Linear regression does not require errors to be iid, normal, and homoscedastic for it to "work". One of the ways to separate candidates is to push on what (and how) assumptions can be weakened, what the consequences are for estimation and inference, and what sort of corrections can be incorporated for maintaining consistency, improving efficiency, correcting biases, etc. An entry level candidate may not have (nor need to have) a complete understanding of asymptotic theory, but they should know what the purpose of robust standard errors are and how to use them.
Interesting and perhaps shows the cultural differences between ML and stats people. I took a machine learning course in my bachelor's and two more ML courses in my master's (CS). These weren't some "deep learning lite", mess-around-in-Keras courses, because DL wasn't even big back then. We covered lots of stuff, Bayesian linear regression, Gaussian processes, Gibbs sampling, Metropolis-Hastings, hierarchical Dirichlet processes, SVMs, multi-class SVM, PCA, kernel PCA, perceptrons, CMAC neural nets, Hebbian learning, AdaBoost, Fisher vectors, EM algorithms for various distributions, fuzzy logic, optimization methods like conjugate gradients etc etc.
But not once were the "Gauss-Markov conditions" mentioned. Frequentist theory was only marginally addressed. I taught myself some of that stuff from the Internet, such as hypothesis testing theory, p-values, t statistic, ANOVA, etc.
Also, I'd say I'm good with data structures and algorithms, complexity theory, graph theory etc.
I thought these skills would be a good fit for data science jobs, but I guess it's really such a wide umbrella term, that probably you're more looking for people trained in the frequentist, statistical side of it. What application field are you in, if it's no secret?
By tribe I am firmly in the machine learning camp but I have serious doubts that one can be a good hands-on data-science practitioner if one does not have a good foundation in statistics.
Statistics is not really in focus in most CS programs. Indeed I'm not sure where it is. Perhaps in applied math programs. Stats is kinda too dirty and realworld for pure math types, and in science programs and medicine it's usually just taught as a bunch of magic formulas to memorize and rules of thumb passed down from generation to generation without understanding. Perhaps physics departments do have both the necessary math skills and the need for stats so they may provide a good education in this.
But having studied in 3 universities in different countries, CS just doesn't care about stats. Probability theory yes, but frequentist topics like statistical tests not really.
This was my experience at a high ranking engineering public state school in the US. Stats is delegated to the applied math program usually (in fact, my degree was titled "Applied Mathematics & Statistics"). You can choose to concentrate in subjects like algorithms, operations research, fin stuff, statistics, etc. CS as well as other sciences had one required intro to prob & stats, but that's it outside electives.
Further, despite having a fantastic reputation, my program only discussed frequentist ideas with near 0 mention of Bayesian reasoning/methods (outside the same Bayes rule questions asked in the first weeks of every stats class). Overall the education felt too traditional, I would have liked to seen mention of more modern methods like the bootstrap and certainly mention of Bayesian.
> Stats is delegated to the applied math program usually
Which is not unsreasonable considering that these things arent really related to computers (although they happen to involve computation). I think its just an artifact of history and how things happened that ML is associated with CS and EE departments, but really its applied math, not a core CS topic like say compilers, formal languages and complexity.
Data Science jobs cover a wide gamut from theoretical math to applied machine learning to statistics to data engineering to analytics. You can generally tell which one they're aiming for from the job description and requirements. Some are basically looking for a Statistician while other looks for a CS Machine Learning Engineer. If the title is ML Engineer than that generally indicates it's a lot more focused on what you studied than stats.
Not really sure why your comment is marked dead when it is correct. Maybe it's a new account thing? As you say, the Gauss-Markov conditions are necessary (and sufficient) to make OLS BLUE, but OLS still works fine under a variety of pathological conditions, and many of those conditions can be tested for and adjusted for using common techniques.
