Causal Inference for Knowledge Graph Completion
Authors: Changyi Xiao
Xiangnan He
Yixin Cao
Venue: Submitted to ICLR 2023 (2023)
Keywords: Causal Inference
Knowledge Graph Completion

Abstract: The basis of existing knowledge graph completion (KGC) models is to learn the correlations in data, such as the correlation between entities or relations and scores of triplets. Since the world is driven by causality rather than correlation, correlation-driven KGC models are weak in interpretation and suffer from the data bias issue. In this paper, we propose causal KGC models to alleviate the issues by leveraging causal inference framework. Our models are intuitive and interpretable by utilizing causal graphs, controllable by using intervention techniques and model-agnostic. Causal graphs allow us to explain the causal relationships between variables and the data generation process. Under the causal graph, data bias can be seen as confounders. Then we block the bad effect of confounders by intervention operators to mitigate the data bias issue. Due to the difficulty of obtaining randomized data, causal KGC models pose unique challenges for evaluation. Thus, we show a method that makes evaluation feasible. Finally, we show a group theory view for KGC, which is equivalent to the view of causal but further reveals the relationships between causal graphs. Experimental results show that our causal KGC models achieve better performance than traditional KGC models.

Under review as a conference paper at ICLR 2023
CAUSAL INFERENCE FOR KNOWLEDGE GRAPH COM- PLETION
Anonymous authors Paper under double-blind review
ABSTRACT
The basis of existing knowledge graph completion (KGC) models is to learn the correlations in data, such the correlation between entities, relations and scores of trippets. Since correlation is not as reliable as causation, correlation-driven KGC models are weak in interpretability and suffer from the data bias issues. In this pa- per, we propose causal KGC models to alleviate the data bias issues by leveraging causal inference framework. Our method intuitive and interpretable by utilizing causal graphs, controllable by using intervention techniques and model-agnostic. Causal graphs allow us to explain the causal relationships between variables and study the data generation processes. Under the causal graph, data bias can be seen as confounders. Then we block the bad effect confounders by intervention oper- ators to mitigate the data bias issues. Due the difficulty of obtaining randomized data, causal KGC models pose unique challenges for evaluation. Thus, we show a method that makes evaluation feasible. Finally, we show a group theory view for KGC, which is equivalent to the view of causal but further reveals the causal rela- tionships. Experimental results show that our causal KGC models achieve better performance than traditional KGC models on three benchmark datasets.
INTRODUCTION
knowledge graph (KG) consists of large number of triplets in the form of (head entity, relation, tail entity). Many KGs suffer from the incompleteness problem. To complement the KGs, knowl- edge graph completion (KGC) models define scoring function measure the likelihood of triplets. The core of traditional KGC models is to learn the correlation in data, such as the correlation be- tween entities or relations and scores of triplets. Since correlation is not as reliable as causation, purely modeling the correlation leads to poor interpretability and the data bias issues. For example, due to igmoring popularity bias in KG data, KGC models are biased towards popular entities and relations (Mohamed al. (020).
In this paper, we propose causal KGC models to solve the data bias issues by utilizing causal infer- ence techniques (Pearl 2009b). Our method is model-agnostic and just needs to add an extra term to the traditional KGC models. Causal inference defines causal graphs to describe the causal relation- ships between variables. Causal graphs can help build intuitive, interpretable and controllable KGC models. Traditional KGC models are only concerned with the correlations in the data, while ignor- ing the causation and the data generation process, which can lead to incorrect correlations between entities, relations and scores of triplets. Causal graphs allow us to explain the causal relationships between variables and study the data generation processes. Under the causal graph, data bias can be seen as confounders, where confounders in KG data are variables that simultaneously affect entities or relations and scores of triplets. We utilize intervention operators to eliminate the bad effect of confounders, which remove the path from confounders entities and relations in the causal graph. Then we can estimate the causal effect or correct correlations in KG data by backdoor adjustment formula (Pearl 2009b).
Causal KGC models present special challenges for evaluation, which need to evaluate on a random- ized test set. However, randomized test set is often difficult infeasible to obtain. Therefore, we define new evaluation metric to measure the performance causal KGC models based on the popularity of entities and relations.

