In some earlier posts (e.g. here,
here),
I discussed a theory of word acquisition developed by Medina, Snedeker,
Trueswell and Gleitman (MSTG) that I took to question whether learning in the
classical sense ever takes
place. MSTG propose a theory they dub
“Propose-but-Verify” (PbV) that postulates that word learning in kids is (i)
essentially a one trial process where everything but the first encounter with a
word is essentially irrelevant, (ii) at any given time only one hypothesis is
being entertained (i.e. there is no hypothesis testing;/comparison going on)
and (iii) that updating only occurs if the first guess is disconfirmed, and
then it occurs pretty rapidly. MSTG’s
theory has two important features. First, it proceeds without much counting of
any sort, and second, the hypothesis space is very restricted (viz. it includes exactly one hypothesis at any
given time). These two properties leave relatively little for stats to do as
there is no serious comparison of
alternatives going on (as there’s only one candidate at a time and it gets
abandoned when falsified).
This story was always a little too good to be true. After
all, it seems quite counterintuitive to believe that single instances of disconfirmation
would lead word acquirers (WA) to abandon a hypothesis. And not surprisingly, as is often the case,
those things too good to be true might not be. However, a later reconsideration
of the same kind of data by a distinguished foursome (partially overlapping,
partially different) argues that the earlier MSTG model is “almost” true, if not exactly spot on.
In a new paper (here)
Stevens, Yang, Trueswell and Gleitman (SYTG) adopt (i)-(iii) but modify it to
add a more incremental response to relevant data. The new model, like that
older MSTG one, rejects “cross situational learning” which SYTG take to involve
“the tabulation of multiple, possibly all, word-meaning associations across
learning instances” (p.3) but adds a more gradient probabilistic data evaluation procedure. The process works as
follows. It has two parts.
First, for “familiar” words, this account, dubbed “Pursuit
with abandon” (p. 3) (“Pursuit” (P) for short), selects the single most highly
valued option (just one!) and rewards it incrementally if consistent with the
input and if not it decreases its score a bit while also randomly selecting a
single new meaning from “the available meanings in that utterance” (p. 2) and
rewarding it a bit. This take-a-little, give-a-little is the stats part. In
contrast to PbV, P does not completely dump a disconfirmed meaning, but only
lowers its overall score somewhat. Thus,
“a disconfirmed meaning may still remain the most probable hypothesis and will
be selected for verification the next time the word is presented in the
learning data” (p. 3). SYTG note that replacing MSTG’s one strike you’re out
“counting” procedure, with a more gradient probabilistic evaluation measure
adds a good deal of “robustness” to the learning procedure.
Second, for novel words, P encodes “a probabilistic form of
the Mutual Exclusivity Constraint…[viz.] when encountering novel words,
children favor mapping to novel rather than familiar meanings” (p. 4). Here too the procedure is myopic, selecting
one option among many and sticking with it until it fails enough to be replaced
via step one above.
Thus, the P model, from what I can tell, is effectively the
old PbV model but with a probabilistic procedure for, initially, deciding on
which is the “least probable” candidate (i.e. to guide an initial pick) and for
(dis)confirming a given candidate (i.e. to up/downgrade a previously
encountered entry). Like the PbV, P is
very myopic. Both reject cross situational learning and concentrate on one
candidate at a time, ignoring other options if all goes well and choosing at
random if things go awry.
This is the P model. Using simulations based on Childes
data, the paper goes on to show that this system is very good when compared
both with PbV and, more interestingly, with more comprehensive theories that
keep many hypothesis in play throughout the acquisition process. To my mind,
the most interesting comparison is with Bayesian approaches. I encourage you to
take a look at the discussion of the simulations (section 3 in the paper). The bottom line is that the P model bested
the three others on overall score, including the Bayesian alternative. Moreover, SYTG was able to identify the main
reason for the success: non-myopic comprehensive procedures fail to
sufficiently value “high informative cues” provided early in the acquisition
process. Why? Because comprehensive
comparison among a wide range of alternatives serves to “dilute the probability
space” for correct hits, thereby “making the correct meaning less likely to be
added to the lexicon” (P. 6-7). It seems
that in the acquisition settings found in CHILDES (and in MSTGs more realistic visual
settings), this dilution prevents WAs from more rapidly building up their
lexicons. As SYTG put it:
The advantage of the Pursuit model
over cross-situational models derives from its apparent sub-optimal design. The
pursuit of the most favored hypothesis limits the range of competing meanings.
But at the same time, it obviates the dilution of cues, especially the highly
saline first scene…which is weakened by averaging with more ambiguous leaning
instances…[which] are precisely the types of highly salient instances that the
learner takes advantage of…(p. 7).
There is a second advantage of the P model as compared to a
more sophisticated and comprehensive Bayesian approach. SYTG just touch on this, but I think it is worth
mentioning. The Bayesian model is computationally very costly. In fact, SYTG
notes that full simulations proved impractical as “each simulation can take
several hours to run” (p. 8). Scaling up
is a well-known problem for Bayesian accounts (see here),
which is probably why Bayesian proposals are often presented as Marrian level 1
theories rather than actual algorithmic procedures. At any rate, it seems that
the computational cost stems from precisely the feature that makes Bayesian
models so popular: their comprehensiveness. The usual procedure is to make the
hypothesis space as wide as possible and then allow the “data” to find the
optimal one. However, it is precisely this feature that makes the obvious
algorithm built on this procedure intractable.
In effect, SYTG show the potential value of myopia, i.e. in
very narrow hypothesis spaces. Part of the value lies in computational
tractability. Why? The narrower the hypothesis space, the less work is required
of Bayesian procedures to effectively navigate the space of alternatives to
find the best candidate. In other words,
if the alternatives are few in number, the bulk of explaining why we see what
we get will lie not with fancy evaluation procedures, but with the small set of
options that are being evaluated. How to count may be important, but it is less
important the fewer things there are to count among. In the limit,
sophisticated methods of counting may be unnecessary, if not downright
unproductive.
The theme that comprehensiveness may not actually be
“optimal” is one that SYTG emphasize at the end of their paper. Let me end this
little advertisement by quoting them again:
Our model pursues the [i.e. unique
NH] highly valued, and thus probabilistically defined, word meaning at the
expense of other meaning candidates. By
contrast, cross-situational models do not favor any one particular meaning, but
rather tabulate statistics across learning instances to look for consistent
co-occurrences. While the cross-situational
approach seems optimally designed [my emph, NH], its advantage seems
outweighed by its dilution effects that distract the learner away from clear
unambiguous learning instances…It is notable that the apparently sub-optimal
Pursuit model produces superior results over the more powerful models with
richer statistical information about words and their associated meanings: word
learning is hard, but trying to hard may not help.
I would put this slightly differently: it seems that what
you choose to compare may be as (more?) important than how you choose to
compare them. SYTG reinforces MSTG’s earlier warning about the perils of
open-mindedness. Nothing like a well designed narrow hypothesis space to aid
acquisition. I leave the rationalist/empiricist overtones of this as an
exercise for the reader.
