Artificial neural network, Advanced Statistics

Artificial neural network: A mathematical arrangement modelled on the human neural network and designed to attack various statistical problems, particularly in the region of pattern recognition, multivariate analysis, memory and learning. The significant feature of such a structure is a network of the simple processing elements (such as arti?cial neurons) coupled together (the hardware or software), such that they cooperate. From the set of 'inputs' and an associated set of the parameters, the arti?cial neurons produce an 'output' which provides a possible solution to the problem under the investigation. In number of neural networks the relationship between the input received by the neuron and its output.

 The most is determined by the generalized linear model ordinary form is the feed-forward network which is fundamentally an extension of the idea of the perception. In this type of network the vertices can be numbered so that all the connections go from a vertex to one with the one possessing the higher number; the vertices are organised in the form of layers, with connections only to the higher layers. This is illustrated in the figure draw below each neuron sums its inputs to form a whole input

xj and applies the function fj to xj to give the result yj. The links have weights wij which multiply the signals travelling along them by the factor. Number of ideas and activities familiar to statisticians can be expressed in the neural-network notation, consisting regression analysis, generalized additive models, and the discriminant examination. In any practical problem the statistical equivalent of specifying architecture of the suitable network is specifying a appropriate model, and training the network to perform well with the reference to a training set is equivalent to estimating the parameters of the model given as the set of data.


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