Local Polynomial Regression


Synopsis

Generates word vectors from a single text.


Description

This operator provides functionality to perform a local regression. That means, that if the label value for a point in the data space is requested, the local neighborhood of this point is searched. For this search the distance measure specified in the distance measure parameter is used. After the neighborhood has been determined, its datapoints are used for fitting a polynomial of the specified degree using the weighted least squares optimization. The value of this polynom at the requested point in data space is then returned as result. During the fitting of the polynom, the neighborhoods data points are weighted by their distance to the requested point. Here again the distance function specified in the parameters is used. The weight is calculated from the distance using the kernel smoother, specified in the parameters. The resulting weight is then included into the least squares optimization. If the training example set contains a weight attribute, the distance based weight is multiplied by the example's weight. If the parameter use_robust_estimation is checked, a Generate Weight (LPR) is performed with the same parameters as the following Local Polynomial Regression. For different settings the operator Generate Weight (LPR) might be used as a preprocessing step instead of checking the parameter. The effect is, that outlier will be downweighted so that the least squares fitting will not be affected by them anymore.

Since it is a local method, the computational need for training is minimal: In fact, each example is only stored in a way which provides a fast neighborhood search during application time. Since all calculations are performed during application time, it is slower than for example SVM, LinearRegression or NaiveBayes. In fact it really much depends on the number of training examples and the number of attributes. If a higher degree than 1 is used, the calculations take much longer, because implicitly the polynomial expansion must be calculated.


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ExampleProcess