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The main feature of causal is invariance or symmetry (Arjovsky al. 2020). Group theory is language to describe symmetry. Thus, we finally show a view of group theory for KGC, which is equivalent to the view of causal but further uncovers the causal relationships. The view of group theory transcends the view of causal and shows potential applications.
The main contributions of this paper are listed below:
1. To the best of our knowledge, are the first show the necessity of introducing causation into KGC and apply causal inference to KGC.
2. We propose causal KGC models to enhance the interpretability of KGC models and alleviate the data bias issues. Then we show method evaluate causal KGC models observation datasets.
We show view of group theory for KGC further reveal the causal relationships.
We empirically show that causal KGC models outperform traditional KGC models on three benchmark datasets.
BACKGROUND
In this section, we introduce the related background of our model, knowledge graph completion and causal inference.
2.1 KNOWLEDGE GRAPH COMPLETION
Let & denote the set of entities and denote the set of relations, a KG is composed of set of triplets
D [h, })} C & x R x ε, where h is a head entity, r is relation and t is tail entity. Lacroix al. (2018) propose to augment every triplet (h, L) in with its inverse triplet (1,r-1, 1.r-i,h). h). With this augmentation, KGC can be formulated predicting the tail entities that satisfy query (h, r, ?)- A KG can also be represented by 3rd-order binary tensor X {0, 10 1E| with X =1 (h,r, E D and Xn.r.t if (, r, D.
KGC models define scoring function f(h, r,,) measure the likelihood of tripler (h, r,,r;) based on the corresponding embedding (h, r. t). A number of KGC models have been proposed (Zhang al. 202 we list four popular KGC models that we consider in our experiments.
TransE (Bordes et al. 2013), a representative model of translation- based models, defines the scoring function the negative distance between h + and t, i.e.,
f(h, r, f) - + t||
where (h, is the corresponding embeddings of (h,r, h, r. R is the dimension of embedding and || || is norm of a vector. RotatE (Sun et al. 2018)) generalizes the embedding from real vector space complex vector space to model various relation patterns, and the scoring function is defined as
f(h, t) = - h -
where h r, C and is Hadamard product.
DistMult (Yang et al., 2014), a representative model multiplicative models, defines the scoring function the inner product of h, and i.e.,
f(h, Σ h
where h, te R". ComplEx (Trouillon al. 2017) extends DistMult to complex vector space to handle asymmetric relation patterns and defines the scoring function
f(h,r,t) = Re
hrr,t)))
1=1
where h. r, E CP, E is the complex conjugate of t, and Re(-) is the real part of complex number.
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Figure 1: (a) deseribes the causal graph of traditional KGC models. (b) describes the causal graph with three confounders. (c) describes the causal graph after the intervention do H, R, T').
2.2 CAUSAL INFERENCE
Causal inference is the process of inferring the causal relationships from data Yaoo et al. 202 There are two representative frameworks for causal inference: structural causal models (SCMs) proposed by Pearl (2009b) and potential outcome framework developed by Rubin (1974). As shown in (Pearl 2009a). the two frameworks are logically equivalent. Since the causal graph in SCMs describes the causal relationships more intuitively, we select the SCMs framework in this paper.
SCMs abstract the causal relationships between variables into a set of functions and then estimate the causal effects of intervention counterfactual. Every SCM is associated with causal graph, which is a directed acyclic graph where the nodes denote variables and the edges indicate causal relationships between variables.
Given the causal graph, a fundamental manipulation on the causal graph is the intervention. Tech- nically, the intervention the effect of H's ss parents and sets the value of H as h. For example, do H = h) in Figure D will remove the path Zμ - and force H be h. In SCMs framework, the probability function P(Y do ()) describes the causal effect of a variable H on a variable Y.
variable I/ is formulated with do-calculus, do (I h), which blocks
The backdoor adjustment formula commonly used estimate the causal effect P (o(()d(H))) (H)). Given causal graph in which a set of variables Zи are the parents of a variable H, then the causal effect P(Y(do(F) (H)) can be obtained by the backdoor adjustment formula: P(Y = do H h)) = ExAE, hh zh. P(t.). Thus, the causal effect P(Y y jod H h)) is the weighted sum of the conditional probability P(ylh, 2x). Then to obtain P(Y = y/do(H -)).
estimate P(ylh, 2h) from the observation data
3 METHOD
In this section, we first propose our causal KGC models by utilizing causal inference techniques. Then, show the method of evaluating causal KGC models. Finally, we show group theory view for KGC to further reveal the causal relationships.
