PhD

The LaTeX sources of my Ph.D. thesis
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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.