21 July 2009

Non-parametric as memorizing, in exactly the wrong way?

There is a cool view of the whole non-parametric Bayes thing that I think is very instructive. It's easiest to see in the case of the Pitman-Yor language modeling work by Frank Wood and Yee Whye Teh. The view is "memorize what you can, and back off (to a parametric model) when you can't." This is basically the "backoff" view... where NP Bayes comes in is to control the whole "what you can" aspect. In other words, if you're doing language modeling, try to memorize two grams; but if you haven't seen enough to be confident in your memorization, back off to one grams; and if you're not confident there, back off to a uniform distribution (which is our parametric model -- the base distribution).

Or, if you think about the state-splitting PCFG work (done both at Berkeley and at Stanford), basically what's going on is that we're memorizing as many differences of tree labels as we can, and then backing off to the "generic" label when memorization fails. Or if we look at Trevor Cohn's NP-Bayes answer to DOP, we see a similar thing: memorize big tree chunks, but if you can't, fall back to a simple CFG (our parametric model).

Now, the weird thing is that this mode of memorization is kind of backwards from how I (as an outsider) typically interpret cognitive models (any cogsci people out there, feel free to correct me!). If you take, for instance, morphology, there's evidence that this is exactly not what humans do. We (at least from a popular science) perspective, basically memorize simple rules and then remember exceptions. That is, we remember that to make the past tense of a verb, we add "-ed" (the sound, not the characters) but for certain verbs, we don't: go/went, do/did, etc. You do little studies where you ask people to inflect fake words and they generally follow the rule, not the exceptions (but see * below).

If NP Bayes had its way on this problem (or at least if the standard models I'm familiar with had their way), they would memorize "talk" -> "talked" and "look" -> "looked" and so on because they're so familiar. Sure, it would still memorize the exceptions, but it would also memorize the really common "rule cases too... why? Because of course it could fall back to the parametric model, but these are so common that the standard models would really like to take advantage of the rich-get-richer phenomenon on things like DPs, thus saving themselves cost by memorizing a new "cluster" for each common word. (Okay, this is just my gut feeling about what such models would do, but I think it's at least defensible.) Yes, you could turn the DP "alpha" parameter down, but I guess I'm just not convinced this would do the right thing. Maybe I should just implement such a beast but, well, this is a blog post, not a *ACL paper :P.

Take as an alternative example the language modeling stuff. Basically what it says is "if you have enough data to substantiate memorizing a 5 gram, you should probably memorize a 5 gram." But why? If you could get the same effect with a 2 or 3 gram, why waste the storage/time?!

I guess you could argue "your prior is wrong," which is probably true for most of these models. In which case I guess the question is "what prior does what I want?" I don't have a problem with rich get richer -- in fact, I think it's good in this case. I also don't have a problem with a logarithmic growth rate in the number of exceptions (though I'd be curious how this holds up empirically -- in general, I'm a big fan of checking if your prior makes sense; for instance, Figure 3 (p16) of my supervised clustering paper). I just don't like the notion of memorizing when you don't have to.

(*) I remember back in grad school a linguist from Yale came and gave a talk at USC. Sadly, I can't remember who it was: if anyone wants to help me out, I'd really appreciate it! The basic claim of the talk is that humans actually memorize a lot more than we give them credit for. The argument was in favor of humans basically memorizing all morphology and not backing off to rules like "add -ed." One piece of evidence in favor of this was timing information for asking people to inflect words: the timing seemed to indicate a linear search through a long list of words that could possibly be inflected. I won't say much more about this because I'm probably already misrepresenting it, but it's an interesting idea. And, if true, maybe the NP models are doing exactly what they should be doing!

147 comments:

Peter Turney said...

We (at least from a popular science) perspective, basically memorize simple rules and then remember exceptions.

I just don't like the notion of memorizing when you don't have to.

I'm only a cogsci dilettante, but my intuition is that memory is a lot cheaper than computation in the human brain. Rules are a last resort, when memory fails.

Yoav said...

(I didn't get the connection to the PCFG-state-split work)

On the word inflection task, I think you could quite easily get a more "cognitively-plausible" model and still remain NP-Bayesian if you assume a hierarchical model in which you first choose your inflection mechanism, and then do the inflection itself. If modeled correctly I think this can naturally default to the standard rule(s) for most cases, except for a specific memorized list of special inflections.

Chris said...

