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« Judge Alito & Statistics | Main | Expansion of Economics »
2 November 2005
Amy Perfors
If it's of interest, I will be blogging every so often about the numerous ways that humans seem to be remarkably adept statistical learners. This is a big question in cognitive science for two reasons. First, statistical learning looks like a promising approach to help answer the open question of how people learn as well and as quickly as they do. Second, better understanding how humans use statistical learning may be a good way to improve our statistical models in general, or at least investigate in what ways they might be applied to real data.
One of the more impressive demonstrations of human statistical learning is in the area usually called "implicit grammar learning." In this paradigm, people are presented with strings of nonsense syllables like "bo ti lo fa" in a continuous stream for a minute or two. One of the first examples of this paradigm, by Saffran et. al., studied word segmentation -- for example, being able to tell that "the" and "bird" are two separate words, rather than guessing it is "thebird" or "theb" and "ird." If you ever listen to a foreign language, you realize that word boundaries aren't signaled by pauses, which is a huge problem if you're trying to learn the words. Anyway, in the study, syllables occurred in groups of three, thus making "words" like botifa or gikare. As in natural language, there was no pause between words; the only cues to word segmentation were the different transition probabilities between syllables -- that is, "ti" might be always followed by "fa" but "fa" could be followed by any of the first syllables of any other words. Surprisingly, people can pick up on these subtleties: adults who first heard a continuous stream of this "speech" were then able to identify which three-syllable items they heard were "words" or "nonwords" in the "language" they had just heard. That is, the people could correctly say that "botifa" was a word, but "fagika" wasn't, at an above chance level. Since the only cues to this information were in the transition probabilities, people must have been calculating those probabilities implicitly (none had the conscious sense they were doing much of anything). Most surprisingly of all, the same researchers demonstrated in a follow-up study that even 8-month old infants can use these transitional probabilities as cues to word segmentation. Work like this has led many to believe that statistical learning might be one of the most powerful resources infants use during the difficult problem of language learning.
From the modeling perspective, this result can be captured by Markov models in which the learner keeps track of the string of syllables and the transition probabilities between them, updating the transition probabilities as they hear more data. More recent work has begun to investigate whether humans are capable of statistical learning that cannot be captured by a Markov model -- that is, learning nonadjacent dependencies (dependencies between syllables that do not directly follow each other) in a stream of speech. For instance, papers by Gomez et. al. and Onnis et. al. provide evidence that discovering even nonadjacent dependencies is possible through statistical learning, as long as the variability of the intervening items is low or high enough. This has obvious implications for how statistical learning might help in acquiring grammar (in which many dependencies are nonadjacent), but it also opens up new modeling issues, since simple Markov models are no longer applicable. What more sophisticated statistical and computational tools are necessary in order to capture own unconscious, amazing abilities?
Posted by James Greiner at November 2, 2005 4:20 AM
This is very interesting indeed at least to those of us who are interested in the more behavioural approaches to economics like myself.
Posted by: nikete at November 2, 2005 10:04 PM
Yes, very interesting. Not least because you are finding evidence of a statistical abilities not unlike ones found badly lacking in conscious human decision making. It reminds me of the old evolutionary psych experiments that showed that people were adept at using logical devices such as contraposition in natural social context such as determining who cheated on whom, even though they can't do it in the abstract and on purpose to save their lives.
Posted by: Slacker at November 3, 2005 11:23 PM
This is really interesting, Amy. Do we have any idea why it is that humans are such surprisingly good natural statisticians when they don't think about it, but most people are are quite bad at making probability calculations and statistical inferences when they explicitly try (such as the birthday problem or the monte hall problem), except after considerable study?
Gary
Posted by: Gary King
at November 5, 2005 11:21 AM
Slacker: yes, it's a very interesting parallel to other types of failures at conscious, formal reasoning though we can succeed quite well informally. We don't really have a great understanding of why humans seem much better at "conscious" vs "unconscious" statistical reasoning - and the distinction probably get a bit more complex than that, but it will do as a first approximation - but it seems to have something to do with the process of trying to translate it into actual numbers. There's some very interesting work by a researcher named Gigerenzer arguing that when you present statistical information numerically, people have a great deal of trouble remembering it and using it correctly; but present the same information in a different way, and they can.
Some people believe that this is because we have essentially two "types" of reasoning abilities, roughly distinct in our brains - one is evolutionary older, more unconscious, and good at statistical inference but very poor at rule-based thinking; the other is much more frontal-lobe based, recent, and rule-based and abstract. And many of our "errors" in formal thought come because we have to learn how to consciously deploy the rule-based type of thinking. This is all quite speculative, and I'm not quite sure I'm doing it justice in describing it (nor have I made up my mind how much I believe it myself), but I think it might make an interesting post in the future.
Posted by: Amy at November 6, 2005 9:03 AM