IMPLEMENTING USER-DOMAIN SKILLS

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time, which can be inferred from the axioms of probability, but not directly computed. This conformance can be a lot less trivial than one might like. Suppose, for example, that an AACR needs 12 hours to retrospectively analyze a particular day s experiences. It is 10 pm. It has observed for the week that its owner rises at 6 am each day, so it predicts that it has 8 hours to digest the day s experiences, not the 12 it predicts that it needs. Today is Friday. The CR estimates that the owner will rise at 6 am on Saturday with a simple model of waking up, for example, from TDL, which is a descriptive model that the owner rises each day between 5:50 and 6:10 am because that has happened ve times, all the mornings since it was purchased. The observations might even be a good match to a Gaussian distribution with mean 6:01 am and standard deviation of a few minutes. The AACR starts its <Sleep/> cycle. At 10 am, it detects the loud noises of the owner awaking and moving about the house. If Waking-Up is the event WU, it is the time, tWU, of the event WU that the AACR needs to estimate: P(tWU = t) Pt(WU) (11-7)

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In the CRA, there is no requirement to ascribe a probability distribution to tWU, but it is helpful to do that since such events are among the daily patterns of the <User/>. Is there a probability distribution here of the type needed for Bayesian inference If so, then waking up is a certain event, P(WU) = 1.0 (not 99.9 but 1.0). The owner could die in his sleep, so P(WU) 1.0. There are, then, events not yet included among the observations of the CR that can result in a change to WU (not just tWU) so there is no true Pt(WU), only Et(WU), an expectation or degree of belief about both the fact of and the time of the Wake-Up event. In fact, in the <User/> domain, the prejudice is that events do not obey probability axioms. When an AML algorithm discovers a set of events like WU that behaves very much like a probability, then that model may be exploited for planning. The space , the space of all possible events, is invariably unknown, yet the probability of a <Novel/> event is often treated algorithmically as if it were in nitesimal. 11.4.5 Causality and Probability

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Suppose the owner is young and in good health, so P(death-in-sleep) 0. Then Et(WU) Pt(WU). That is, the degree of belief is behaving like a probability, so the CR may safely use the probability function as a degree of belief. Suppose owner says, I m not feeling so good, so I m going to sleep-in tomorrow until maybe 10 am. Does the CR have a causal model [296] It is easy to see that, given the remark, P(WU; 5:50 < tWU < 6:10) 0 (11-8)

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In other words, the probability that the CR had modeled as an event distributed in the vicinity of 6 am is not going to be so distributed tomorrow

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UNCERTAINTY

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morning. The alarm clock may even go off, but the owner plans to hit snooze and put the alarm in the off position. The owner might ask the AACR not to wake him up at the usual time. Conditioning on weekdays, Saturday, and Sunday yields three unimodal distributions. Until the user goes on vacation. Or has to cut the grass on Saturday morning before the predicted rain that afternoon. Or, or, or, or. Counting or RL with context detection reveals the multidimensional nature of the owner s life as follows: counting with context Day Friday Saturday Sunday Monday Time WU 606 1005 823 600 Context Work Yes No No Yes Context Home No Yes +Church No

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By detecting contextual features, a causal space time map appears for which the somewhat random yet patterned distributions establish probability as a reasonable way to model the likely time of events. The space time context <Observation/>s give the AACR a suf ciently high dimensionality feature space in which to infer causality. The owner could still fail to wake up, but there is no probabilistic requirement that he/she live forever, only that the P(Not (WU)) 0. Some aspects of the <User/> domain lend themselves to probabilistic modeling, which typically is enhanced by an appropriate choice of distribution. 11.4.6 Using Probability Distributions

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Bayesian analysis also requires one to accurately estimate the a priori probabilities of an event in order to determine the a posteriori probability, which typically is the objective. Probability in the <User/> domain typically is subjective rather than exact. How does an AACR estimate the prior probability that the <User/> is in the living room That might be useful information if the AACR is in the bedroom and wants to be taken to work today. It could send a message care of the WiFi network to be broadcast through the current TV program: Sir, did you mean to take me to work with you today If so, I m still in the bedroom. To ascribe probability, typically one measures the relative frequency of occurrence of events and matches this distribution to well-known distributions to establish a probability model. Analytical tools like Matlab, Mathcad, and Analytica [297] among others offer many standard distributions that could be embedded into AACR. Questions to be addressed in selecting a model include whether the system is discrete or continuous (and if so, is it bounded), the number of modes, and its symmetry. The embedding

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