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Thanks for this. Please com...Very nice information. Thanks for this. Please come visit my site <a href="http://www.louisvillekyguide.com" rel="nofollow">Aurora Phone Book</a> when you got time.rr8004https://www.blogger.com/profile/17668784480317088693noreply@blogger.comtag:blogger.com,1999:blog-19803222.post-56671626467592106442010-01-10T00:40:12.030-07:002010-01-10T00:40:12.030-07:00Very nice information. Thanks for this. Please com...Very nice information. Thanks for this. Please come visit my site <a href="http://www.louisvillekyguide.com" rel="nofollow">Colorado CO Phone Directory</a> when you got time.rr8004https://www.blogger.com/profile/17668784480317088693noreply@blogger.comtag:blogger.com,1999:blog-19803222.post-69395853048935670382010-01-03T13:24:20.799-07:002010-01-03T13:24:20.799-07:00@Bob
That Shannon link is very nice. In statistic...@Bob<br /><br />That Shannon link is very nice. In statistics, as far as I can tell, Box (1980) and Rubin (1984) are viewed by many as the first clear statements of posterior predictive checks from a calibrated Bayes perspective, but the Shannon example is great; I'll definitely cite it from now on.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-19803222.post-60335330964897619092009-12-31T21:34:32.182-07:002009-12-31T21:34:32.182-07:00Well, I've been skiing so hard the last two da...Well, I've been skiing so hard the last two days, exploiting the bounty of yesterday's Tahoe storm, that I'm too tired to produce much in the way of technical comment. I'll just note that "I don't care at all if feature 18329 has x% effect on predicting whether a word is a determiner or not!" sounds a bit like sour grapes ;) If you had that information, it could help you debug your model when it goes badly wrong because of a change in the data distribution. Most academic ML work is not forced to deal with that critical issue because it is based on fixed datasets.Fernando Pereirahttps://www.blogger.com/profile/05849361902113771573noreply@blogger.comtag:blogger.com,1999:blog-19803222.post-58992577735994204002009-12-31T14:56:53.070-07:002009-12-31T14:56:53.070-07:00Anonymous: By "prior" I meant it in the ...Anonymous: By "prior" I meant it in the Bayes' rule sense, not in the Bayesian sense... i.e., it is something like p(true image) which then gets corrupted into p(observation | true image). the "prior" then is, actually, a posterior given data, and it's that that doesn't generate anything remotely like images.<br /><br />Analogously in NLP, as Bob says, a language model doesn't generate anything like sentences (see previous post of small changes begetting negative examples).<br /><br />I actually think people <i>do</i> do a fair amount of something roughly analogous to posterior predictive simulations, but in the one-best sense that Bob doesn't like. That is, people run their models, see what they do, and make adjustments as appropriate. This is probably one of the major ways in which progress is made.<br /><br />But Bob is totally right: I don't care at all if feature 18329 has x% effect on predicting whether a word is a determiner or not!<br /><br />Back when I was a student, I took a class from Roni Rosenfeld where we had to build a system to disambiguate between true English sentences and sentences generated by a trigram language model. It's actually quite hard, until you start looking at using parsers and things like that. Nowadays I'd replace that with a fivegram and I bet it would be even more difficult. Of course, people do it with no effort at all (the bad ones "hurt" to read).halhttps://www.blogger.com/profile/02162908373916390369noreply@blogger.comtag:blogger.com,1999:blog-19803222.post-42623296624599614532009-12-31T14:32:30.652-07:002009-12-31T14:32:30.652-07:00@Anonymous Computer scientists only tend to care ...@Anonymous Computer scientists only tend to care about the predictive accuracy of their models. <br /><br />My main beef is that they only tend to consider first-best predictions (e.g. 0/1 loss for classification) and not care about the probability assigned (e.g. log loss). This makes it hard to trade off recall for precision (or sensitivity for specificity) in an application, and most applications require either high precision or high recall.<br /><br />Computer scientists don't usually evaluate individual parameters for significance or give them causal interpretations. That's because they're not interested in assessing the effect of education on income, but are rather interested in a single prediction such as "should I give this person a credit card?". <br /><br />For language models, lack of predictive checks isn't so surprising when you consider that no one has ever built a language model (and I'm not talking just n-gram models here) that generates anything like sensible documents from the posterior predictive distribution. <br /><br />You do see just this kind of posterior predictive checking in section 3 of Shannon's 1948 <a href="http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf" rel="nofollow">Mathematical Theory of Communication</a> (yes, that's 61+ years ago) paper that introduced n-gram language models! What you see right away is the Markovian nature of n-gram models not representing long-term topical or syntactic consistency (as in Stephen Merrit's song title "Doris Day the Earth Stood Still").<br /><br />On the other hand, you can do posterior predictive checks on smaller units than full docs. For instance, you could scatterplot expectated versus empirical counts of the next word given the previous word(s). You also see this in comparing prior coefficient distributions to posteriors (e.g. Goodman's paper on the Laplace [double exponential] prior).Bob Carpenterhttp://lingpipe-blog.com/noreply@blogger.comtag:blogger.com,1999:blog-19803222.post-48153183705639180422009-12-30T20:07:32.468-07:002009-12-30T20:07:32.468-07:00I've always looked at the image problem as an ...I've always looked at the image problem as an argument for posterior predictive checks rather than straight draws from the prior. It's possible that your original prior may be pretty diffuse but still puts probability enough mass on real images. Given data, the posterior should then be able to generate new images similar to the data, which is the standard textbook argument for posterior predictive checks (e.g. Gelman et al, 2003). Clearly all the current models fail. But posterior predictive checks should give hints about how to improve image models.<br /><br />The same applies to language models. The prior doesn't need to generate sensible documents, but posterior predictive simulations should, given enough training data. Otherwise your model isn't rich enough and your prior doesn't put enough weight on true images.<br /><br />Coming from a stats background, I've actually been surprised at how little iteration there is between posterior predictive checks and model building in computer science literature. This is a huge theme by statisticians doing applied Bayesian work in other fields. The payoff seems particularly big in CS applications because the models are so bad/hard.Anonymousnoreply@blogger.com