> A statistical model is a mathematical model which is modified or trained by the input of data points.
> A probabilistic model specifies a probability distribution over possible values of random variables, e.g., P(x, y), rather than a strict deterministic relationship, e.g., y = f(x).
For example, by these definitions, we could use a linear regression as a statistical model that is not a probabilistic model; we could make a bayes network (using known distributions) as a probabilistic model that is not a statistical model; and we could make a Hidden Markov Model trained on sample data that would be both a statistical and probabilistic model.
Usually, every statistical model is a special case of a probabilistic model in which its parameters have been estimated by data.
The regression E[Y|X] is basically the mean of a gaussian distribution of Y given X with sigma set to the error term. The whole gaussian distribution part is the probabilistic model. But to estimate wich parameters make up this model in a particular application (together with how to check if it is valid or not) is the statistical modeling part.
I used to think the same way. But after spending the last few years getting frustrated trying to create more complex linguistic systems, e.g., dialog systems or scientific articles understanding, I am coming to the conclusion that the current statistical approach is a dead end. It’s actually impeding the field because it’s working so well for certain tasks that when people are trying to build systems with real understanding, they can’t match the performance obtained by gigantic language models. But the answer is not Chomsky, it’s semantic grounding in the real world rather than looking at language as a sequence of symbols.
I agree. I think Norvig is right that interpretation and understanding may be inherently probabilistic problems, but the accuracy of statistical models sure seems to just be a matter of "playing the odds"; correctly performing some task doesn't imply any real "understanding" by the model. If the system had "semantic grounding" as you call it, that would go a long way towards disambiguating during interpretation & understanding tasks.
Norvig didn't really seem to address the "collecting butterflies" part. At least, not sufficiently such I noticed.
Sure, science/engineering are fine with allowing for numerous failures and dead ends. Yeah that tracks with history, but is that a good justification?
And what about the economy? Doesn't this imply investment into these models is going to be of diminishing value sooner than later?
This is Chomsky. Not hard to see it as a tacit indictment of corporate investment these days as well. Corporate is not above manipulation curriculum for their gains. Chomsky is a hardcore proponent of academic freedom.
Are we investing a lot of time and money on the wrong efforts? Would we easily acknowledge if we were?
This is a fantastic challenge for computer engineers: create an interpreter or compiler for a programming language, based on statistic modeling. How likely is it that combining the token "foo" with "bar" using a mathematical operator is a valid construct, based on experience from other programs? What will the resulting value usually be, based on prior experience?
Let me rephrase the debate, in a way that can hopefully clarify the main point of contention:
C: Your statistical models are woefully inadequate at describing language.
N: That inadequacy is related particularly to Markov models and Ngram models. More sophisticated statistical models will be adequate.
C: Then why haven't you built the more sophisticated models? Why are you still using Markov models and Ngrams?
N: Those work well enough for engineering applications.
The attitude of "it works well enough for engineering" is what Chomsky is actually criticizing. And that criticism is entirely valid: an empirical scientist would never claim that a theory is true because it can be used in engineering.
It's funny to me that Norvig holds up the PCFG as an example of a new and improved statistical model of language. The PCFG is actually terrible in many ways, the most obvious of which is that it doesn't take into account the Theta Criterion [1], one of the most fundamental phenomena of language. An example of this rule is that a noun phrase can only have one determiner. This restriction is so strong that it will never be violated in any kind of professionally composed text. But it is very awkward to try to encode this rule in a PCFG (you essentially have to split the NP symbol into DetNP vs UndetNP). I wrote a blog post describing the problems of the PCFG formalism:
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[ 5.3 ms ] story [ 49.2 ms ] threadIf you have a low IQ, you should pick your responsibilities carefully and do everyone a favor.
> A probabilistic model specifies a probability distribution over possible values of random variables, e.g., P(x, y), rather than a strict deterministic relationship, e.g., y = f(x).
For example, by these definitions, we could use a linear regression as a statistical model that is not a probabilistic model; we could make a bayes network (using known distributions) as a probabilistic model that is not a statistical model; and we could make a Hidden Markov Model trained on sample data that would be both a statistical and probabilistic model.
> y_t = x_t + e_t
where e_t is some error term. Would this be a statistical or probabilistic model?
We do know that the best predictor is just the conditional expectation (in a linear setting bla bla)
> y_pred = E[x_t + e_t | .. ] = x_t
Or is this what you mean with "model"? The predictor? Sorry for being a bit confused.
The regression E[Y|X] is basically the mean of a gaussian distribution of Y given X with sigma set to the error term. The whole gaussian distribution part is the probabilistic model. But to estimate wich parameters make up this model in a particular application (together with how to check if it is valid or not) is the statistical modeling part.
https://news.ycombinator.com/item?id=11951444 (2016)
https://news.ycombinator.com/item?id=2591154 (2011)
Sure, science/engineering are fine with allowing for numerous failures and dead ends. Yeah that tracks with history, but is that a good justification?
And what about the economy? Doesn't this imply investment into these models is going to be of diminishing value sooner than later?
This is Chomsky. Not hard to see it as a tacit indictment of corporate investment these days as well. Corporate is not above manipulation curriculum for their gains. Chomsky is a hardcore proponent of academic freedom.
Are we investing a lot of time and money on the wrong efforts? Would we easily acknowledge if we were?
Some video clips of this interview by Yarden Katz: http://yarden.github.io/pages/chomsky/
C: Your statistical models are woefully inadequate at describing language.
N: That inadequacy is related particularly to Markov models and Ngram models. More sophisticated statistical models will be adequate.
C: Then why haven't you built the more sophisticated models? Why are you still using Markov models and Ngrams?
N: Those work well enough for engineering applications.
The attitude of "it works well enough for engineering" is what Chomsky is actually criticizing. And that criticism is entirely valid: an empirical scientist would never claim that a theory is true because it can be used in engineering.
It's funny to me that Norvig holds up the PCFG as an example of a new and improved statistical model of language. The PCFG is actually terrible in many ways, the most obvious of which is that it doesn't take into account the Theta Criterion [1], one of the most fundamental phenomena of language. An example of this rule is that a noun phrase can only have one determiner. This restriction is so strong that it will never be violated in any kind of professionally composed text. But it is very awkward to try to encode this rule in a PCFG (you essentially have to split the NP symbol into DetNP vs UndetNP). I wrote a blog post describing the problems of the PCFG formalism:
https://ozoraresearch.wordpress.com/2017/03/17/chuckling-a-b...
[1]: https://en.wikipedia.org/wiki/Theta_criterion