3.1 CAUSAL KGC MODELS
Data Bias in KGs Data bias in KGs refers to the biased data collection that does not faithfully reflect the likelihood of triplets. Many popular KGs (e.g. DBpedia, Wikidata, and YAGO) are au- tomatically constructed from unstructured text by using information extraction algorithms (Ji al.) 2021). The collected KG data often suffers from data bias, such as popularity bias, algorithm bias and For example, Mohamed al. (2000) show that the distribution of entities and relations in the benchmark KGs highly skewed. The collected KG data is also affected by the information extraction algorithms, which may only extract simple knowledge from the unstructured text while

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ignoring complex knowledge. Existing correlation-driven KGC models not only learn the desired likelihood of triplets but also the data bias, which leads to incorrect correlation.
A Causal View for KGC Causal inference allows us to find the fundamental cause of data bias by studying the generation process of KG data and alleviates the effect of data bias. In most cases, data bias can be seen as confounders in causal graph, where confounders in KG data are variables that simultaneously affect entities or relations and scores of triplets. Ignoring confounders can lead to incorrect correlations between entities, relations and scores of triplets. To eliminate confounding effects, we abstract the data generation process into a causal graph, identify confounders, and then block the effect of confounders by intervention.
Causal graphs are intuitive and allow us to explain the causal relationships between variables. Figure D shows three causal graphs. Figure aa) describes the causal graph of traditional KGC models, which ignores the confounders. Figure [ describes the causal graph with three confounders. TigureDec describes the causal graph after the intervention of the causal graph in Figure The nodes and edges are illustrated as follows:
1. Nodes:
Node H denotes the head entity variable. Node R denotes the relation variable. Node T denotes the tail entity variable. Node Y denotes the score of triplets variable, which measures the likelihood of triplets. Node Zu, Zn and Zr denote variables that not explicitly considered by traditional KGC models, e.g., the popularity of entities or relations.
2. Edges: Edges {H. R,T) - Y denote that (H, R,T) are the cause of Y, which is exactly what the traditional KGC models consider. Edges (H, R, T, Zu, Zn. ZT) - Y denote that {H, R, T, HH, ZT, Zr} are the cause of Y, which have three extra edges ZH + Y. ZR - Y and ZT + Y compared to edges {H, T} + Y. Edge ZH - YIZR + YIZ# + Y means that Zz is also contributed to Y. Edge ZH - {H>/ZR (R) - {T) denotes that the variables ZH/ /Zz/Zy can influence the data generation process of H H/R/T.
The causal graph in Figure [b) shows that ZH ZH/ZRA /ZT simultancously affects H/RIT and Y, so Zu / nz/ Z/r are confounders. The confounder ZH leads to two paths from Zμ to Y: Z4 + and Zu + H - Y. The first path combines edges {H, R, T) 4 Y to model Y, expected. For example, if Zh denotes the popularity of persons, then persons with high Zh are more likely to have relation is friend of with others. Therefore, Zn is also cause of Y. The second path means that Zn can affect the data generation of H. For example, if Zn denotes the popularity of head entities, then ZH will influence the likelihood of head entities being collected, making the collected data biased toward popular head entities (Mohamed et al. (022). This causes bias amplification, which should be avoided because a KGC model should faithfully estimate the likelihood of triplets and not be affected by the way of data collection. The confounders Zn and ZT are similar to Zh- Thus, the bad effect caused by the paths ZH - H. ZR + R and Z + T should be blocked.
