Cookbook for chi_square distance #4324
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… the chi_square distance
| Chi Square Distance | ||
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| The Chi Square Distance for real valued features x and x' extends the concept of :math:`\chi^{2}` metric to negative values. |
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since you are using x and x' downstream, pls put them into (inline) math mode here as well
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We need more clarity here :-) The distance extends the concept of the metric, what does this mean? I think distance and metric are commonly used interchangeably. Explain specifically what is meant by extending to negative values.
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Can we have some updates here pls? :)
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@iglesias @karlnapf The classical chi square distance is defined as:
This is for only positive values. However, the implementation in shogun is for both positive and negative values, since the denominator is (|x_i|+|y_i|) so it extends the chi square distance to the negative values too. Is this more clear?
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To some extent. What reference are you using for this classical definition?
From I have read after checking shortly out there, a use case of this Chi-2 distance is to calculate distance between histograms. In that use case the values are positive of course. I suppose that people found other use cases where values are not necessary positive. I suspect that this dichotomy you have observed (definitions with and without the absolute value) may come from there.
It is fine for me if you want to leave the text as it is. I would not play with saying the distance extends the concept of metric to negative values since because I find it rather vague and potentially misleading.
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| d(\bf{x},\bf{x'}) = \sum_{i=1}^{n}\frac{(x_{i}-x'_{i})^2}{|x_{i}|+|x'_{i}|} \quad \bf{x},\bf{x'} \in R^{n} |
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Should I add "for any natural number n" ?
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I think it should be fine for defining n if you just put that the features belong to R^n the first time you introduce them. By the way, for extra mathy happiness, use \mathbb with R 🤓
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Thanks for this!
@shubham808 @vinx13 @FaroukY Pls let this be the last "distance" cookbook. We have enough of those already. (meta examples still need to be ported)
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| Chi Square Distance | ||
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| The Chi Square Distance for real valued features x and x' extends the concept of :math:`\chi^{2}` metric to negative values. |
There was a problem hiding this comment.
We need more clarity here :-) The distance extends the concept of the metric, what does this mean? I think distance and metric are commonly used interchangeably. Explain specifically what is meant by extending to negative values.
…ion of the metric
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* updated csv_file in chi_square.sg to new api and wrote a cookbook for the chi_square distance
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