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Structures of the Bacterial Ribosome in Classical and Hybrid States of tRNA Binding
Mapping the NPHP-JBTS-MKS Protein Network Reveals Ciliopathy Disease Genes and Pathways
Double-Strand Break Repair-Independent Role for BRCA2 in Blocking Stalled Replication Fork Degradation by MRE11
Establishment and Maintenance of Alternative Chromatin States at a Multicopy Gene Locus
An Epigenetic Signature for Monoallelic Olfactory Receptor Expression
Distinct p53 Transcriptional Programs Dictate Acute DNA-Damage Responses and Tumor Suppression
An ADIOL-ERβ-CtBP Transrepression Pathway Negatively Regulates Microglia-Mediated Inflammation
A Hormone-Dependent Module Regulating Energy Balance
Class IIa Histone Deacetylases Are Hormone-Activated Regulators of FOXO and Mammalian Glucose Homeostasis
Physics: for groundbreaking experiments regarding the two-dimensional material graphene
Chemistry: for palladium-catalyzed cross couplings in organic synthesis
Physiology or Medicine: for the development of in vitro fertilization
What doesn't Chomsky like about statistical models?
I said that statistical models are sometimes confused with probabilistic models; let's first consider the extent to which Chomsky's objections are actually about probabilistic models. In 1969 he famously wrote:
But it must be recognized that the notion of "probability of a sentence" is an entirely useless one, under any known interpretation of this term.
His main argument being that, under any interpretation known to him, the probability of a novel sentence must be zero, and since novel sentences are in fact generated all the time, there is a contradiction. The resolution of this contradiction is of course that it is not necessary to assign a probability of zero to a novel sentence; in fact, with current probabilistic models it is well-known how to assign a non-zero probability to novel occurrences, so this criticism is invalid, but was very influential for decades. Previously, in Syntactic Structures (1957) Chomsky wrote:
I think we are forced to conclude that ... probabilistic models give no particular insight into some of the basic problems of syntactic structure.
I never, ever, ever, ever, ... fiddle around in any way with electrical equipment. She never, ever, ever, ever, ... fiddles around in any way with electrical equipment. * I never, ever, ever, ever, ... fiddles around in any way with electrical equipment. * She never, ever, ever, ever, ... fiddle around in any way with electrical equipment.
This criticism is correct, but it is a criticism of Markov-chain models—it has nothing to do with probabilistic models (or trained models) at all. Moreover, since 1957 we have seen many types of probabilistic language models beyond the Markov-chain word models. Examples 1-4 above can in fact be distinguished with a finite-state model that is not a chain, but other examples require more sophisticated models. The best studied is probabilistic context-free grammar (PCFG), which operates over trees, categories of words, and individual lexical items, and has none of the restrictions of finite-state models. We find that PCFGs are state-of-the-art for parsing performance and are easier to learn from data than categorical context-free grammars. Other types of probabilistic models cover semantic and discourse structures. Every probabilistic model is a superset of a deterministic model (because the deterministic model could be seen as a probabilistic model where the probabilities are restricted to be 0 or 1), so any valid criticism of probabilistic models would have to be because they are too expressive, not because they are not expressive enough.
In Syntactic Structures, Chomsky introduces a now-famous example that is another criticism of finite-state probabilistic models:
Neither (a) 'colorless green ideas sleep furiously' nor (b) 'furiously sleep ideas green colorless', nor any of their parts, has ever occurred in the past linguistic experience of an English speaker. But (a) is grammatical, while (b) is not.
"It is neutral green, colorless green , like the glaucous water lying in a cellar." The Paris we remember, Elisabeth Finley Thomas (1942).
, like the glaucous water lying in a cellar." The Paris we remember, Elisabeth Finley Thomas (1942). "To specify those green ideas is hardly necessary, but you may observe Mr. [D. H.] Lawrence in the role of the satiated aesthete." The New Republic: Volume 29 p. 184, William White (1922).
is hardly necessary, but you may observe Mr. [D. H.] Lawrence in the role of the satiated aesthete." The New Republic: Volume 29 p. 184, William White (1922). "Ideas sleep in books." Current Opinion: Volume 52, (1912).
But regardless of what is meant by "part," a statistically-trained finite-state model can in fact distinguish between these two sentences. Pereira (2001) showed that such a model, augmented with word categories and trained by expectation maximization on newspaper text, computes that (a) is 200,000 times more probable than (b). To prove that this was not the result of Chomsky's sentence itself sneaking into newspaper text, I repeated the experiment, using a much cruder model with Laplacian smoothing and no categories, trained over the Google Book corpus from 1800 to 1954, and found that (a) is about 10,000 times more probable. If we had a probabilistic model over trees as well as word sequences, we could perhaps do an even better job of computing degree of grammaticality.
Furthermore, the statistical models are capable of delivering the judgment that both sentences are extremely improbable, when compared to, say, "Effective green products sell well." Chomsky's theory, being categorical, cannot make this distinction; all it can distinguish is grammatical/ungrammatical.
