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An Introduction to Probabilistic Graphical Models (2003) [pdf]

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21–30 of 37 posts

Re: An Introduction to Probabilistic Graphical Models (2003) [pdf]

#21

There's an excellent course on PGM by Koller on Coursera. My friend took it and now he's a PGM evangelist. If you are wondering where PGM lies in the spectrum of machine learning, you should research the difference between generative and discriminate modeling. We have been driven to PGM to solve our ML problem that was hard to frame as A NN. Mainly because we had some priors we needed to encode to make the problem tr…

The hot use-case of the PGMs approach has often been in the discriminative setting (see M^3 and latent SVM) - which is good because discriminative classifiers work well with fewer data points (see Ng, Russel).

Re: An Introduction to Probabilistic Graphical Models (2003) [pdf]

#22
post #2

PGM seems to me harder than neural nets, but the trend in the last couple of years is to include probabilities in neural nets, so they're hot.

Not an expert but PGMs are mostly a superset of NN, so it's kinda understandable.

They are not.

Re: An Introduction to Probabilistic Graphical Models (2003) [pdf]

#23
post #8

A few comments have mentioned neural nets in this post. adamnemecek mentions in this thread that PGMs are a superset of neural networks, and and Thomas Wiecki has a few excellent blog posts on creating bayesian neural networks using pymc3.[0][1][2] If you're curious about how these two concepts can be brought together I highly recommend reading through these three posts. [0] http://twiecki.github.io/blog/2016/06/01/b…

Do they train with backpropagation efficiently?

No, back-propagation would not give full Bayesian inference (although there are some tricks [0]). They instead use variational inference[1], which allows for fast inference of continuous PGMs.

[0] http://mlg.eng.cam.ac.uk/yarin/blog_2248.html

[1] https://arxiv.org/abs/1603.00788

Re: An Introduction to Probabilistic Graphical Models (2003) [pdf]

#24
post #17

Earlier quoted context omitted.

It's linear in singly connected networks, not for multiply connected graphs. However NP-hard is the worst case as I mentioned (p288 Koller & Friedman)

by multiply connected graphs do you mean graphs with cycles ?

Yes, although in directed acyclic graphs the 'cycles' manifest as multiple paths to a node.

Re: An Introduction to Probabilistic Graphical Models (2003) [pdf]

#25
post #24

Earlier quoted context omitted.

by multiply connected graphs do you mean graphs with cycles ?

Yes, although in directed acyclic graphs the 'cycles' manifest as multiple paths to a node.

cycles can be handled in two ways: if you are happy with approximate solutions, loopy BP can give that (still linear, but may take longer and there's parameter tuning), for exact solutions you can rewrite the graph to "carry" dependencies (latest paper by Frey)

Re: An Introduction to Probabilistic Graphical Models (2003) [pdf]

#29

This course also referred M.I Jordan book: http://imagine.enpc.fr/~obozinsg/teaching/mva_gm/fall2016/ One of the best course I have ever taken, F. Bach and G. Obozinski are incredible teachers.

I couldn't agree more! This course features has slides, which many will prefer.

Re: An Introduction to Probabilistic Graphical Models (2003) [pdf]

#30
post #13

Earlier quoted context omitted.

What is the connection other than "they both have graphs somewhere in them"? I sort of see what you mean since NNs transport information across a graph in a straightforward (non-loopy) way, and PGMs can propagate information in crazy (neverending loops) ways when doing belief propagation...

From my limited understanding, pure NNs are not able to express confidence in predictions. By adding probability to the NN, we can have both predictions and confidence scores. In practice, noise is being injected, or connections dropped out randomly, then predictions averaged over multiple runs.

Sure they can, many output probabilities: http://deeplearning.net/tutorial/mlp.html#mlp
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