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Huffman coding compresses an i.i.d. source with a known distribution p(x) to its entropy limit H (X). However, if the code is designed for some incorrect distribution q(x), a penalty of D(p||q) is incurred. Thus, Huffman coding is sensitive to the assumed distribution. What compression can be achieved if the true distribution p(x) is unknown Is there a universal code of rate R, say, that suf ces to describe every i.i.d. source with entropy H (X) < R The surprising answer is yes. The idea is based on the method of types. There are 2nH (P ) sequences of type P . Since there are only a polynomial number of types with denominator n, an enumeration of all sequences x n with type Px n such that H (Px n ) < R will require roughly nR bits. Thus, by describing all such sequences, we are prepared to describe any sequence that is likely to arise from any distribution Q having entropy H (Q) < R. We begin with a de nition. De nition A xed-rate block code of rate R for a source X1 , X2 , . . . , Xn which has an unknown distribution Q consists of two mappings: the encoder, (11.72) fn : X n {1, 2, . . . , 2nR },

c represents the probability of being in latent class c (e.g., the expected proportion of females). x|c represents the probability of response x to the latent class indicator, conditional on membership in latent class c (e.g., the probability of responding female to the indicator of sex, given membership in the female group). a|c represents the probability of being in latent status a at Time 1 conditional on membership in latent class c (e.g., the probability of being in the depression latent status, given membership in the female group). i|a,c represents the probability of response i to Item 1 at Time 1, conditional on membership in latent status a at Time 1 and membership in latent class c (e.g., the probability of responding yes to could not shake the blues, given membership in the female group and membership in the depression latent status); similarly, i |b,c represents the same quantity for Time 2. j|a,c represents the probability of response j to Item 2 at Time 1, conditional on membership in latent status a at

With regard to learning with ANNs, the most relevant neuroevolutionary methods presented in last few years are SANE [31], a cooperative coevolutionary algorithm that evolves a population of neurons instead of complete networks; ESP [32], similar to SANE, but which allocates a separate population for each of the units in the network, and where a neuron can be recombined only with members of its own subpopulation; and NEAT [33], nowadays the most-used neuroevolutionary algorithm It can evolve networks of unbounded complexity from a minimal starting point and is based on three fundamental principles: employing a principled method for the crossover of different topologies, protecting structural innovation through speciation, and incrementally growing networks from a minimal structure Some of these neuroevolutionary techniques have been tested in nonstationary periodic tasks using external memory elements [29, 32].

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In order to deal with the particularities of the learning processes involved in the MDB, we were confronted with the need of developing a new neuroevolutionary algorithm able to deal with general dynamic problems, that is, combining both memory elements and the preservation of diversity This algorithm was called the promoter-based genetic algorithm (PBGA) In this algorithm the chromosome is endowed with an internal or genotypic memory and tries to preserve diversity using a genotype phenotype encoding that prevents the loss of relevant information throughout the generations An external memory is added to improve the adaptive capabilities of the algorithm The basic operation and the main features of this algorithm within the MDB are presented in the next section..

2.0 1.5 1.0 2.0 1.5 1.0

Listing 16-1 (continued)

Note: Some robots don t have a right dirt detector. You can tell by removing the brushes. The dirt detectors are metallic disks. For robots with no right dirt detector this byte is always 0.

(11.94)

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