Deconfounded KGC Models To eliminate the bad effect of confounders {ZH, ZR. Zr). we should rule out the paths Zu - H, Zn - R and 7, - T from the causal graph in Figure [b), that is exactly do H, R, T) operator, which results the causal graph in Figure Ic.. Thus, the causal effect of {H, R,T) on Y can be measured by probability function P(Y [do R. T)) in Figure [b), i.e., PH R, T) in Figure (c). To estimate P(Y [o((H, R, T)), one method is to conduct randomized experiments. During the data collection process, we randomly select head en- tities, relations and tail entities, and then judge whether the corresponding triplets are true. This can make ( [H, R. T} unaffected by confounders {Z ZR. Zr). However, randomized experiments are difficult to conduct. On the one hand, only the data collector can decide how the data is collected. On the other hand, since the triplets are obtained indirectly from unstructured text by algorithms, even the data collectors may not be able to manipulate the way of data collection. Therefore, it is crucial to estimate PYY [do Rt T') from only the observation data. Our method is to first convert P(Y do H, R, T)) into statistical estimate. Then the statistical estimate can be obtained from the observation data.
The backdoor adjustment enables satisfy the backdoor criterion because they block all the backdoor paths from variables {H, R, T) to variable Y. Then P(Y y/do H h, R r, T = t)) can be obtained with backdoor adjustment
achieve it (Pearl 2009b). The variables (ZH, Zn. Zy
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as follows:
P(Y - yldo(H = - -=
Σ
Piyl,, r, Zh, Rr, P(n 2r, ze)
on A.EZM,R,EZ.REEB
Thus, can first estimate P(ylh, r,t, 2h: 2r, 21) from the observation data, which is feasible. Then we compute P(yldo(h, L)) by backdoor adjustment formula. P(ylk, r; 4, Zb. Zy, zt) is relevant to the triplet (h, 1) and the confounders (zn, ūr, 2)) Thus, need to define the confounders (Zh, Zr, 21) The confounders are reflected in the observation data, so they are functions of a 3rd- order binary tensor X. We define two types of confounders as follows:
Artificially designed confounders:
Fn = In(1 veo Xn,,)) = In([[(ho, ro, (0) E Di/o = h)) = In(d(h))
2, In(1" vee X xn,) = In(K((o, to) E D rg = =r}) = In(d(r))
2: In(1 (ec (..))) In(1[(ho, To. to) E D to +)() In(d(t))
where 1 is a vector of appropriate size whose elements are all and vec(.) is an operation that expands a tensor into a vector. We define (hr)/d(r)/d() as the popularity of a head entity h/a relation r/a tail entity t. The logarithmic function to prevent the training unstable for the case where d(h)/d(r)/ (t() is too large. The computational complexity of 2n 2n/2//2 2 is (1)) because we can compute the value of zn/ ///2 2z in advance.
2. Learnable confounders: 2n qu (Xn,.)) b, qu (r.) qu (X....)
where qr (z2l (-rr(-) can be L-layer neural network. We implement (+r(-) one-layer neural network for efficiency, i.e. Qıs (Xn.,)))) = matrix and by is the bias vector. (r(()) and (+(() are similar to qn(()- Then the computational complexity of 2n/ /2/2//2 is
+ by, where Wir is the weight
Let r,, t) be scoring function of a traditional KGC model. We define P(ylh, t, Rhs 2r, 24) as P(ylh, r, Eh, Zr. Fr. 2x) X g(h, r, Zh, žr, 2)) [J r, 2,, where -sh,r r, 0n Or + 0x
zh, Fr, 2x)
and 0g are hyper- syper-parameters to control the weight of confounders. Since P(ylh, r, 2,, žr, 21) is used to rank tail entities, we do not need to normalize Plylh, r, 2h, Ery ze)
to make it rigorous probability function. In principle, g(-) can be any function, we implement g-)
as the addition of f(h r, t) and a + a, + 042t for simplicity. g(h, r, t, 2h 2r, 21) can be seen the new scoring function from the old scoring function f(,, r,t). If an ar as 0, g(,, r, t, Zn. 2r, 2) reduces to the traditional scoring function f(h,r, r,,,.,,.
Now we can train a model to get g(h, r, t, Ehi 2r, ze). We the multi-class loss function in [Lacroix et al. 2018). For a training triplet (h, t), our loss function is
Eg(h, r, L, Zh, Zn, 21)) g(h,, r, 2h, 2rg 2x) + log
2, ))) Rr. 26)
where {zh: Zr, Ze } is the value of confounding variables corresponding the triplet (h, r, t¹).
