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| ==== Probability ==== | ==== Probability ==== |
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| | \\ What It Is | Probability is a concept that is relevant to a situation where information is missing, which means it is a concept relevant to //knowledge//. \\ A common conceptualization of probability is that it is a measure of the likelihood that an event will occur [[https://en.wikipedia.org/wiki/Probability|REF]]. \\ If it is not know whether event **X** will be (or has been) observed in situation **Y** or not, the //probability// of **X** is the percentage of time **X** would be observed if the same situation **Y** occurred an infinite number of times. | | | \\ What It Is | Probability is a concept that is relevant to a situation where information is missing, which means it is a concept relevant to //knowledge//. \\ A common conceptualization of probability is that it is a measure of the likelihood that an event will occur [[https://en.wikipedia.org/wiki/Probability|REF]]. \\ If it is not known whether event **X** will be (or has been) observed in situation **Y** or not, the //probability// of **X** is the percentage of time **X** would be observed if the same situation **Y** occurred an infinite number of times. | |
| | \\ Why It Is Important \\ in AI | 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// (small, simple) phenomenon, we can expect our prediction of what may happen to be pretty good, or at least //**practically useful**//. 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. | | | \\ Why It Is Important \\ in AI | 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// (small, simple) phenomenon, we can expect our prediction of what may happen to be pretty good, or at least //**practically useful**//. 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 Compute Probabilities | 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 useful for representing an (intelligent) agent's knowledge of some environment, task or phenomenon. | | | How To Compute Probabilities | 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 useful for representing an (intelligent) agent's knowledge of some environment, task or phenomenon. | |
| | Judea Pearl | Most fervent advocate (and self-proclaimed inventor) of Bayesian Networks in AI [[http://ftp.cs.ucla.edu/pub/stat_ser/R246.pdf|REF]]. | | | Judea Pearl | Most fervent advocate (and self-proclaimed inventor) of Bayesian Networks in AI [[http://ftp.cs.ucla.edu/pub/stat_ser/R246.pdf|REF]]. | |
| | \\ Conceptualization of Probability in This Course | It is useful, in the context of this course, to think about probability as 'that which is not fully known': \\ The World contains a mechanism, **M**, whose operation is not fully known, **K(M)<n** (where **n=[0,1]** and **n=1** is full knowledge). The part **m** which is unknown about **M** implies that predictions, statements, and actions that involve **M**, if repeated, will be reliable only part of the time. As such repetitions tend to infinity, **m** tends to the percentage of **M** that is unknown, representing the **probability** that any single statement, prediction and action about **M** is reliable. | | | \\ Conceptualization of Probability in This Course | It is useful, in the context of this course, to think about probability as 'that which is not fully known': \\ The World contains a mechanism, **M**, whose operation is not fully known, **K(M)<n** (where **n=[0,1]** and **n=1** is full knowledge). The part **m** which is unknown about **M** implies that predictions, statements, and actions that involve **M**, if repeated, will be reliable only part of the time. As such repetitions tend to infinity, **m** tends to the percentage of **M** that is unknown, representing the **probability** that any single statement, prediction and action about **M** is reliable. | |
| | Determinism | The idea of Platonic cause-effect relations; a deterministic relationship between A and B means that there exists a universal guarantee for this relationship, for all eternity, of the inevitable and unbreakable kind. | | | Determinism | The idea that cause-effect relations in the world are Platonic (inherent, absolute, deterministic, eternal). \\ A deterministic relationship between **A** and **B** means that there exists a universal guarantee for this relationship, for all eternity, of the inevitable and unbreakable kind. | |
