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mlthoughts2018

Several subfields of PAC learning also deal with quantifying error bounds under other assumptions about the KL divergence between your sampling distribution and the true distribution. Variational Bayesian methods also provide results on generalization in these cases.

You seem to care a lot that these approaches rely on assumptions, but I find that silly.

Further in _most_ specific applications of e.g. CNNs for computer vision tasks or RNNs for time series or sequential prediction tasks, you _do_ control the entire sampling distribution (e.g. user photos with exactly satisfied criteria), and you really can fully and unambiguously guarantee that the training and testing set come from the “true” distribution you care about. And in many other cases the degree to which that assumption fails is so minor that it makes no practical difference.

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Some domains are chaotic, some are very large, some are dynamic. In some domains errors of some types matter much more than other errors.

Minor assumption failures can suddenly matter alot.

The distinction between a lab result and a field trial has been somewhat lost in ml, there will be hell to pay in the long term...

> Minor assumption failures can suddenly matter alot.

Indeed. In fact this is nowadays painfully obvious in Fisher's maximum-likelihood based estimators -- they do not have nice 'continuity' properties that will give a graceful degradation. We figured out how to deal with this once the problem was recognized.

However, we see the same problem raising its head in some of the deep neural net literature. Tiny variations often does not cause tiny distortions in the output -- thats cause for some legitimate concern.

>> You seem to care a lot that these approaches rely on assumptions, but I find that silly.

Thanks, I'll keep that in mind.

>> Further in _most_ specific applications of e.g. CNNs for computer vision tasks or RNNs for time series or sequential prediction tasks, you _do_ control the entire sampling distribution (e.g. user photos with exactly satisfied criteria), and you really can fully and unambiguously guarantee that the training and testing set come from the “true” distribution you care about.

One of my pet peeves is the Deep Gaydar Paper from Stanford (https://osf.io/zn79k/).

The authors trained a CNN to identify sexuality (gay or straight) from images of faces. The images were self-submitted to a US dating site and the users also stated their sexuality. The dataset included different numbers of images for each user, but of the users that had at least one image in the dataset (i.e. all users) 50% had stated their sexuality as "gay" and 50% as "straight"- this, for both men and women. The research concluded that it was possible to train an image classifier, a CNN, to identify sexuality from facial features. The authors justified this with a theory about the relation between the hormonal environment in the womb.

I hold this up as a perfect example of why this assumption, that you can control the distribution in the real world because you can choose the attributes of a dataset that you wish to work with, is very risky. And I don't mean for the social implications of that reprehensible publication. The researchers chose a uniform distribution for their gay and straight subjects. The paper itself cites a 7% estimate of the chance that a person is "gay"- so what, exactly, did their classifier learn to represent? That "gay features" and "straight features" are equally distributed?

In any case, "fully and unambiguously guarantee" is not something that happens outside science fiction. Not in machine learning, not in physics or medicine, not in any subject of knowledge. Guarantees always come with assumptions. If assumptions are violated, or if they were bad assumptions to begin with, guarantees fly out the window in haste.

Yeah, I agree that gaydar example illustrates your point, but it’s just such an egregious outlier that overall it just further refutes the idea that this distinction matters much.

About zero serious, mainstream papers or open-source libraries or business case studies each year resemble the poor experiment design from that gaydar paper. It’s a silly one to emphasize in terms of generalization error except I guess for basic 101 pedagogy for people who have never worked with models like this before.

It's an especially egregious example, but everybody makes assumptions that they can't guarantee will hold.

The first part of your comment doesn’t seem related to the second part, and neither part seems related to the question of whether most applied problems do or do not benefit from making a distinction between the sampling distribution used for generating training and test data and the “true” distribution.

I used to believe that generalization is about some nice concentration bound that one can design carefully in terms of the optimization algorithm. After many years practice, I began to firmly question about the basic assumption about data distributions. For many real applications, assuming the data are from the same unknown true distribution is fundamentally incomplete. In the real world, information is always partial and adversarials always exist. It never is a closed world where adding samples eventually has diminished value. Instead, it's an open world where long tail phenomenons are often observed. It never is about a single objective that the optimization algorithm cares about. Instead, it's entangled with many coupled but conflicting interests.

The existing statistical learning theory is having a hard time on addressing questions like combinatorial generalizability. Hopefully, the new stability analysis and adversarial analysis can lead us somewhere theoretically.

I’ve had the opposite experience. After finishing grad school and working in industry for a long time now, applying ML to computer vision, NLP, causal inference and quant finance for production systems, the vast, vast majority of problems are such that the training and test set are defined by very precise business operating constraints and it’s known with a high degree of certainty that future examples to which the model is required to generalize will also be from the same distribution reflected in model training, and any differences are so minor as to be practically ignorable all the time, and requiring really special evidence to show the super rare cases when it cannot be ignored.

(Those cases also are most often just solved by collecting new/ more training & testing data and re-training / fine-tuning / calibrating the model to some slight shift in the distribution, and require no formal modeling techniques related to tricky generalization distribution differences).

This has been true across commercial ML products or services at large tech companies, small startups, quant finance firms, defense research labs, and academic labs. Across projects ranging from face recognition, high-traffic search engine and related services like machine translation, trending models, search ranking, dimensionality reduction models in time series forecasting, reverse image search, audio similarity models, advertising models, and many more.

It just turns out that in industry, the problems that have meaningful utility to the business are almost always defined by intrinsic constraints that nearly guarantee there won’t be a meaningful difference in the distribution of future prediction-time examples compared with training & testing distribution.

I find all this very hard to square with my understanding. I mean, what kind of "business operating constraints" stay the same over months or years? Or do you mean that, when constraints change, you just train a new model?

I think basically what you're saying is "we choose the data we want to reprsent, so we know when we're representing it well". But that's just what I say above, about measuring progress by hitting the targets you choose, completely arbitrarily.

It's as if I shot a bunch of arrows and then painted targets around them, then claimed I'm a great archer because I always hit bullseye.

I don't think that's the result of some fundamental difference in understanding between academia and industry, either. Perhaps, in the industry, assuming that reality will comply with your assumptions helps achieve business aims, but that's not because the systems work. It's becaus they can be made to look like they do and there's no good way to show they don't, as there's no good way to show they do.

It sounds like you haven’t worked on many real world applied problems.

I would add that I have had my fair share of industry scale problems where labeled data is not drawn from the same distribution as where the system will be deployed. But as you pointed out earlier, there are theoretical and practical methods to deal with this. For someone who wants to get familiar with this territory, domain adaptation, transfer learning, transductive learning, semi-supervised learning, etc would be some of the keywords to seed an initial literature search with.

If you mean that measuring generalisation is a poorly defined problem and we need to develop new theoretical tools- I'm totally with you. Unfortunately, in machine learning, the ratio of theory to practice is 1:100, or so.

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