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e g(x) e 2.69195 = = 0.06345 1 + e g(x) 1 + e 2.69195 That is, the estimated probability that a 35-year-old divorced female with 12 years of education working 30 hours per week with no capital gains or losses will have an income greater than $50,000 is reported by models based on both data sets to be between 6.3 and 6.5%. There is a difference of only 0.00158 between the point estimates, which is slightly better (i.e., smaller) than the estimate for the 50-year-old male.

[70] B M Hochwald, G Caire, B Hassibi, and T L Marzetta (Eds) IEEE Trans Inf Theory, Special Issue on Space-Time Transmission, Reception, Coding and Signal-Processing, Vol 49, Oct 2003 [71] L Boltzmann Beziehung Zwischen dem zweiten Hauptsatze der mechanischen W rmertheorie und der Wahrscheilichkeitsrechnung respeka tive den Saetzen uber das W rmegleichgwicht Wien Ber, pages 373 435, a 1877 [72] R C Bose and D K Ray-Chaudhuri On a class of error correcting binary group codes Inf Control, 3:68 79, Mar 1960 [73] H J Brascamp and E J Lieb Best constants in Young s inequality, its converse and its generalization to more than three functions Adv Math, 20:151 173, 1976 [74] L Breiman The individual ergodic theorems of information theory Ann Math Stat, 28:809 811, 1957 With correction made in 31:809-810 [75] L Breiman Optimal gambling systems for favourable games.

Selecting informative inputs is a critical task for an automatic modeling system such as an inferential (soft) sensor. The complexities of this task are rooted in the inherent relationships between input physical variables and input output relationships/dependencies, which are (normally) highly nonlinear and nonstationary. Conventionally, this task is performed as part of preprocessing of ine before the modeling of the real system. In classi cation- and data mining related literature it is called feature selection or sensitivity analysis. Typical approaches used to address this problem include principal component analysis (PCA) (Fukunaga, 1990; Li et al. 2000), genetic programming (Kordon & Smits, 2001), and partial least squares (Fortuna et al., 2007). It is dif cult, however, to obtain appropriate training samples. The method for online input variables selection (see 2) allows us to evaluate online the importance of input variables based on the sensitivity of the output, qyi qxj ; i 1; 2; . . . R; j 1; 2; . . . ; n because of the (partially) linear consequences in terms of the inputs (Angelov, 2006): qyi aij qxj 14:2

In Fourth Berkeley Symposium on Mathematical Statistics and Probability, Vol 1, pages 65 78 University of California Press, Berkeley, CA, 1961 [76] L Breiman, J H Friedman, R A Olshen, and C J Stone Classi cation and Regression Trees Wadsworth & Brooks, Paci c Grove, CA, 1984 [77] L Brillouin Science and Information Theory Academic Press, New York, 1962 [78] J A Bucklew The source coding theorem via Sanov s theorem IEEE Trans Inf Theory, pages 907 909, Nov 1987 [79] J A Bucklew Large Deviation Techniques in Decision, Simulation, and Estimation Wiley, New York, 1990 [80] J P Burg Maximum entropy spectral analysis PhD thesis, Department of Geophysics, Stanford University, Stanford, CA, 1975 [81] M Burrows and D J Wheeler A Block-Sorting Lossless Data Compression Algorithm (Tech Rept 124) Digital Systems Research Center, Palo Alto, CA, May 1994 [82] A R Calderbank.

Suppose I choose a ball at random (arbitrarily) from a large hat containing colored balls. The ball I choose is red. Does the fact that all of the balls in the hat are red explain why this particular ball is red No. . . All A s are B s cannot explain why this A is a B because it does not say anything about how its being an A is connected with its being a B. (p. 20)

The art of signaling: fty years of coding theory IEEE Trans Inf Theory, pages 2561 2595, Oct 1998 [83] A R Calderbank and P W Shor Good quantum error-correcting codes exist Phys Rev A, pages 1098 1106, 1995 [84] A Carleial Outer bounds on the capacity of the interference channel IEEE Trans Inf Theory, IT-29:602 606, 1983 [85] A B Carleial A case where interference does not reduce capacity IEEE Trans Inf Theory, IT-21:569 570, 1975 [86] G Chaitin Information-Theoretic Incompleteness World Scienti c, Singapore, 1992 [87] G J Chaitin On the length of programs for computing binary sequences J ACM, pages 547 569, 1966..