Introduction to Support Vector Machines in Machine Learning

Once upon a time, when I used to hire data people, I'd ask them to tell me about a recent data project. They'd normally mention some kind of complex model, and I'd ask them how much better it was than linear/logistic regression. A really large proportion of candidates (around 50%) couldn't answer this because they'd never compared their approach to anything simpler.

One person told me that linear regression wasn't in the top 10 Kaggle models, so they would never use it.

NN’s are universal function approximators. They can have arbitrary model capacity, and you can sort of control that with architecture decisions, loss function/regularization choices, and early stopping, but depending on the problem they can cause more problems than they solve. Usually you don’t really know if your NN will generalize well outside of your train/test distributions, so many times it’s better to have a simpler, more predictable model that you can control the behavior of. This is all from my personal experience and is completely moot when we’re talking about e.g. NLP or vision tasks or situations where you’re drowning in data. NNs are super interesting and powerful, don’t mean to suggest otherwise but the mantra is: “what is the right solution to my problem”. Lots of great advantages to NN’s as well (you can get them to do anything with enough cajoling and they can be solutions to major headaches you would usually have in e.g. kernel methods).

Ah I see yea, if you’re talking about hyperpriors and marginalization and MCMC I totally agree; these are really valuable in science, and this is the “full Bayesian solution” but with many caveats, one big one being that it’s very easy to be overly confident in the results of some unwieldy hierarchical model and ignore the fact that the priors (or hyperpriors) are often times fudge factors because it’s so damn hard to articulate your prior belief as a bona fide distribution. A lot of times you run into a “garbage in garbage out” problem and it might not be obvious right away since we are probably busy patting ourselves on the back and popping champagne bottles because we’ve gotten our MCMC chains to converge.

> For example Ridge regression where you put a gaussian prior on the predictor then guess at its variance as a hyperparameter for a quadratic penalty (with cross validation or something) is MAP but not actually "Bayesian". Bayesians also put a prior distribution on the hyperparameter itself making life extra difficult.

Yea right — nothing wrong with cross validation in a lot of cases. Since yea we could go with the “full Bayesian solution” and marginalize over some distribution of our hyperprior, but that very well might not give you anything more than cross validation (or maybe will give you something worse if you have a bad hyperprior).

> Even in deep learning it's simple to put a penalty term on the loss or weights for that matter, so you could call it a MAP estimate. That's implemented everywhere.

Agreed, my only argument is that it’s helpful to know where all of these terms come from in a general sense rather than treat each one as some ad hoc solution.

> For that matter you can claim any neural net classifier with a sigmoid or softmax at the final layer is doing logistic regression. With multilayer networks just adding a representation learning stage to it.

Agree and that’s exactly the sort of valuable insight that’s helpful to have (though maybe this one isn’t really an insight from Bayesian stats).

> As I said cheers to statistics, just that stopping at MAP estimates will cover most everything. If one goes looking for a Bayesian methods text or review article it will be well beyond that.

Sure, if you know MAP and what it means, then you know what a posterior means and you know that every model you fit and loss function you use comes from that, and you know if you care about more than a mode or mean of the posterior you can use lots of tools to deal with that. I’ve never really encountered MCMC in the work I do and i don’t think it would really bring any additional insight into what we’re doing, but sometimes we care about uncertainty and Laplace approximation or variational inference can do the job just fine.

> By scaling problems I basically the fact that monte carlo doesn't work in large numbers of dimensions, where the parameters of the joint distribution of everything are vast.

While I would agree MCMC and it’s variants are certainly not a good idea a lot of the time because they require a lot of time and computation, very rarely they are (you want insights from your data to use internally or something and you really want to explore implications of many different assumptions), and HMC etcetera can deal with very high dimensional settings (> millions of parameters). But generally I agree, if you’re talking about “scalable solutions” it usually means MCMC is not really what you want to be doing.