Is equal #2
Is equal #2
Conversation
gracetian6
requested review from
andrewvyrros,
cwagaman,
pdurbin,
raprasad,
Shoeboxam and
silviacasac
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| \begin{theorem} | ||
| For every setting of the input parameters to \texttt{make\_is\_equal}, the transformation returned by \texttt{make\_is\_equal} has the following properties | ||
| \begin{enumerate} |
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need to add domain-metric compatibility
is_equal/is_equal.tex
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| We want to show that $\abs{MultiSet(function(v)) \Delta MultiSet(function(w))} \leq d_{out}$. %\\$\abs{MultiSet(function(v))\Delta MultiSet(function(w))} = \norm{h_{is\_equal(v)} - h_{is\_equal(w)}}_1 \leq d_{out}$. | ||
| To do so, we consider the symmetric distance between the multiset transformations $function(v)$ and $function(w)$. We claim that for any pair of set elements $v^* \in Multiset(v)$ and $w^* \in Multiset(w)$ $$\abs{MultiSet(function(v)) \Delta MultiSet(function(w))} \leq \abs{MultiSet(v) \Delta MultiSet(w)}$$ | ||
| We consider 4 cases. |
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this sentence doesn't parse. It says "We claim that for any pair v^* and w^, STATEMENT holds", but STATEMENT makes no reference to v^ and w^*.
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I think you are trying to use the Path Property for SymmetricDistance, but you need to do so formally (referring to the defs and lemmas in the proof_defns doc) if you want to do that. Else you can follow the simplified proof outline I suggested in clamp.tex.
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Got it, will look at path property to formalize this proof.
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You may find the proof strategy suggested in clamp.tex to be simpler than using the path property.
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New edits of 7/26 include
I'm planning to update with a new round of edits using the new proof outline Salil suggested for row by row transformations. Will need to push new changes for the make_row_by_row transformation and it's corresponding pseudocode and proofs. PRIORITIZE: does the proof for appropriate output domain make sense? |
The Is Equal function takes in a vector of type T and returns a boolean indicator vector of whether each element is equal to
value.This contains
Please look at is_equal pdf as you review the PR!