Another part of Chomsky's objection is "we cannot seriously propose that a child learns the values of 109 parameters in a childhood lasting only 108 seconds." (Note that modern models are much larger than the 109 parameters that were contemplated in the 1960s.) But of course nobody is proposing that these parameters are learned one-by-one; the right way to do learning is to set large swaths of near-zero parameters simultaneously with a smoothing or regularization procedure, and update the high-probability parameters continuously as observations comes in. And noone is suggesting that Markov models by themselves are a serious model of human language performance. But I (and others) suggest that probabilistic, trained models are a better model of human language performance than are categorical, untrained models. And yes, it seems clear that an adult speaker of English does know billions of language facts (for example, that one says "big game" rather than "large game" when talking about an important football game). These facts must somehow be encoded in the brain.
It seems clear that probabilistic models are better for judging the likelihood of a sentence, or its degree of sensibility. But even if you are not interested in these factors and are only interested in the grammaticality of sentences, it still seems that probabilistic models do a better job at describing the linguistic facts. The mathematical theory of formal languages defines a language as a set of sentences. That is, every sentence is either grammatical or ungrammatical; there is no need for probability in this framework. But natural languages are not like that. A scientific theory of natural languages must account for the many phrases and sentences which leave a native speaker uncertain about their grammaticality (see Chris Manning's article and its discussion of the phrase "as least as"), and there are phrases which some speakers find perfectly grammatical, others perfectly ungrammatical, and still others will flip-flop from one occasion to the next. Finally, there are usages which are rare in a language, but cannot be dismissed if one is concerned with actual data. For example, the verb quake is listed as intransitive in dictionaries, meaning that (1) below is grammatical, and (2) is not, according to a categorical theory of grammar.
The earth quaked. ? It quaked her bowels.
Steve Abney points out that probabilistic models are better suited for modeling language change. He cites the example of a 15th century Englishman who goes to the pub every day and orders "Ale!" Under a categorical model, you could reasonably expect that one day he would be served eel, because the great vowel shift flipped a Boolean parameter in his mind a day before it flipped the parameter in the publican's. In a probabilistic framework, there will be multiple parameters, perhaps with continuous values, and it is easy to see how the shift can take place gradually over two centuries.
Thus it seems that grammaticality is not a categorical, deterministic judgment but rather an inherently probabilistic one. This becomes clear to anyone who spends time making observations of a corpus of actual sentences, but can remain unknown to those who think that the object of study is their own set of intuitions about grammaticality. Both observation and intuition have been used in the history of science, so neither is "novel," but it is observation, not intuition that is the dominant model for science.
Now let's consider what I think is Chomsky's main point of disagreement with statistical models: the tension between "accurate description" and "insight." This is an old distinction. Charles Darwin (biologist, 1809–1882) is best known for his insightful theories but he stressed the importance of accurate description, saying "False facts are highly injurious to the progress of science, for they often endure long; but false views, if supported by some evidence, do little harm, for every one takes a salutary pleasure in proving their falseness." More recently, Richard Feynman (physicist, 1918–1988) wrote "Physics can progress without the proofs, but we can't go on without the facts."
Butterflies Butterflies
On the other side, Ernest Rutherford (physicist, 1871–1937) disdained mere description, saying "All science is either physics or stamp collecting." Chomsky stands with him: "You can also collect butterflies and make many observations. If you like butterflies, that's fine; but such work must not be confounded with research, which is concerned to discover explanatory principles."
Acknowledging both sides is Robert Millikan (physicist, 1868–1953) who said in his Nobel acceptance speech "Science walks forward on two feet, namely theory and experiment ... Sometimes it is one foot that is put forward first, sometimes the other, but continuous progress is only made by the use of both."
The two cultures
Leo Breiman Leo Breiman
After all those distinguished scientists have weighed in, I think the most relevant contribution to the current discussion is the 2001 paper by Leo Breiman (statistician, 1928–2005), Statistical Modeling: The Two Cultures. In this paper Breiman, alluding to C.P. Snow, describes two cultures:
First the data modeling culture (to which, Breiman estimates, 98% of statisticians subscribe) holds that nature can be described as a black box that has a relatively simple underlying model which maps from input variables to output variables (with perhaps some random noise thrown in). It is the job of the statistician to wisely choose an underlying model that reflects the reality of nature, and then use statistical data to estimate the parameters of the model.
Second the algorithmic modeling culture (subscribed to by 2% of statisticians and many researchers in biology, artificial intelligence, and other fields that deal with complex phenomena), which holds that nature's black box cannot necessarily be described by a simple model. Complex algorithmic approaches (such as support vector machines or boosted decision trees or deep belief networks) are used to estimate the function that maps from input to output variables, but we have no expectation that the form of the function that emerges from this complex algorithm reflects the true underlying nature.
