Pursuing the Next Level of Artificial Intelligence

“A mathematical theoretician, she has made contributions in areas like robotics and biology. Her biggest accomplishment — and at age 39, she is expected to make more — is creating a set of computational tools for artificial intelligence that can be used by scientists and engineers to do things like predict traffic jams, improve machine vision and understand the way cancer spreads.”

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“Called the Bayesian approach, it centers on a formula for updating the probabilities of events based on repeated observations. The Bayes rule, named for the 18th-century mathematician Thomas Bayes, describes how to transform a current assumption about an event into a revised, more accurate assumption after observing further evidence.”

Ms. Koller has led research that has greatly increased the scope of existing Bayesian-related software. “When I started in the mid- to late 1980s, there was a sense that numbers didn’t belong in A.I.,” she said in a recent interview. “People didn’t think in numbers, so why should computers use numbers?”

Ms. Koller is beginning to apply her algorithms more generally to help scientists discern patterns in vast collections of data.”

To start with, P(A|B)=the probability of A given B…to find the probability of a certain A given B, start out with the probability of that A times the probability of B given that A, divided by the total probability of B (given each of the different As)…where B could be a condition such as the subject was cured by a drug, and each A is a different possible drug treatment…so the denominator would be the total probability of being cured across all of the drugs, and the numerator would be the probability of being cured based on taking one of those particular treatments…or something like that.

I like how probability is about sets…multiplication for joint probability, intersection of sets, and addition for union of sets (minus any intersection). Or something like that. It’s neat how the joint probability tables pretty much mirror the tables/arrays/matrices made by multiplication generally…they should teach us this stuff in junior high!

Also see:

And Behind Door No. 1, a Fatal Flaw

“Like Monty Hall’s choice of which door to open to reveal a goat, the monkey’s choice of red over blue discloses information that changes the odds. If you work out the permutations (see illustration), you find that when a monkey favors red over blue, there’s a two-thirds chance that it also started off with a preference for green over blue — which would explain why the monkeys chose green two-thirds of the time in the Yale experiment, Dr. Chen says.”

I guess it would be a good idea for researchers to always sketch out a probability tree diagram/decision tree for their experiments?

Filed under: math | Tagged: artificial intelligence, computing, economics, probability, psychology, research, statistics |

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