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| -rw-r--r-- | posts/2018-12-02-lime-shapley.md | 12 |
1 files changed, 12 insertions, 0 deletions
diff --git a/posts/2018-12-02-lime-shapley.md b/posts/2018-12-02-lime-shapley.md index 5ccf701..0e80c88 100644 --- a/posts/2018-12-02-lime-shapley.md +++ b/posts/2018-12-02-lime-shapley.md @@ -123,6 +123,18 @@ The LIME model has a more general framework, but the specific model considered in the paper is the one described above, with a Lasso for feature selection. +One difference between our account here and the one in the LIME paper +is: the dimension of the data space may differ from $n$ (see Section 3.1 of that paper). +But in the case of text data, they do use bag-of-words (our $X$) for an "intermediate" +representation. So my understanding is, in their context, there is an +"original" data space (let's call it $X'$). And there is a one-one correspondence +between $X'$ and $X$ (let's call it $r: X' \to X$), so that given a +sample $x' \in X'$, we can compute the output of $S$ in the local model +with $f(r^{-1}(h_{r(x')}(S)))$. +As an example, in the example of $X$ being the bag of words, $X'$ may be +the embedding vector space, so that $r(x') = A^{-1} x'$, where $A$ +is the word embedding matrix. + Shapley values and LIME ----------------------- |