On Chomsky and the Two Cultures of Statistical Learning (2011)

Re:On Chomsky and the Two Cultures of Statistical Learning (... by Rainymood on Thursday March 01, 2018 @03:46AM (#16490525)

In the linear regression model the points (x,y) have the following relationship (in the most simple example)

> 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.

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Re:On Chomsky and the Two Cultures of Statistical Learning (... by in9 on Thursday March 01, 2018 @03:35PM (#16496001)

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.

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