Unless your startup's core strategy involves machine learning, statistics tends to come handier than machine learning in the early days. Most likely, what moves your company is not a data product built atop machine learning models but the ability to draw less wrong conclusions from your data, which is the very definition of statistics. Also, in the early days of a startup, you experience small/missing data problems: You have very few customers, very incomplete datasets with a lot of gotchas. Interpreting such bad data is no small feat, but it's definitely different from training your Random Forest model against millions of observations.
Great read for anyone interested in the debate.
Probabilistic programming is already a hint of this. The most general class of probability distributions is that of non-deterministic programs. ML is just a quick and dirty way to write these programs.
The correct complement to machine learning is cryptography -- trying to intentionally build things that are provably intractable to reverse engineer.
I like the complement with cryptography. I would add another coding method: compression - Approximating the simplest model with explanatory power.
I find the machine learning approach is far more humble. It starts out by saying that I, as a domain expert or a statistician, probably don't know any better than a lay person what is going to work for prediction or how to best attribute efficacy for explanation. Instead of coming at the problem from a position of hubris, that me and my stats background know what to do, I will instead try to arrive at an algorithmic solution that has provable inference properties, and then allow it to work and commit to it.
Either side can lead to failings if you just try to throw an off-the-shelf method at a problem without thinking, but there's a difference between criticizing the naivety with which a given practitioner uses the method versus criticizing the method itself.
When we look at the methods themselves I see much more care, humility, and carefulness to avoid statistical fallacies in the machine learning world. I see a lot of sloppy hacks and from-first-principles-invalid (like NHST) approaches in the 'statistics' side. And even when we consider how practioners use them, both sides are pretty much equally as guilty of trying to just throw methods at a problem like a black box. Machine learning is no more of a black box than a garbage-can regression from which t-stats will be used for model selection. However, all of the notorious misuses of p-values and conflation over policy questions (questions for which a conditional posterior is necessarily required, but for which likelihood functions are substituted as a proxy for the posterior) seem very uniquely problematic for only the 'statistics' side.
Three papers that I recommend for this sort of discussion are:
[1] "Bayesian estimation supersedes the t-test" by Kruschke, http://www.indiana.edu/~kruschke/BEST/BEST.pdf
[2] "Statistical Modeling: The Two Cultures" by Breiman, https://projecteuclid.org/euclid.ss/1009213726
[3] "Let's put the garbage-can regressions and garbage-can probits where they belong" by Achen, http://www.columbia.edu/~gjw10/achen04.pdf
Besides, it is easy to get wrong explanation and, as Vladimir Vapnik in his 3 metaphors for complex world observed, http://www.lancaster.ac.uk/users/esqn/windsor04/handouts/vap... , "actions based on your understanding of God’s thoughts can bring you to catastrophe".
SVM's were so popular, pretty much because they had a firm theoretical basis on which they were designed (or "cute math" as deep learners may call it). As Patrick Winston would ask his students (paraphrasing): "Did God really meant it this way, or did humans create it, because it was useful to them?". Except maybe for the LSTM, deep learning models are not God-given. We use them because, in practice, they beat other modeling techniques. Now we need to find the theoretical grounding to explain why they work so well, and allow for better model interpretability, so these models can more readily be deployed in health care and under regulation.
If some regulations shall require such explanation, the end result will be fake stories like parents tell to the children that Moon do not fall because it is nailed to the sky.
The problem is to replace inept employees who believe "business decisions" are not scientific questions, so that over time there is a convergence to using the scientific method, with legitimate statistical rigor, when making a so-called business decision.
Generally speaking, the only people who want for there to be a distinction between a "business question" and a "scientific question" are people who can profit from the political manipulation that becomes possible once a question is decoupled from technological and statistical rigor. Once that decoupling happens, you can use almost anything as the basis of a decision, and you can secure blame insurance against almost any outcome.
This is why many of the experiments testing whether prediction markets, when used internally to a company, can force projects to be completed on time and under budget are generally met with extreme resistance from managers even when they are resounding successes.
The managers don't care if the projects are delivered on time or under budget. What they care about is being able to use political tools to argue for bonuses, create pockets of job security, backstab colleagues, block opposing coalitions within the firm. You can't do that stuff if everyone is expected to be scientific, so you have to introduce the arbitrary buzzword "business" into the mix, and start demanding nonsense stuff like "actionable insight" -- things that are intentionally not scientifically rigorous to ensure there is room for pliable political manipulation for self-serving and/or rent-seeking executives, all with plausible deniability that it's supposed to be "quantitative."
