The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World

by Pedro Domingos

But, Laplace went on, if the past is any guide to the future, every day that the sun rises should increase our confidence that it will continue to do so. After five thousand years, the probability that the sun will rise yet again tomorrow should be very close to one, but not quite there, since we can never be completely certain. From this thought experiment, Laplace derived his so-called rule of succession, which estimates the probability that the sun will rise again after having risen n times as (n + 1) / (n + 2). When n = 0, this is just ½; and as n increases, so does the probability, approaching 1 when n approaches infinity. This rule arises from a more general principle. Suppose you awake in the middle of the night on a strange planet. Even though all you can see is the starry sky, you have reason to believe that the sun will rise at some point, since most planets revolve around themselves and their sun. So your estimate of the corresponding probability should be greater than one-half (two-thirds, say). We call this the prior probability that the sun will rise, since it’s prior to seeing any evidence. It’s not based on counting the number of times the sun has risen on this planet in the past, because you weren’t there to see it; rather, it reflects your a priori beliefs about what will happen, based on your general knowledge of the universe. But now the stars start to fade, so your confidence that the sun does rise on this planet goes up, based on your experience on Ea...