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I'm more giddy to respond to questions like this than I should be, given that information criteria are an area of my research. AIC and BIC are approximations t
by bendysnowflakes 9y ago
I'm more giddy to respond to questions like this than I should be, given that information criteria are an area of my research.
AIC and BIC are approximations to other quantities under certain common but idealized scenarios. What's become clear over the last 20 years or so is that for most other scenarios those approximations are not nearly as good as other approximations, or just calculating the targeted values of interest.
So, for something like DL models, criteria such as AIC and BIC are less applicable. But what is confusing to me is why other information criteria aren't pursued more. There's literature on the asymptotic equivalence of cross-validation and certain information criteria, and CV has certain problems that those criteria overcome (I've been looking citations but Google thinks I'm spamming it or something).
I think part of the reason for the adoption of CV is a cultural one, to be honest, and due to historical quirks. Like bootstrapping and other empirical simulation methods, it has an appeal due to its relatively nonparametric nature. But there is a ton of mischaracterizations about CV (e.g., relative to bootstrapping) and its warts have been overlooked in general due to the position it has attained in applied settings.
There is also a huge gap between the literature on information criteria and the rest of statistics and applied data analysis. People tend to learn about AIC and BIC through certain standard sources, sources mostly pertaining to their initial derivation, or that follow the same line of reasoning. But there's other literature that derives AIC and BIC through other means, or approach them from other perspectives, and that literature tends to get ignored. As a result there's a lot of misleading statements that are made about each, even from talented individuals (e.g., that the rationale for BIC depends on Bayesianism, or that there is a true model under consideration), and a lot of advances in the area are totally ignored. It's like there's two literatures, one attended to by people who are interested in information criteria, and another by people that "just want to understand AIC and BIC." It's confusing to me really, because I generally see some kind of trickle-down in other areas of statistics, but with information criteria, it's like there's an enormous gap.
- nerdponx 9y agoGlad to see an expert respond. Are you able to comment on my ramblings here? https://news.ycombinator.com/item?id=16096865 https://news.ycombinator.com/item?id=16096865 How do you feel about stuff like the DIC and WAIC for machine learning and other "predictive" modeling?
- bendysnowflakes 9y agoI like the links--thanks. About DIC and WAIC, etc. ... that's a huge topic for me. There's a relatively well-cited result that shows that you can arbitrarily choose any penalty in an information criterion (i.e., penalty in the form -logL + penalty), as long as it meets certain weak conditions, and it will eventually work with big enough samples. So the issues of most importance are usually how selection accuracy increases with sample size, not its asymptotic performance. The leads to a certain hesitancy for me in terms of why I should pay attention to any particular IC. Having said that, DIC and WAIC are pretty elegant in my mind, and I've been glad to see research on them. Predictive scenarios aren't really my focus, although I've become much more interested in them the last couple of years for various reasons. Most of my work is in what might be thought of as unsupervised models.
- srean 9y agoI would chime in that cross-validation and its variants are extremely flexible in the sense they make very few assumptions on the model. No likelihood function ? no problem. Non-parametric no problem. Need non asymptotic numbers ? no problem. The model changed ? No problem again. One can use the exact same code and procedure. AIC is controlled by the number of parameters and the quality of fit, but it is known in theory, as well as in practice that for many models, for example, neural networks, linear regression with additive iid Gaussian noise, the norm of the parameters matter more for prediction accuracy than the sheer number of parameters. Not claiming that CV is the best model selection criteria, just listing out a few pluses for CV. The last word on model selection is yet to be spoken. It goes right to one of the core questions about model fitting and prediction.
- bendysnowflakes 9y agoYeah, I don't mean to make it sound like there's no good reason for CV... I came across as sort of harsh. I just feel like CV got taken up in application a lot because it makes intuitive sense but with relatively little in terms of theoretical scrutiny, especially relative to other alternatives. When it has been compared to alternatives, the comparisons are sort of weak in that they often involve strawman or unrepresentative assumptions. CV involves certain assumptions itself, for example, in terms of choices, that affect results in sort of unpredictable ways sometimes. I'm a big fan of bootstrapping too and have often felt that that avenue hasn't been explored as much as it could be.
- srean 9y agoOh your original comment wasn't harsh at all. I was just listing a few of CV's strengths which may have played a role in making it a popular choice