Machine learning in trading: theory, models, practice and algo-trading - page 3586
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I call a rectangle not a two-dimensional figure, but a multidimensional figure with dimension equal to the number of features (n-hyperrectangle). It is more convenient for me, so you should understand it as well.
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It is also possible to search for a multidimensional figure, but it is more complicated. However, I find it doubtful to search on all predictors at once - even in theory I cannot imagine how it can be.
A pair of features can be connected by the same logic.
We were talking about trees that do nothing but cut the space of N features into N rectangles.
Suppose we do have some N-rectangle in the feature space in which one class strongly dominates the other. To select it with a tree we need to make at least 2N splits and get a total of 3^N (this is a huge number at large N) N-rectangles. Isn't it better to search for one N-rectangle at once?
The main idea is that the task of complete "mapping" of the feature space is too ambitious - the limited information contained in the sample is wasted. What if we limit ourselves to trying to simply cut out the "good" pieces from it?
the feature space is overly ambitious - wasting the limited information contained in the sample. What if we limit ourselves to trying to simply cut out the "good" bits from it?
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Chewing the same gum....
In much deliberation of realisation came to euristic search, symvoyl regression and logical rules as the final product.
Faced with the problems of the curse of dimensionality (despite the large amount of data\quotations of good examples/patterns found 5-20 instances) and moral burnout :).