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I want to measure how well I predict a vector $Y$ (vector not a label) for observation $X$.

Both $X$ and $Y$ have the same set of features ($1\times n$).

For that, I thought of "scoring" the correlation between each pair of the $n$ features, based on previous data I have, i.e. create $n\times n$ matrix $S$, where $S(i,j)$ is the score how well feature $i$ goes with feature $j$.

When predicting for observation $X$, a vector $Y$, I want to take the dominant features (say, above threshold $e$) from $X$ and $Y$, and look in $S$ for their score, if it is above threshold $t$ then I can say my prediction was ok.

My questions are:

  1. Is there any other way to do that?

  2. What can I use as the scoring function? I thought of mutual information, or the frequencies of $i$ and $j$ appearing together in the data set.

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