Mathematics – Logic
Scientific paper
2010-05-17
Mathematics
Logic
36 pages, 3 figures. Substantially expanded, with minor corrections. Full version; extended abstract appeared in Proceedings o
Scientific paper
As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe even more complex probabilistic models and inference algorithms. What are the limits of mechanizing probabilistic inference? We investigate the computability of conditional probability, a fundamental notion in probability theory and a cornerstone of Bayesian statistics, and show that there are computable joint distributions with noncomputable conditional distributions, ruling out the prospect of general inference algorithms, even inefficient ones. Specifically, we construct a pair of computable random variables in the unit interval such that the conditional distribution of the first variable given the second encodes the halting problem. Nevertheless, probabilistic inference is possible in many common modeling settings, and we prove several results giving broadly applicable conditions under which conditional distributions are computable. In particular, conditional distributions become computable when measurements are corrupted by independent computable noise with a sufficiently smooth density.
Ackerman Nathanael L.
Freer Cameron E.
Roy Daniel M.
No associations
LandOfFree
On the computability of conditional probability does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the computability of conditional probability, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the computability of conditional probability will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-299731