PTransE.md

PTransE

https://arxiv.org/pdf/1506.00379.pdf

Introduction

TransE model only using single-step relation to map knowledge graph to low dimension space. And TransE has issues when modeling 1-to-N, N-to-1, and N-to-N relations.

It is Known that there are also substantial multiple-step relation paths between entities indicating their semantic relationships.

For example, if I want know a language of a movie, In fact, the language of the film is derived from the language of the director(most of). so I can through the language of the director of movie infer the language of a movie.

Model

loss of TransE

There are relational tuple(h,r,t) in KG, where h is head entity, t is tail entity, r is relation.

$ E(h,r,t) = ||h+r-t||$

loss of PTransE

$G(h,r,t)=E(h,r,t)+E(h,P,t)$

where

$E(h,P,t) = \frac{1}{Z}\sum_{p\in P(h,t)}R(p|h,t)E(h,p,t)$

where $R(p|h,t)$ indicates the reliability of the relation path $p$ given the entity pair $(h,t)$, and

$ Z=\sum_{p\in P(h,t)}R(p|h,t)$

is a normalization factor.

path-constraint resource allocation (PCRA) algorithm

Set head entity as source node, like flood flow in different path, the reliability of the path p from head h to tail t $R(p|h,t) = R_p (t)$ is how much water can be well translated.

Relation Path Representation

ADD

$p = r_1 + ... + r_l$

MUL

$p = r_1 \cdot ... \cdot r_l$

RNN

$ci = f(W [c_{i-1}; ri]) $

and

$E(h, p, t) = ||p-(t-h)|| = ||p-r|| = E(p, r) $

which is expected to be a low score when the multiple-relation path p is consistent with the direct relation r, and high otherwise, without using entity embeddings.

Optimization and Implementation Dentails

Reverse Relation Addition

there are BornInCity, so infer CityWhereBornIn, so add Reverse Relation to KG

Path Selection Limitation

We unable to make use of large amount of relations and facts about each entity pair. so, like n-gram, we only consider 2-step or 3-step paths.

Task

Knowledge base completion

KB completion aiming to predict the missing entities or relations in given triples only based on existing KBs.

Relation extraction

This topic I don't care now.