Ability to Generalize

It is convenient to introduce the growth function, g(n), defined as the maximum number of different binary functions realizable by a net on any set Af of n N-dimensionEil vectors. Since there are 2 possible dichotomies (see above), we know that g n) 2 . Vapnik and Chervonenkis [vapnik71] studied the behavior of g n) and showed that g n) always starts out equaling 2 for small n, but that its growth rate slows down at a point n = dye called the VC-dimension. If dye = oo, then g(n) = 2 for all n. If dye is finite, however, then g(n) + 1 and g n) does 

A partial listing of phonemes and pronunciations used by NETtalk after appendix A 

Sejnowski and Rosenberg used two different sets of words for training (1) 1024 words taken from phonetic transcriptions of informal continuous speech by children and (2) a subset of the 1000 most commonly used words selected from Miriam Webster s Pocket Dictionary. NETtalk was trained on a DEC VAX 11/780 minicomputer. 

NETtalk s output steadily improved to the point of intelligibility. 

Finally, it is interesting to compare NETtalk s skills with the skills of commercially available text-to-speech systems such as DECtalk. Unlike NETtalk, DECtalk uses both extensive (and labor intensive) look up tables that store the phonetic transcription of common and not so common words and sets of phonological rules for words not in its main look up table. While DECtalk performs undeniably better than NETtalk, the comparison is not really a fair one. DECtalk is a combined r sult of many years worth of careful linguistic analysis and codification. NETtalk, on the other hand, is a self-contained. system that (in the span of a few hours worth of DEC VAX CPU time) can learn enough on its own from a set of simple examples to be both intelligible and accurate. 

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They have the ability to generalize from given training data to unseen data. 

Without adequate controls and appropriate methodology, the ability to generalize is compromised, bringing into question a study s validity, the interpretation of its results, or both. 

Sample is unique in time and location. Approach limits the ability to generalize from the data to other times and locations. 

Ability to generalize results to other waters is limited. 

Despite their expense and the limited ability to generalize from the data that results, concentrate studies are difficult to abandon completely. A literature has developed that illustrates in certain instances, at least, fairly clear-cut indications of adverse health effects (3,4). There are even more instances in which data have been suggestive of carcinogenic and mutagenic hazards (5-7). However, efforts to identify the responsible chemicals have been less than completely successful. For example, in an artificial mixture of byproducts produced from the chlorination of humic acids, less than 1% of the mutagenic activity could be accounted for by extensive chemical analyses (8). 

Among the most wide-spread neural networks are feedforward networks, namely multilayer perceptron (MLP). This network type has been proven to be universal function approximators [11], Another important feature of MLP is the ability to generalization. Therefore MLP can be powerful tool for design of intrusion detection systems. 

The ability to generalize on given data is one of the most important performance characteristics. With appropriate selection of training examples, an optimal network architecture, and appropriate training, the network can map a relationship between input and output that is complete but bounded by the coverage of the training data. 

The validation procedures based on resampling theory mimic the theoretical process of repetitive sampling from an unobserved population however, the samples are drawn from an empirically observed population rather than a theoretical, unobserved one. The limitation of resampling procedures is the representativeness of the observed population unless the observed population is representative, the ability to generalize the model remains biased. 

This assumption is more restrictive than the assumption of constant relative volatilities, or relative X-values, that is used in the Fenske and Underwood methods. The payback for this assumption is the ability to generalize the model to different degrees of column complexity. The success of the method is dependent on proper evaluation of effective /C-values or other model parameters that would represent actual behavior of the column section. The equilibrium coefficient is commonly lumped with the vapor and liquid molar flows in the column to define the stripping factor. 

Recommendations. In a prospective randomized comparative clinical trial, the biostatistician should be primarily concerned with the ability to generalize from the results of the trial to the future population of subjects who may receive the new therapeutic product. To do so, the sampling frame must be constructed to represent the... 

A few examples have been described of Diels-Alder-like reactions with imides formally derived from sulfur trioxide.58 N-Sulfonylimides are quite reactive in a [2 + 2] fashion with alkenes, but their ability to generally act as dienophiles is yet to be established. Sulfonylimines do react with highly oxygenated dienes to give adducts after hydrolysis [Eq. (35)]. 

The test set data records were extracted from herbarium specimens of cultivated trees of known taxonomic identity, but where that identity was not known to the ANN during training. Thus, final testing was performed using an independent dataset derived from 30 herbarium specimens of trees cultivated at Kew, the specimens themselves being held in the cultivated folders of the Kew Herbarium. In a few rare instances, some character states were not readily visible on the specimen and it was necessary to collect further material from the original tree. This material was pressed, dried and mounted before examination. The final evaluation with the test set, therefore, represents an independent test of the effectiveness of the identification system and its ability to generalize -a test that is only rarely performed with conventional taxonomic keys. 

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