Two big challenges in machine learning [pdf]
icml.cc
icml.cc
https://research.facebook.com/researchers/1558013787807218/l...
See: LeCrun's What Wrong With Deep Learning https://drive.google.com/file/d/0BxKBnD5y2M8NVHRiVXBnOVpiYUk...
One of the problems (in my opinion) with networks is that the analysis has always been post hoc. Personally, I think it's more preferable to build a method starting from theory [2] which can then be tested empirically to see if the assumptions of the theory hold. Then augment the theory, the method, and experiment again.
Now, there's nothing inherently wrong with post hoc analysis - it's just a different start point in the loop of science. However, because we didn't start from theory, the burden is then to extract some theory from empirical observation. Again IMO, this is can be problematic because:
1) It more easily allows for confirmation bias.
2) It leads to a multitude fragmented theories.
The second is why everything surrounding neural networks seems so incredibly ad hoc.
[1]: https://www.cs.nyu.edu/~yann/talks/lecun-20071207-nonconvex....
[2]: The principles could be based on statistical learning (see SVM), neurophysiology (see work by Poggio or Olshausen), mathematical invariants (see work by Mallat), etc...
I'd be even more pessimistic about one's ability to go forward from empirical observation of opaque mechanisms.
Aside from your incisive observations, there's the point that if you have a "good" "working" "theory of how neural networks operate", what is it a "theory of"? It's dependent on the mechanisms that gather the test data, the sort of answer that a certain kind of person wants out of the test data and so-forth - the "epistemological" questions you didn't answer and couldn't answer will come to bite you.
I'd add that SVMs do seem more firmly founded but their ultimate tweak, the kernel trick plus projection onto feature space, is basically ad-hoc too - still much closer to a "real" probability model etc. The problem with SVMs is that they wind-up more or less equivalent to a 1st order neural network and thus they don't scale - once data becomes truly huge, they require too much storage.
Ironically, I think the best single overall critique of AI efforts was articulated by Paul Allen[1]. The problem is that in building large systems, people encounter a "complexity" barrier that prevents further progress[1]. Creating more complex systems to tackle that tends to fail as people wind-up understanding less and less of their own complex systems.
The problems with all the neurophysiological models is that raw neurons are very complex things and one doesn't know immediately which parts even carrying meaningful signals, a problem made worse by not having a model of what those "meaningful signals" might be.
Consider that if aliens looked at human-made microchips and tried to model them fully, they get the clock signal and various nonlinearities in the transitors right but have enough computation errors that no program would run on it.
Another good argument is that just all our methodology hinges on classical Western epistemology and a change in that may be necessary[2].
[1] http://www.technologyreview.com/view/425733/paul-allen-the-s...
[2] http://aeon.co/magazine/technology/david-deutsch-artificial-...
I think we should make the distinction between theory pertaining to a task and theory pertaining to methods that perform (or approximate) the task. Certainly, the former can be incorporated into the latter, so the boundary is fuzzy. Actually, the previous is quite important because known principles of the task can be expressed mathematically and incorporated functionally into the approximation method. In this sense, a network architecture could arise naturally. In fact, it sort of does with anything with a cascade-type pattern.
On the other hand, if we're going to talk about the method (networks, in particular) independently of the task, this is more difficult. The question is now: is the network model remarkable in some sense? Meaning: is there some class of functions which are "best" or "more efficiently represented" by network approximations, and what are the properties of the class that make this the case? Yoshua Bengio has touched on this with regards to depth from the point of view of circuit theory, but the argument is basically: "here's a couple circuits which are more efficiently represented by increased depth, therefore deep = good always". It would be more interesting if there was a more rigorous analysis from a function approximation view. Perhaps literature exists on this. I'm not sure - I'm sort of rambling now.
> kernel trick plus projection onto feature space, is basically ad-hoc too
The choice of kernel - yes I agree, but the driving theory of the method is to maximize the margin, not choose the best kernel.
> Creating more complex systems to tackle that tends to fail as people wind-up understanding less and less of their own complex systems.
Interesting. Maybe there's something going on with the relationship between entropy and complexity.
Machine learning is about approximate reasoning but with no real guarantees of the approximation. Even if the approximation is usually very good, being occasionally bad can be "deeply problematic" when we don't have control over exactly how exactly the bad recommendations are created.
I think the biggest takeaways are...
1) Machine learning in large software projects is complex because decisions made by one algorithm can influence the data of other algorithms, creating massive biasing.
2) Simple cross-validation / hold back methodology is limited as we expand what we want machine learning to be able to handle. Reason: big data is too big and "correctness" is difficult to evaluate for things like Q/A systems.
Plus read the article/presentation. It goes into the issue with great depth and clarity.