| | "Adequate Determinism" | A philosophical label for the kind of 'determinism' found in the physical world. \\ See the [[https://www.informationphilosopher.com/freedom/adequate_determinism.html|Adequate Determinism]] blurb on The Information Philosopher | | | "Adequate Determinism" | A philosophical label for the kind of 'determinism' found in the physical world. \\ See the [[https://www.informationphilosopher.com/freedom/adequate_determinism.html|Adequate Determinism]] blurb on The Information Philosopher | |
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| | \\ Knowledge of Causation Supports Action | We may know that **A** and **B** correlate, but if we don't know whether **B** is a result of **A** or vice versa, and we want **B** to disappear, we don't know whether it will suffice to modify **A**. \\ //Example: The position of the light switch and the state of the light bulb correlate. Only by knowing that the light switch controls the bulb can we go directly to the switch if we want the light to turn on. // | | | \\ Knowledge of Causation Supports Action | We may know that **A** and **B** correlate, but if we don't know whether **B** is a result of **A** or vice versa, and we want **B** to disappear, we don't know whether it will suffice to modify **A**. \\ //Example: The position of the light switch and the state of the light bulb correlate. Only by knowing that the light switch controls the bulb can we go directly to the switch if we want the light to turn on. // | |
| | **Causal Models** \\ Are Necessary To Guide Action | While correlation gives us indication of causation, the direction of the "causal arrow" is critically necessary for guiding action. \\ Luckily, knowing which way the arrows point in any large set of correlated variables is usually not too hard to find out, by empirical experimentation. | | | **Causal Models** \\ Are Necessary To Guide Action | While correlation gives us indication of causation, the direction of the "causal arrow" is critically necessary for guiding action. \\ Luckily, knowing which way the arrows point in any large set of correlated variables is usually not too hard to find out, by empirical experimentation. | |
| | Judea Pearl | Most Fervent Advocate of causality in AI, and the inventor of the Do Calculus. \\ C.f. [[https://ftp.cs.ucla.edu/pub/stat_ser/r284-reprint.pdf|Bayesianism and Causality, or, Why I am Only a Half-Beyesian]]. | | | Judea Pearl | Most Fervent Advocate of causality in AI, and the inventor of the 'Do Calculus'. \\ C.f. [[https://ftp.cs.ucla.edu/pub/stat_ser/r284-reprint.pdf|Bayesianism and Causality, or, Why I am Only a Half-Beyesian]]. | |
| | \\ State Of The Art | Recent work by Judea Pearl demonstrates clearly the fallaciousness of the statistical stance, and fixes some important gaps in our knowledge on this subject which hopefully will rectify the situation in the coming years. \\ [[https://www.youtube.com/watch?v=8nHVUFqI0zk|YouTube lecture by J. Pearl on causation]]. | | | \\ State Of The Art | Recent work by Judea Pearl demonstrates clearly the fallaciousness of the statistical stance, and fixes some important gaps in our knowledge on this subject which hopefully will rectify the situation in the coming years. \\ [[https://www.youtube.com/watch?v=8nHVUFqI0zk|YouTube lecture by J. Pearl on causation]]. | |
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| | Why is it Relevant Here? | Like individual learning, it involves dealing with new phenomena and //figuring them out//. | | | Why is it Relevant Here? | Like individual learning, it involves dealing with new phenomena and //figuring them out//. | |
| | \\ Are the Methods Identical? | Very similar. Science is a systematized, organized approach to what individuals do when they learn. This involves: \\ - Exploring \\ - Hypothesizing \\ - Trying out \\ - Recording results \\ - Unifying and consolidating related information \\ - Creating coherent stories about what has been found (theorizing) | | | \\ Are the Methods Identical? | Very similar. Science is a systematized, organized approach to what individuals do when they learn. This involves: \\ - Exploring \\ - Hypothesizing \\ - Trying out \\ - Recording results \\ - Unifying and consolidating related information \\ - Creating coherent stories about what has been found (theorizing) | |
| | Bottom line | The most powerful mechanism for generating reliable knowledge known to mankind has a lot in common with A(G)I. | | | Bottom line | The most powerful mechanism for generating reliable knowledge known to mankind has a lot in common with how future A(G)I must work. | |
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