Unifying Probabilistic and Rules Based Approaches AI

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The probabilistic approach to artifical intelligence has been responsible for most of the recent progress in artificial intelligence, such as voice recognition systems, or the system that recommends movies to Netflix subscribers. But Noah Goodman, an MIT research scientist whose department is Brain and Cognitive Sciences but whose lab is Computer Science and Artificial Intelligence, thinks that AI gave up too much when it gave up rules. By combining the old rule-based systems with insights from the new probabilistic systems, Goodman has found a way to model thought that could have broad implications for both AI and cognitive science.

Church programs did a significantly better job of modeling human thought than traditional artificial-intelligence algorithms did. Chater cautions that, while Church programs perform well on such targeted tasks, they’re currently too computationally intensive to serve as general-purpose mind simulators. “It’s a serious issue if you’re going to wheel it out to solve every problem under the sun,” Chater says. “But it’s just been built, and these things are always very poorly optimized when they’ve just been built.” And Chater emphasizes that getting the system to work at all is an achievement in itself.

Early AI researchers saw thinking as logical inference: if you know that birds can fly and are told that the waxwing is a bird, you can infer that waxwings can fly. One of AI’s first projects was the development of a mathematical language — much like a computer language — in which researchers could encode assertions like “birds can fly” and “waxwings are birds.” If the language was rigorous enough, computer algorithms would be able to comb through assertions written in it and calculate all the logically valid inferences. Once they’d developed such languages, AI researchers started using them to encode lots of commonsense assertions, which they stored in huge databases.

The problem with this approach is, roughly speaking, that not all birds can fly. And among birds that can’t fly, there’s a distinction between a robin in a cage and a robin with a broken wing, and another distinction between any kind of robin and a penguin. The mathematical languages that the early AI researchers developed were flexible enough to represent such conceptual distinctions, but writing down all the distinctions necessary for even the most rudimentary cognitive tasks proved much harder than anticipated.

n probabilistic AI, by contrast, a computer is fed lots of examples of something — like pictures of birds — and is left to infer, on its own, what those examples have in common. This approach works fairly well with concrete concepts like “bird,” but it has trouble with more abstract concepts — for example, flight, a capacity shared by birds, helicopters, kites and superheroes. You could show a probabilistic system lots of pictures of things in flight, but even if it figured out what they all had in common, it would be very likely to misidentify clouds, or the sun, or the antennas on top of buildings as instances of flight. And even flight is a concrete concept compared to, say, “grammar,” or “motherhood.”

As a research tool, Goodman has developed a computer programming language called Church — after the great American logician Alonzo Church — that, like the early AI languages, includes rules of inference. But those rules are probabilistic. Told that the cassowary is a bird, a program written in Church might conclude that cassowaries can probably fly. But if the program was then told that cassowaries can weigh almost 200 pounds, it might revise its initial probability estimate, concluding that, actually, cassowaries probably can’t fly.


Church: a language for generative models (10 page pdf)

Formal languages for probabilistic modeling enable re-use, modularity, and descriptive clarity, and can foster generic inference techniques. We introduce Church, a universal language for describing stochastic generative processes. Church is based on the Lisp model of lambda calculus, containing a pure Lisp as its deterministic subset. The semantics of Church is defined in terms of evaluation histories and conditional distributions on such histories. Church also includes a novel language construct, the stochastic memoizer, which enables simple description of many complex non-parametric models. We illustrate language features through several examples, including: a generalized Bayes net in which parameters cluster over trials, infinite PCFGs, planning by inference, and various non-parametric clustering models. Finally, we show how to implement query on any Church program, exactly and approximately, using Monte Carlo techniques.

Probabilistic Models of Cognition Tutorial [WIKI]

Simple Generative Models [part of the wiki]

Inference in Structured Models

Probabilistic programming workshop from 2008

Use Church to compactly specify a range of problems, including nonparametric Bayesian models, planning as inference, and Bayesian learning of programs from data.

Fragment Grammars: Exploring Computation and Reuse in Language (65 page pdf)

Computer Science and Artificial Intelligence Laboratory (CSAIL) website


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