure math approach, loosely, while ML comes from an applied math approach, loosely. ML works spectacularly well on a class of problems. Why it does what it does is (in)conveniently brushed under the rug. How you treat that (in)convenience is left to you.
[1] - https://www.quantamagazine.org/20151203-big-datas-mathematic...
very curious to hear about your point of view. Statistics is not linear regression and ANOVA, or whatever catalogue of techniques in a freshman book, not even the library of techniques available in R.
Statistics is the application of probability (or more broadly, math) to data.
That said statisticians did miss the neural net wave because of their flippant reaction to it. They said, "oh well yet another non-parametric function approximator we have worked out the asymptotics 30 years ago".
To paraphrase someone wise: asymptotically we are all dead. Not enough heed was paid to that. Among their other lacks were expertise in algorithms and optimization. Mind you, optimization has been at the core of their craft from their very genesis, its just that they did not feel it important enough to ride the cutting edge of research on optimization. Note: you cannot do maximum likelihood with solving an optimization problem. Gauss was doing it several hundreds of years ago for statistics. If I go on a bit further with my rant, they got a bit carried away with their fetish over bias and asymptotic normality. They missed the wave, sure.
But all said and done, by any accepted definition of statistics, NN is very much also statistics.
And who says frequentist and Bayesian are the only two views. Where would you shelve prequential statistics then ? Or nonparametric regression
Prediction has definitely been a part of statistics but often, as you rightly claim, as a byproduct. And yes i would characterize the focus of stats and ml exactly as you did
Statistics works the other way. You basically always start with some kind of probabilistic model. And then, if you even bother with prediction, you work towards prediction from the probabilistic model. With stats you don't need to interpret or add probability after the fact, it's already there.
Obviously stats and ML are enormous fields, with quite some overlap. And people tend to go after low hanging fruit; if many people who studied neural nets have formal probability backgrounds it simply makes sense that someone will write a paper on it. And I'm generalizing here (same goes with frequentist & Bayesian comment). But there absolutely is justification for saying "neural nets are not really a statistical technique".
nns are in no way less fundamentally associated with probability than say linear regression. In both cases you can start with a probability model and derive the final form as a logical consequence, or you can start with the final form and slap a consistent probabilistic model on top.
The main thing is that any test you come up with that carves nns away from stats is going to carve a whole lot of other things that people have no trouble calling them stats. This controversy essentially stems from the need to claim a technique for ones own tribe and not concede to another. I am making no moral claim here just an observation and neither is it a novel one.
BTW I am firmly from the ml camp and not stats. I enjoy poking a little bit of fun at statisticians and try being gracious about their criticism of ml. That said i feel no need to make a groundless claim to a technique when they have no less rights to it in terms of objective claims. Rights steeped in culture, fiat and history are a different matter.
I would say applied statistics draws a line just prior to implementation concerns (say, real-world resource usage measured in time, space and energy) whereas these would be fully within scope and of interest in machine learning.
As an example, applied statistics could provide a useful approach to a vision/image recognition problem, and this approach might be provably unrealizable in practice using real-world execution units (e.g. CUDA cores). Nonetheless, it might still be a very worthwhile theoretical result in applied statistics, although of no immediate interest within ML except to hint at potential new area of research.
To to do anything beyond use tools other people have made (and never be sure whether results are meaningful or not) statistics are required
Of course, to make money from the ML boom you can probably get away with coincidence and correlation
Statistics: A mathematical science concerned with data collection, presentation, analysis, and interpretation.
Statistic: A quantity calculated from the data in a sample, which characterises an important aspect in the sample (such as mean or standard deviation).
If "statistics" is the term for taking a mathematical approach to understanding data, then "machine learning" is basically an applied subset of that. But you seem to be specifically using the "a statistic" definition to describe what you think the "study of statistics" is entirely concerned with.