In this case it can easily turn out that the noise in the distances between. The feature vectors appears brighter than meaningful information and the model will not work. In this case a more advancd model is needed. More advancd models are often built according to the following principle. Let us have a universal function. Here and as before are the space of features and the set of categories. Is the space of the so-calld model parameters. These parameters for a particular instance of the model can also be. Thought of as a vector of numbers often very multidimensional – it can have tens of millions of elements.
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By changing the parameters of the model. The function F can be fittd to the function f that is of interest to us. It can be imagind like this. Let f: R → Ris an ordinary one-dimensional continuous boundd. Function with a parameter-number and a value-number and with the domain. Let our model be a polyline with n segments and the abscissas of the ends Bahamas Email List of the segments are locatd at equal distances within the interval. Then the space Θ consists of n+ -dimensional vectors from the ordinates of the ends of the polyline segments. Obviously we can choose a vector Θ from Θ so that the broken line FxΘapproximates fxas best as possible and by increasing n we can make the approximation arbitrarily accurate.
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Fig pic Exh Rice An example of a function To obtain the optimal value of the parameter vector the fitting of the parameters to the training sample is used. It’s done like this: We initialize the parameters BLB Directory with random values Repeat until sufficient model accuracy is achieved. – We take the next x yfrom the training sample. If the sample is over we return to its beginning – Calculate Fx Calculate the error value LFx Θ y- often this is the usual square of the distance between points – Shift each element of a little so as to reduce L There are many subtleties here that are solvd differently for different models.