After getting g(h, r, t, 2hs Zr, ze), we can compute P(Y = yldo(H = h, R = r, = t)) by back-
door adjustment:
y = =P y)do(H = -
Σ
Pluh,, r, Zh, žr, 24 P(ān, Zr, #c)
in E En
x
E
g(h,r,,, 2h, Zr, 2() Zr,
zn E2
Σ
(f(h,r,t) + ah a, + 0121) a12)) 2r, 20)
r))
Σ
(anzh + a, a
2n En
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Since E EoneZ use [h,, r. () surrogate P(Y y|do H h R r; t)).
(ah2) 0,2, + 24 P (2h: :h: 2r, 21) is equal for all triplets (h, t),
Our final result easy, we only need to add an extra term (22 24 0, + 2 to the traditional KGC model f(h, r, in the training process and then get the deconfounded/causal KGC model f(,,r, (). Our method is model-agnostic, which can be appilied to any traditional KGC model.
3.2 EVALUATION OF CAUSAL KGC MODELS
Traditional KGC models are trained on set of true triplets and evaluated on holdout test triplets. The ranking metrics, MRR and H N (Bordes et al. (013), are often used to evaluate the KGC models. The definitions of MRR and H@N are as follows:
MRR = (( [D] rank(h.ray) where rank r,) is the rank of tail entity in the predicted list for the query (h, r, ?). Higher MRR indicates better performance.
E(hnateD [D [(rank(h,, r) & N), where II(-) is the indicator function. H@N is the ratio of the ranks that more than N. Higher H@N indicates better performance.
H@N =
However, causal KGC models present unique challenges for evaluation. Which test set should we use to evaluate causal KGC models? If we evaluate the models on the observation test set, the result gives a biased evaluation: it favours popular entities and relations. One solution is to evaluate on randomized test set. However, randomized test set is often difficult to obtain. Another solution is to evaluate the models on the observation test set with new evaluation metrics. |Mohamed et al. 2020) propose new evaluation metric based the popularity of entities and relations. Similar to Mohamed et al. 2020), we define a weighted evaluation metric W-Metric(3A. 3r.3, as
W-Metric(B1,, Br)
Σ (KiA)))
w(h,rr,t)(hh,,
where w(h, r,t) Eminnee d(r) Ethr, wh, = 1, d(h)/d(r)/d((t) is the popularity of h/r/t and u(h, r,t) rank(h.r..) or u(h, t) = I(rank(h, r,t) $ NN.
d(k)Phd(e) d(t)
We denote W-Metric Sr, B.) W-MRR(3,, 3r, Br) if u(h,r, r,,r, rank(h,r.c) and denote
W-Metric (Br, Br, 3,) as W-H@N( Br, (h, r. [(rank(h,, (,, S N).
Let 3₁ B, = = O, then W-Metric (B,, Br, 3,) = W-Metric(O, 0, =MRR or H@N. Thus, W-Metric (8,, Br, 3r) can seen as generalization MRR or H@N. Let 3n = 1, = 0, 0, then
1/d(h)
W-Metric(Bn, Br, Bi) -W-Metric(11,0.)
Σ
u(,, r,
E(hrtee 1/d(h)
u(h, to) d(h)
Σ
11h Eld(h)
heE,d(h)>0
(Do
v(h) kh E Eld(h) > 0}
where ehh) Σ (hho.ro.t fo) ho=h putes the mean of uh,, ro, 4o), i.e., e(h). While popular head entities receive more u(h, ro, ro,4)), 4o), W-Metric(-1, 0) 0) treats all head entities equally, regardless of the popularity d(h). This can elim- inate the influence of d(h). W-Metric(-1, O, 0) then computes the mean of vhh) all head entities. Thus, W-Metric(-1, 0, is to evaluate the average per-head-entity v(h).
u(h.rgda)
d(h) For each head entity h, W-Metric(-1100.0 first com-
Similarly, W-Metric -1, W)//-Metrii 0, -1) is to evaluate the average per-relation/per- tail-entity v(r)/o(t). Combining these three metries, we evaluate causal KGC models with W-Metric(-1,-11, -1, -1) which simultancously takes into account the popularity of head en- tities, relations and tail entities. For every triplet (h,r, (MMetric-11,-1,, use 1/(d())(()dd(t) to weight uh,rr,t
Eohneee 1/(d(h)d())4(3))

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3.3 A GROUP THEORY VIEW FOR KGC
The main feature of causal is invariance or symmetry (Arjovsky al. 2020). Group theory is mathematical language to describe symmetry. Thus, we show a group theory view for KGC, which is equivalent to the view of causal but further reveals the causal relationships.
