On Mon, Sep 19, 2011 at 06:31:34PM +0100, Brian Holt wrote:
> Does [Bayesian Inference](http://en.wikipedia.org/wiki/Bayesian_inference)
> fall under the scope of scikit-learn? Probabilistic graphical models
> are an exciting field in machine learning, with the theory going back
> at least as far as 1982.

Probabilistic graphical models are not synonymous with Bayesian inference,
despite the misleading "Bayesian networks" nomenclature.

Graphical models are simply a formalism for expressing families of
probability distributions on random variables and conditional independence
assumptions between them. They can be (and usually are) fit by maximum
likelihood or MAP estimation, meaning a single point estimate for the
parameters.

Bayesian inference involves placing priors on model parameters and (usually)
integrating out model parameters, either analytically or with Markov Chain
Monte Carlo estimates, to obtain a "predictive distribution" on test points.

In general, it's difficult to write fully general graphical model code in
such a way that learning and inference is acceptably fast, and usually
specialized implementations of specific graphical models (i.e. Hidden Markov
Models, Kalman filters, etc.) are significantly more efficient. It might be
possible to include something like that in scikit-learn but it would be
difficult to both write and maintain.

As for the Bayesian inference setting, there is already PyMC, and I think the
focus should be on improving that project rather than trying to make
scikit-learn do everything.

My $0.02,

David

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