It seems that the algorithmic modeling culture is what Chomsky is objecting to most vigorously. It is not just that the models are statistical (or probabilistic), it is that they produce a form that, while accurately modeling reality, is not easily interpretable by humans, and makes no claim to correspond to the generative process used by nature. In other words, algorithmic modeling describes what does happen, but it doesn't answer the question of why.
Breiman's article explains his objections to the first culture, data modeling. Basically, the conclusions made by data modeling are about the model, not about nature. (Aside: I remember in 2000 hearing James Martin, the leader of the Viking missions to Mars, saying that his job as a spacecraft engineer was not to land on Mars, but to land on the model of Mars provided by the geologists.) The problem is, if the model does not emulate nature well, then the conclusions may be wrong. For example, linear regression is one of the most powerful tools in the statistician's toolbox. Therefore, many analyses start out with "Assume the data are generated by a linear model..." and lack sufficient analysis of what happens if the data are not in fact generated that way. In addition, for complex problems there are usually many alternative good models, each with very similar measures of goodness of fit. How is the data modeler to choose between them? Something has to give. Breiman is inviting us to give up on the idea that we can uniquely model the true underlying form of nature's function from inputs to outputs. Instead he asks us to be satisfied with a function that accounts for the observed data well, and generalizes to new, previously unseen data well, but may be expressed in a complex mathematical form that may bear no relation to the "true" function's form (if such a true function even exists). Chomsky takes the opposite approach: he prefers to keep a simple, elegant model, and give up on the idea that the model will represent the data well. Instead, he declares that what he calls performance data—what people actually do—is off limits to linguistics; what really matters is competence—what he imagines that they should do.
Bill O'Reilly
Laplace Bill O'ReillyLaplace
In January of 2011, television personality Bill O'Reilly weighed in on more than one culture war with his statement "tide goes in, tide goes out. Never a miscommunication. You can't explain that," which he proposed as an argument for the existence of God. O'Reilly was ridiculed by his detractors for not knowing that tides can be readily explained by a system of partial differential equations describing the gravitational interaction of sun, earth, and moon (a fact that was first worked out by Laplace in 1776 and has been considerably refined since; when asked by Napoleon why the creator did not enter into his calculations, Laplace said "I had no need of that hypothesis."). (O'Reilly also seems not to know about Deimos and Phobos (two of my favorite moons in the entire solar system, along with Europa, Io, and Titan), nor that Mars and Venus orbit the sun, nor that the reason Venus has no moons is because it is so close to the sun that there is scant room for a stable lunar orbit.) But O'Reilly realizes that it doesn't matter what his detractors think of his astronomical ignorance, because his supporters think he has gotten exactly to the key issue: why? He doesn't care how the tides work, tell him why they work. Why is the moon at the right distance to provide a gentle tide, and exert a stabilizing effect on earth's axis of rotation, thus protecting life here? Why does gravity work the way it does? Why does anything at all exist rather than not exist? O'Reilly is correct that these questions can only be addressed by mythmaking, religion or philosophy, not by science.
Chomsky has a philosophy based on the idea that we should focus on the deep whys and that mere explanations of reality don't matter. In this, Chomsky is in complete agreement with O'Reilly. (I recognize that the previous sentence would have an extremely low probability in a probabilistic model trained on a newspaper or TV corpus.) Chomsky believes a theory of language should be simple and understandable, like a linear regression model where we know the underlying process is a straight line, and all we have to do is estimate the slope and intercept.
For example, consider the notion of a pro-drop language from Chomsky's Lectures on Government and Binding (1981). In English we say, for example, "I'm hungry," expressing the pronoun "I". But in Spanish, one expresses the same thought with "Tengo hambre" (literally "have hunger"), dropping the pronoun "Yo". Chomsky's theory is that there is a "pro-drop parameter" which is "true" in Spanish and "false" in English, and that once we discover the small set of parameters that describe all languages, and the values of those parameters for each language, we will have achieved true understanding.
Dana Carvey Dana Carvey
The problem is that reality is messier than this theory. Here are some dropped pronouns in English:
From the beginning, Chomsky has focused on the generative side of language. From this side, it is reasonable to tell a non-probabilistic story: I know definitively the idea I want to express—I'm starting from a single semantic form—thus all I have to do is choose the words to say it; why can't that be a deterministic, categorical process? If Chomsky had focused on the other side, interpretation, as Claude Shannon did, he may have changed his tune. In interpretation (such as speech recognition) the listener receives a noisy, ambiguous signal and needs to decide which of many possible intended messages is most likely. Thus, it is obvious that this is inherently a probabilistic problem, as was recognized early on by all researchers in speech recognition, and by scientists in other fields that do interpretation: the astronomer Laplace said in 1819 "Probability theory is nothing more than common sense reduced to calculation," and the physicist James Maxwell said in 1850 "The true logic for this world is the calculus of Probabilities, which takes account of the magnitude of the probability which is, or ought to be, in a reasonable man's mind."