Editing Artificial intelligence (section)

=== Probabilistic methods for uncertain reasoning ===
[[File:SimpleBayesNet.svg|class=skin-invert-image|thumb|upright=1.7|A simple [[Bayesian network]], with the associated [[conditional probability table]]s]]
Many problems in AI (including reasoning, planning, learning, perception, and robotics) require the agent to operate with incomplete or uncertain information. AI researchers have devised a number of tools to solve these problems using methods from [[probability]] theory and economics.<ref name="Stoch">Stochastic methods for uncertain reasoning: {{Harvtxt|Russell|Norvig|2021|loc=chpt. 12–18, 20}}, {{Harvtxt|Poole|Mackworth|Goebel|1998|pp=345–395}}, {{Harvtxt|Luger|Stubblefield|2004|pp=165–191, 333–381}}, {{Harvtxt|Nilsson|1998|loc=chpt. 19}}</ref> Precise mathematical tools have been developed that analyze how an agent can make choices and plan, using [[decision theory]], [[decision analysis]],<ref>[[decision theory]] and [[decision analysis]]: {{Harvtxt|Russell|Norvig|2021|loc=chpt. 16–18}}, {{Harvtxt|Poole|Mackworth|Goebel|1998|pp=381–394}}</ref> and [[information value theory]].<ref>[[Information value theory]]: {{Harvtxt|Russell|Norvig|2021|loc=sect. 16.6}}</ref> These tools include models such as [[Markov decision process]]es,<ref>[[Markov decision process]]es and dynamic [[decision network]]s: {{Harvtxt|Russell|Norvig|2021|loc=chpt. 17}}</ref> dynamic [[decision network]]s,<ref name="Stochastic temporal models"/> [[game theory]] and [[mechanism design]].<ref>[[Game theory]] and [[mechanism design]]: {{Harvtxt|Russell|Norvig|2021|loc=chpt. 18}}</ref>

[[Bayesian network]]s<ref>[[Bayesian network]]s: {{Harvtxt|Russell|Norvig|2021|loc=sects. 12.5–12.6, 13.4–13.5, 14.3–14.5, 16.5, 20.2–20.3}}, {{Harvtxt|Poole|Mackworth|Goebel|1998|pp=361–381}}, {{Harvtxt|Luger|Stubblefield|2004|pp=~182–190, ≈363–379}}, {{Harvtxt|Nilsson|1998|loc=chpt. 19.3–19.4}}</ref> are a tool that can be used for [[automated reasoning|reasoning]] (using the [[Bayesian inference]] algorithm),{{Efn|
Compared with symbolic logic, formal Bayesian inference is computationally expensive. For inference to be tractable, most observations must be [[conditionally independent]] of one another. [[AdSense]] uses a Bayesian network with over 300&nbsp;million edges to learn which ads to serve.{{Sfnp|Domingos|2015|loc=chpt. 6}}
}}<ref>[[Bayesian inference]] algorithm: {{Harvtxt|Russell|Norvig|2021|loc=sect. 13.3–13.5}}, {{Harvtxt|Poole|Mackworth|Goebel|1998|pp=361–381}}, {{Harvtxt|Luger|Stubblefield|2004|pp=~363–379}}, {{Harvtxt|Nilsson|1998|loc=chpt. 19.4 & 7}}</ref> [[Machine learning|learning]] (using the [[expectation–maximization algorithm]]),{{Efn|Expectation–maximization, one of the most popular algorithms in machine learning, allows clustering in the presence of unknown [[latent variables]].{{Sfnp|Domingos|2015|p=210}}}}<ref>[[Bayesian learning]] and the [[expectation–maximization algorithm]]: {{Harvtxt|Russell|Norvig|2021|loc=chpt. 20}}, {{Harvtxt|Poole|Mackworth|Goebel|1998|pp=424–433}}, {{Harvtxt|Nilsson|1998|loc=chpt. 20}}, {{Harvtxt|Domingos|2015|p=210}}</ref> [[Automated planning and scheduling|planning]] (using [[decision network]]s)<ref>[[Bayesian decision theory]] and Bayesian [[decision network]]s: {{Harvtxt|Russell|Norvig|2021|loc=sect. 16.5}}</ref> and [[Machine perception|perception]] (using [[dynamic Bayesian network]]s).<ref name="Stochastic temporal models"/>

Probabilistic algorithms can also be used for filtering, prediction, smoothing, and finding explanations for streams of data, thus helping perception systems analyze processes that occur over time (e.g., [[hidden Markov model]]s or [[Kalman filter]]s).<ref name="Stochastic temporal models">Stochastic temporal models: {{Harvtxt|Russell|Norvig|2021|loc=chpt. 14}}
[[Hidden Markov model]]: {{Harvtxt|Russell|Norvig|2021|loc=sect. 14.3}}
[[Kalman filter]]s: {{Harvtxt|Russell|Norvig|2021|loc=sect. 14.4}}
[[Dynamic Bayesian network]]s: {{Harvtxt|Russell|Norvig|2021|loc=sect. 14.5}}</ref>

[[File:EM_Clustering_of_Old_Faithful_data.gif|thumb|upright=1.2|[[Expectation–maximization algorithm|Expectation–maximization]] [[cluster analysis|clustering]] of [[Old Faithful]] eruption data starts from a random guess but then successfully converges on an accurate clustering of the two physically distinct modes of eruption.]]