appendix.tex (4406B)
1 \chapter{List of Assumptions} 2 \label{chap:assumptions} 3 Modeling hypotheses are central to relation extraction approaches, especially unsupervised ones (see Chapter~\ref{chap:relation extraction}). 4 This appendix list all assumptions introduced in the previous chapters in alphabetical order, with reference to the section in which it was introduced, and whenever possible a counterexample exposing what kind of construct cannot be captured by making this hypothesis. 5 6 \typeassumption[\(1\to1\)]{onetoone}% 7 Appeared Section~\refAssumptionSection{onetoone}.\\ 8 Counterexample: ``Josetsu \textsl{born in} Kyushu'' and ``Minamoto no Shunrai \textsl{born in} Kyushu.'' 9 10 \bigskip 11 12 \typeassumption[1-adjacency]{oneadjacency}% 13 Appeared Section~\refAssumptionSection{oneadjacency}.\\ 14 Counterexample: ``Khayyam \textsl{born in} Nishapur'' and ``Khayyam \textsl{died in} Nishapur.'' 15 16 \bigskip 17 18 \typeassumption[1-neighborhood]{oneneighborhood}% 19 Appeared Section~\refAssumptionSection{oneneighborhood}.\\ 20 Counterexample: \textsl{born in} and \textsl{died in}. 21 Since the arc-neighborhood \(\gfeneighbors\) is split between in-and out-neighborhood, this hypothesis is close to \hypothesis{type}. 22 The main difference being that the partitions (types) of \hypothesis{type} can't overlap. 23 While a relation which can have any type as a subject can't be modeled under the \hypothesis{type} hypothesis, it will simply correspond to a distribution with mass on all entities in the \hypothesis{1-neighborhood} assumption. 24 25 \bigskip 26 27 \typeassumption[biclique]{biclique} 28 Appeared Section~\refAssumptionSection{biclique}.\\ 29 Counterexample: most relations should infringe this assumption since it is decomposable into two unary predicates: whether the entity is part of \(A\) and whether it is part of \(B\). 30 For example ``Alonzo Church \textsl{died in} Hudson'' and ``Alan Turing \textsl{died in} Wilmslow'' are true but ``Alonzo Church \textsl{died in} Wilmslow'' is false. 31 32 \bigskip 33 34 \typeassumption[blankable]{blankable} 35 Appeared Section~\refAssumptionSection{blankable}.\\ 36 Counterexample: some surface forms are mapped to different relations depending on the nature of the entities; in FewRel, ``\uhead{~?~} is part of \utail{~?~}'' can both convey \textsl{part of} and \textsl{part of constellation}. 37 38 \bigskip 39 40 \typeassumption[\ctxoneadj]{ctxoneadjacency} 41 Appeared Section~\refAssumptionSection{ctxoneadjacency}.\\ 42 Finding a counterexample for this assumption is quite difficult since it depends on the operation performed by the contextualization function \(\operatorname{ctx}\). 43 In this sense, it is a weak assumption. 44 45 \bigskip 46 47 \typeassumption[distant]{distant} 48 Appeared Section~\refAssumptionSection{distant}.\\ 49 Counterexample: ``Chekhov found himself coughing blood, and in 1886 the attacks worsened, but he would not admit his tuberculosis to his family or his friends.'' does not convey the fact ``Anton Chekhov \textsl{cause of death} Tuberculosis,'' it only conveys ``Anton Chekhov \textsl{has medical condition} Tuberculosis.'' 50 51 \bigskip 52 53 \typeassumption[multi-instance]{multiinstance} 54 Appeared Section~\refAssumptionSection{multiinstance}.\\ 55 Counterexample: Even though ``Josetsu \textsl{born in} Kyushu'' is present in Wikidata, at the time of writing, this information is missing from its English Wikipedia page, thus an alignment of \(\dataSet=\text{Wikipedia}\) with \(\kbSet=\text{Wikidata}\) would not verify \hypothesis{multi-instance}. 56 57 \bigskip 58 59 \typeassumption[pullback]{pullback} 60 Appeared Section~\refAssumptionSection{pullback}.\\ 61 Entails \hypothesis{1-adjacency}.\\ 62 Counterexample: Unless the reader is familiar with biographies of early Chinese philosophers, the relation between \wdent{1362266} ``Gongsun Long'' and \wdent{197430} ``Zhao'' should not be immediately obvious. 63 64 \bigskip 65 66 \typeassumption[type]{type} 67 Appeared Section~\refAssumptionSection{type}.\\ 68 Counterexample: ``Deneb \textsl{part of} Summer Triangle'' (type pair: star--con\-stel\-la\-tion) and ``Mitochondrion \textsl{part of} Cytoplasm'' (type pair: organelle--cellular component). 69 70 \bigskip 71 72 \typeassumption[uniform]{uniform} 73 Appeared Section~\refAssumptionSection{uniform}.\\ 74 Counterexample: The relation ``\textsl{worshipped by}'' generally appears quite a lot less than ``\textsl{place of burial}'' whether measured through the number of facts in Wikidata or as the number of sentences conveying these relations in Wikipedia.