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--- public:t_720_atai:atai-18:lecture_notes_experience-based_learning [2018/11/01 15:52] – [Lecture Notes, W9: Probabilities, Causation & Experience-Based Learning] thorisson
+++ public:t_720_atai:atai-18:lecture_notes_experience-based_learning [2024/04/29 13:33] (current) – external edit 127.0.0.1
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 |  Why It Is Important  | Probability enters into our knowledge of anything for which the knowledge is incomplete. As in, everything that humans do every day in every real-world environment. With incomplete knowledge it is in principle impossible to know what may happen. However, if we have very good models for some limited phenomenon, we can expect our prediction of what may happen to be pretty good. This is especially true for knowledge acquired through the scientific method, in which empirical evidence and human reason is systematically brought to bear on the validity of the models.    |
 |  How To Do It  | Most common method is Bayesian networks, which encode the concept of probability in which probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief [[https://en.wikipedia.org/wiki/Bayesian_probability|REF]]. Which makes it ideal for representing an (intelligent) agent's knowledge of some environment, task or phenomenon [[]].   |
-|  How It Works  | <m>P(a|b)={P(a|b)P(a)}/{P(b)}</m>    |
+|  How It Works  | <m>P(a|b)={P(b|a)P(a)}/{P(b)}</m>    |
 |  Judea Pearl   | Most Fervent Advocate of Bayesian Networks in AI [[http://ftp.cs.ucla.edu/pub/stat_ser/R246.pdf|REF]].    |
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 ==== Causation ====
-|  What It Is  | A causal variable can (informally) be defined as a variable whose relationship with another variable is such that when changed it will change the other variable. \\ Example: A light switch is designed specifically to //cause// the light to turn on and off. \\ In //a causal analysis// based on **abduction** one may reason that a light that was OFF but is now ON may indicate that someone or something flipped the light switch. (The inverse - a light that was on but is now off - has a larger set of reasonable causes, in addition to someone turning it off, a power outage or bulb burnout.     |
+|  What It Is  | A causal variable can (informally) be defined as a variable whose relationship with another variable is such that when changed it will change the other variable. \\ Example: A light switch is designed specifically to //cause// the light to turn on and off. \\ In //a causal analysis// based on **abduction** one may reason that, given that light switches don't tend to flip randomly, a light that was **off** but is now **on** may indicate that someone or something flipped the light switch. (The inverse - a light that was on but is now off - has a larger set of reasonable causes, in addition to someone turning it off, a power outage or bulb burnout.     |
 |  Why It Is Important  | Causation is the foundation of empirical science. Without knowledge about causal relations it is impossible to get anything done.     |
 |  History  | David Hume (1711-1776) is one of the most influential philosophers addressing the topic. From the Encyclopedia of Philosophy: "...advocate[s] ... that there are no innate ideas and that all knowledge comes from experience, Hume is known for applying this standard rigorously to causation and necessity." [[https://www.iep.utm.edu/hume-cau/|REF]] \\ This makes Hume an //empiricist.//   |