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Deep Learning vs. Probabilistic Graphical Models vs. Logic

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Re: Deep Learning vs. Probabilistic Graphical Models vs. Logic

#22
Anyone interested in Logic and Probability should take the time to read through (at least) chapters 1 & 2 of Jaynes' Probability: the Logic of Science [0]. Jaynes' is the arch-Bayesian and in these chapters mathematically develops what is essentially an alternate Universe model of probability which, in his view, arrives as the natural extension of Aristotlean logic. There's no "coin flipping" in these chapters, and when he finally derives the method calculating probabilities the fact that his model matches with coin-flipping models is written off almost as a happy accident. If you're familiar with Bayesian analysis but have not read Jaynes it is very likely that you aren't familiar with quite how (delightfully) extreme his views are.

Jaynes' fundamental metaphor through the book is building a "reasoning robot" so anyone interested in the intersection of logic, probability and AI will get many interesting insights from this book.

[0] PDF of the preprint: http://bayes.wustl.edu/etj/prob/book.pdf

Re: Deep Learning vs. Probabilistic Graphical Models vs. Logic

#23
post #7

Logic based AI is definitely taking a backseat to data driven methods in the current environment but dead is a gross exaggeration. There are a large class of problems for which heuristic search in logic domains is the most performant technique, and a significant class of problems where SAT solvers are feasible solutions. Many of them are real world examples, rather than academic problems. Also, many techniques are ev…

I am starting to get a (what I guess you could call mostly logic-based) AI system off the ground. The first thing I needed to do was create a serious environment that could host it. The necessary attributes of this environment are these: 1) It is fully web-based, and thus it is technically "on" the web, and accessible by everyone 2) It does not deal with any "modern web appy"-type meta-frameworks, and thus it is not,…

Sounds very interesting. Could you elaborate a bit more on the technologies you are using?

Re: Deep Learning vs. Probabilistic Graphical Models vs. Logic

#25
post #24

How hard is it to determine why a probabilistic or "deep learning" system made a specific choice?

The hard part is defining "why". Machine learning methods can produce a model which fits the data very well, and you can easily prove that it fits the data, but understanding "why" is much harder.

There is a tool called Eureqa which was specifically designed to produce understandable models, in the form of mathematical equations. A biologist used it on some data from an experiment of his, and it produced a very simple equation that fit the data perfectly. But he couldn't publish it because be couldn't understand or explained why the equation worked or what it meant.

Re: Deep Learning vs. Probabilistic Graphical Models vs. Logic

#26
post #24

How hard is it to determine why a probabilistic or "deep learning" system made a specific choice?

With PGM you just look at the graph to see how each node is weighted.

That is one of the advantages of PGM, it tells you why it thinks something. Combining this with domain experts is a killer advantage of PGM. For the soundbite: PGM's help the domain expert figure out where to go next.

Re: Deep Learning vs. Probabilistic Graphical Models vs. Logic

#27
post #5

After learning PGMs, I find that I've almost completely eschewed first order logic for my own personal everyday reasoning. Arguments based on logical formulations require that the propositions are not leaky abstractions, and for most problem domains (i.e. not physics), there are going to be so many exceptions that I find very few cases where I can rely on first order logic. The softness of PGMs, and ideas like "expla…

Very curious to know 1. Where you learnt PGMs 2. How you made it part of your 'personal everyday' toolkit Always interested in improving my thought processes...

I learned mostly by doing, through undergraduate research, and then in graduate school. This was far more effective than lectures or books, though those are very helpful for getting started. I had one class that covered an overview of lots of the technology, and was lucky enough to have access to preprints of Koller & Friedman's book as a reference to fill in any gaps. I also read Judea Pearl's book on Bayesian Networks fairly early on.

As far as everyday reasoning, it made me somewhat more skeptical of long chains of A --> B, !B therefore !A, type of thing. It's easy enough to model this type of logic as a special case of PGMs. And the causal stuff is extremely useful for making me skeptical of arguments of the sort "If we did X, then Y would happen," and also how and when correlation is causality. Don't have any pat examples though, it's just something that infuses my thinking, such as learning about biological evolution.

Re: Deep Learning vs. Probabilistic Graphical Models vs. Logic

#28
post #5

After learning PGMs, I find that I've almost completely eschewed first order logic for my own personal everyday reasoning. Arguments based on logical formulations require that the propositions are not leaky abstractions, and for most problem domains (i.e. not physics), there are going to be so many exceptions that I find very few cases where I can rely on first order logic. The softness of PGMs, and ideas like "expla…

Very curious to know 1. Where you learnt PGMs 2. How you made it part of your 'personal everyday' toolkit Always interested in improving my thought processes...

I learned mostly by doing, through undergraduate research, and then in graduate school. This was far more effective than lectures or books, though those are very helpful for getting started. I had one class that covered an overview of lots of the technology, and was lucky enough to have access to preprints of Koller & Friedman's book as a reference to fill in any gaps. I also read Judea Pearl's book on Bayesian Networks fairly early on.

As far as everyday reasoning, it made me somewhat more skeptical of long chains of A --> B, !B therefore !A, type of thing. It's easy enough to model this type of logic as a special case of PGMs. And the causal stuff is extremely useful for making me skeptical of arguments of the sort "If we did X, then Y would happen," and also how and when correlation is causality. Don't have any pat examples though, it's just something that infuses my thinking, such as learning about biological evolution.

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