Probabilistic Reasoning

Probabilistic reasoning is the artificial-intelligence approach to working with uncertain knowledge: it represents what is not known for certain with probabilities and draws conclusions by applying the rules of probability, with Bayes' theorem as the central tool for updating. It is the answer to the problem of uncertainty, which arises when information is incomplete, noisy or partial. It is not intuition or “thinking”: it is the calculation of probabilities over random variables.

Bayesian networks

Its central tool is Bayesian networks, formalized by Judea Pearl in 1988: graphical models in which a directed acyclic graph represents a set of random variables (the nodes) and their conditional dependencies (the edges). Each node carries the probability of its variable given its “parents,” and the network compactly encodes the joint distribution without having to enumerate it in full. They are related to other probabilistic graphical models, such as Markov networks (undirected) or hidden Markov models (for sequences).

What inference means

To infer is to compute the probability of some variables (the query) given others that are observed (the evidence), summing out or “marginalizing” the ones that do not matter. There are two routes: exact inference, such as variable elimination, which gives the precise answer but is only practical in small networks—the general problem is computationally very costly—and approximate inference, based on sampling, such as Markov chain Monte Carlo methods, which trades accuracy for efficiency when the network is large.

Against logical reasoning

Unlike classic logical reasoning, which operates with binary truth—true or false—and strict rules, probabilistic reasoning handles degrees of belief on a continuum between 0 and 1. It is more flexible in the face of uncertainty, which is why it is the basis of the AI that decides without full certainty. Anthropomorphism should be avoided: a system of this kind does not “doubt” or “believe,” but models uncertainty with probability distributions and computes.