HISTOGRAM AS A DISCOVERY ALGORITHM

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K is a integer > 0; Bin( ) is an array-object of K integers from 1 to K Ymax = Ymin = Y(1) For i between 2 and N{ If Y(i) < Ymin then Ymin = Y(i) If Y(i) > Ymax then Ymax = Y(i)} End For Span = Ymax Ymin; // may be zero BinSpan = Span/ K For i from 1 to N { Index = oor{(Y(i)-Ymin)/BinSpan} +1 Bin(Index).Increment} End For Signi cant = Alpha*N/ K //* Alpha is real > 1 which is the threshold of signi cance*// For k between 1 and K{ If (Bin(k) > Signi cant) then Y. and Bin. Annotate (<Interesting/>)} End For

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This is a retrospective or batch histogram because all N values are known before H( ) is computable. H( ) is augmented with pattern detection to identify as potentially <Interesting/> any signi cant divergence from the uniform distribution. H( ) estimates the probability distribution of Y to the degree that relative frequency of occurrence informs probability, speci cally if and only if (1) N is suf ciently large; (2) the random process of Y is stationary (having time-invariant statistics) and the random process is (3) ergodic, that is, the statistical parameters of a time series faithfully represent the statistical structure of the underlying random process(es). In both RF and user domains, this is rarely the case, so design drivers for AACR learning include the detection of noiseless data, of conditions when stationary ergodic assumptions approximate the <Scene/>, and of changes in the underlying processes such as statistical inconsistencies. 4.2.3 Histogram in the Ontology

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For the augmented histogram to be available to an iCR, it is described to the <Self/> via ontological primitives, expressing the capabilities of the algorithm for autonomous use. <Histogram/> may be described in terms of <Function> Finds largest and smallest elements of a vector, counting elements in a uniform range from smallest to largest and identifying <Interesting/> features. </Function>, summarized in RXML as the satisfaction of the <Goal/> to <Discover/> (Expression 4-1). Expression 4-1 Histogram as a Goal-Satisfaction Function <Histogram> <Domain> <Vector> Y <Index> [1 . . . N] </Index> </Vector> </Domain>

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<Range> {<Interesting/> <Uninteresting/>) </Range> <Goal> <Discover> Y </Discover> </Goal> </Histogram> The iCR recognizes, asserts, satis es, and introspects over <Goals/>, including to <Discover/> <Interesting/> things to enhance QoI without knowing exactly what discovery may ensue. The CRA includes the principle that if something is novel, then <Self/> should try to <Discover/> it. Expression 4-2 Novelty Implies Discovery <If> <Novel> Y </Novel> <Then> <Goal> <Discover> Y </Discover> </Goal> </Then> </If> Relating <Histogram/> to <Discovery/> mechanizes bottom-up knowledge bootstrapping. <Discovery/> implies related goals to <Validate/> new knowledge through <Reinforcement/> from <Use/>. As an algorithm, <Histogram/> consumes resources as a function of both input space |Y| = N and analytic complexity K, the number of bins in H( ), so one CRA design rule speci es that such algorithms be described at least in terms of nite, tightly bounded <Memory/> and <Processing/> resources measured in <MIPS/> (millions of instructions per second). The algorithm, goal alignment, and resource model establish <Histogram/> as an ontological primitive AML component via the CRA.

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Suppose a user who is planning a trip stores the Map of the World of Figure 4-4 on his iCR. The Map is novel, so the iCR has a <Goal/> to <Discover/> the Map to assist in planning a trip. Without supervision <Histogram/> detects that Map has exactly two intensity states <Light/> and <Dark/> and is <Interesting/>. The light bits are Land and the dark bits are Ocean. The iCR pursues the <Histogram/> discovery that the Map is <Interesting/> via supervised learning as illustrated in Figure 4-4. Since Map has just two colors, the histogram of intensity for number of bins K = 10 yields a bipolar histogram where the light values are counted in the Ymin bin and the dark values in the Ymax bin, while eight bins between are empty. The gure shows this statistical structure by the two vertical bars and center y-axis. The large number of occurrences of a few discrete values concentrated in a few bins expresses high likelihood of learning compared to H( ) where two bins are only slightly above the mean. <Histogram/> could compute degree of

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