I'll ask around my department for the relevant citations, but as I recall, there is some evidence that inflected forms do get memorized, and abstractions function more as a "back-off". Two sources of evidence for this come to mind: child language acquisition and language change. First, children demonstrate a "u"-shaped performance curve on irregular forms- they start out producing forms like "went", then later overgeneralize to things like "goed", and then finally become adult like. This data can obviously be interpreted in several ways, but it does provide some evidence that memorization is "primary". The second source of evidence comes from the fact that more frequent, but regular, word forms exhibit different patterns of diachronic language change from less common ones. Basically, if the "regular" inflection pattern evolves, more frequently used forms are likely to become "frozen" with the older regular form, thus becoming irregular in the new language. Again, this data is up for interpretation, but it certainly is compatible with a view that memorization of frequent forms occurs, even if they are well explained by a "backoff" model.

Bob Carpenter said...

What Peter said. One place you see this in Cog Sci is in the Newell and Simon-type production system models. There, learning looked like memorizing compositions of productions. The problem is that neurons don't fire fast enough for deep reasoning -- we mainly operate by distributed pattern matching.

As to language change, what happens is that the more frequent a word is, the less subject to regularization it is. That is, if we import a new word from a different language, if it doesn't get really popular, it gets regularized. Jean-Baptiste Michel and crew had a nice paper in Nature.

Nick Chater and Dan Jurafsky have both written about Bayesian approaches to psycholinguistics, but I can never seem to find the time to read them.

Fred said...

What Chris & Bob said. As a linguist-cum-cognitive-scientist, I can't really speak to the connection to machine learning, but certainly in phonology (my field) and morphology, there's a push towards instance-based learning models (we tend to call them "exemplar-based", cf. Keith Johnson 1997 and Janet Pierrehumbert 2001 et seq), where you memorize all (most? who knows?) of your data, use some kind of clustering to classify novel inputs, and use some kind of analogical mechanism when you need to produce novel outputs. From the outside it can end up looking a lot like a system that's using rules and exceptions.

The evidence from diachrony (esp. real-time studies of language change) and psycholinguistics (esp. speech perception) is compelling enough to make me think that this is closer to what people are doing than anything else we've come up with so far.

There are some thorny implementation issues that come up when you want to model this using semi-realistic data that I'm trying to tackle for my thesis work...

Bob Moore said...

Hal, I think you will like my EMNLP 09 paper with Chris Quirk, "Less is more: significance based N-gram selection for smaller, better language models." It is based on the idea that if the higher-order observations for an N-gram don't give you any reason to doubt the lower-order probability estimate for the N-gram, then don't store an explicit higher-order estimate.

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winterkoninkje said...

Access is a lot cheaper than computation in the human brain, but neither is free. While we do (somewhere) have rules like "add -ed", we additionally memorize the results of the most common application of these rules.

This is actually one of the tell-tale markers of how fluent a second-language speaker is: the beginner memorizes everything wholesale, the novice relies on rules alone, the fluent knows the rules but also doesn't need to use them. We can see this effect when exposing people to morphologically complex words and asking them to speak them; if the word is familiar it comes out easily, if it's unfamiliar then there's more "chunkiness" in the speech--- even with native speakers when it's truly unfamiliar (e.g. molecular names). And you can see it in the U-pattern learning of child language acquisition and the other examples people've mentioned.

In short, I think there are two modes in the human process. There's one mode that must remember all the exceptions, but which pushes everything else as far back into the "parametric" model as it can. There's a different mode which memoizes the results of the parametric model. These memos can be flushed and reconstructed easily if memory is a concern. And additionally, for the learning process (which is often ignored in NLP), it serves as a staging ground for data to remain when invalidating or altering the hypothesized rules behind them.

Following the distributed pattern matching theories that have been common of late, the "rules" are likely not stored as such but rather are stored by some clustering or analogical process (that is, the rule pattern is stored extensionally in the relations between the instances of the rule's use). But however they're stored, there's a phase distinction between irregular/subregular clusters vs the dominant productive clusters. Because human memory is finite (no matter how large it may be), this is probably due to the productive models becoming large enough to make it worthwhile/necessary to move toward explicit rules rather than memorized tokens.

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Fazel said...

To discuss your post:
Just came to my mind: it's possible to store all n-grams and just memorize short ones and use them as they needed.
For example: It's like answering/generating short, medium or long sentences to a question!

....

Bob Carpenter said...

@Bob I haven't seen your selection method, but Andreas Stolcke's Entropy-Based Pruning of Backoff Language Models has a similar goal. Stolcke removes nodes based on expected rise in entropy.

And it's not just contexts. You can reduce size by quantizing the floating point values, too, as in Whittaker's Quantization-based Language Model Compression.

Measuring size is tricky, though, because you have to make assumptions about storage costs, and those can be affected not only by representation, but even by distributions if you compress them, as in standard codings for reverse-index for information retrieval.

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