1) it is pretty amazing that normit transformations (map the quantiles of a non-normal distribution onto a Gaussian and use that) don't seem to be on this guy's radar. We use distributions with linearly additive and affine invariant properties (normal plus normal is normal, bernoulli plus bernoulli is bitwise bernoulli) because we find linear algebra very useful. Nonparametric tests and procedures erode your power; normit transformations usually increase it. I did part of my dissertation on this; it's partly to do with asymptotics, but also partly due to the robustness of Gaussian error assumptions thanks to the CLT.

I realized recently that a lot of the trouble people have with training neural networks stems from their lack of training in basic model evaluation. If you stack a bunch of shitty penalized regressions (which is what linear/logistic + relU hinge loss represents) you now have one gigantic shitty regression which is harder to debug. If your early steps are thrown out of whack by outliers, your later steps will be too. Dropout is an attempt to remedy this, but you tend to lose power when you shrink your dataset or model, so (per usual) there really is no such thing as a free lunch. But most of the tradeoffs make more sense when you are able to evaluate each layer as a predictor/filter. Scaling this up to deep models is hard, therefore debugging deep models is hard. Not exactly a big leap.

There is a reason people say "an expert is a master of the fundamentals". Building a castle on a swamp gives poor results. If you can't design an experiment to test your model and its assumptions, your model will suck. This is not rocket surgery. A GPU allows you to make more mistakes, faster, if that's what you want. If you have the fundamentals nailed down, and enough data to avoid overfitting, then nonlinear approaches can be incredibly powerful.

Most of the time a simple logistic regression will offer 80-90% of the power of a DNN, a kernel regression will offer 80-90% of the power of a CNN, and an HMM or Kalman filter will offer 80-90% of the power of an RNN. It's when you need that 10-20% "extra" to compete, and have the data to do it, that deeper or trickier architectures help.

If you can transform a bunch of correlated data so that it is 1) decorrelated and 2) close enough to Gaussian for government work, you suddenly get a tremendous amount of power from linear algebra and differential geometry "for free". This is one reason why Bayesian and graphical hierarchical mixed models work well -- you borrow information when you don't have enough to feed the model, and if you have some domain expertise, this allows you to keep the model from making stupid or impossible predictions.

Anyways. I have had fun lately playing with various deep, recurrent, and adversarial architectures. I don't mean to imply they aren't tremendously powerful in the right hands. But so is a Hole Hawg. Don't use a Hole Hawg when a paper punch is all you really need.

2) What (good) statisticians excel at is catching faulty assumptions. (I'll leave it to the reader to decide whether this data-scientist-for-hire has done a good job of that in his piece) So we plot our data, marginally or via projections, all the damned time. If you don't, sooner or later it will bite you in the ass, and then you too can join the ranks of the always-plotting. However, choosing which margins or conditional distributions to plot in a high-dimensional or sparse dataset is important to avoid wasting a lot of time. So whether via transformation or penalization (e.g. graphical lasso) or both, we usually try to prune things down and home on on "the good stuff". Prioritizing what to do first is most easily done if you have a number and can rank the putative significance by that number. Use Spearman, use energy statistics (distance correlation), use marginal score tests -- IDGAF, just use these as guidelines and plot the damned data.

Corollary: if someone shows you fancy plots and never simple ones containing clouds of individual data points, they're probably full of shit. Boxplots should be beeswarms, loess plots should have scatterplots (smoothed or otherwise) behind them. And for god's sake plot your residuals, either implicitly or explicitly.

3) see above. The author is good at fussing, and brings up some classical points. But they're not really his points. Median and MAD are more robust to outliers than mean and standard deviation, but that makes them less sensitive, too. Check your assumptions, plot everything, use the numbers as advisory quantities rather than final results.