Let X' = E x R x &, a KGC model is to find a scoring function f()) that holds for all triplets x E X, i.e. the form of f(x should be invariant for all x E X. We next show the invariance of the form of f(x) can be associated with the notations of groups. We define a group action 7y of Sx on X' as ((, = a(x), where a E Sx, X and Sx is the the symmetry group of X. Then the orbit of x E X' is Sx I {y(a, E Sxh, which is exactly equal to X' Thus, the form of f(z) should be invariant for all Sx I. Now we have established the correspondence between f(x) and group Sx. We say scoring function [a) satisfies G invariance if the form of fxx) is invariant for all x E G x, where G is subgroup of Sx. Thus, traditional KGC models are to learn Sx invariance scoring function. The causal graph in Figure [a) can correspond to a group Sx.
If we have all the data, we can obviously learn the correct Sx invariance scoring function (xx). However, we only have some of the data, which may not match the overall data due to the data bias. Thus, we should not treat all x E Sx 2 equally, i.., treat only some x E Sx I equally. Therefore, the scoring function learned from data should satisfy G' (a subgroup of Sx) invariance. For example, if G S(n) xRxE, then learning G invariance scoring function can correspond to learning P(ylh, r, i, zn. in causal KGC models. After we learn the G invariance scoring func- tion, we can recover the Sx invariance scoring function by using the quotient group Sx/G to act on P(ylh, r, t, 2n). This can correspond to computing P(y do = h. = r, = t)) = E E2 P(ylh, .t, P(2h) in causal KGC models.
In summary, we want to learn Sx invariance scoring function fz)) However, the biased data only allows us to learn a G invariance scoring function. In order to recover Sxx invariance, we can use the quotient group Sx/G / to act the G' invariance scoring function to get the Sx invariance scoring function (xx).
The advantages of the view of group theory to the view of causal are in three folds. First, some relationships between variables are hard to describe by causal graphs. For example, for the ideal gas law PV = nRT, it is hard to say what causes what (Arjovsky et al. (020). In group theory, we use the invariance to represent the relationships between variables, which is easy to describe. Second, there is no metric to measure the relationships between causal graphs. In group theory. we use the notations of group theory to measure the relationships between groups, such as the order of groups, normal subgroups etc.. which help us understand the invariance. Third, backdoor adjustment formula is only suitable for probability function. In group theory, we can use the group to act any function. Thus, the view of group theory generalizes backdoor adjustment formula to any function.
The potential applications of the view of group theory are in three folds. First, the view of group theory enables KGC models to solve out-of-distribution problem. In this paper, we learn G in- variance scoring function from the biased data and apply a group action to the G invariance scoring function to make it able to evaluate on unbiased data. Thus, the task of this paper can be seen as an out-of-distributie task. We can apply different group actions to the G invariance scoring function to make it adapt to different test sets. Second, learning G invariance scoring function directly may be difficult, the direct product decomposition and subgroup series allow us simplify the group G. Third, the G invariance is pre-specified in this paper. It is worth exploring how to learn the invari- ance from data automatically? Given group action on X, the orbits form a partition of X. Thus, we can transform learning the invariance into learning the orbits of X.
4 RELATED WORK
Data bias refers to data that does not reflect the true distribution. Although the data bias problem has been extensively studied in many machine learning fields, such as imbalanced classification problem (Kraweykk 2016) and data bias in recommendation systems (Chen et al. 2020), there are few works considering data bias in KGs. Mohamed et al. (020)) show that benchmark datasets suffer from the popularity bias and existing KGC models are biased towards popular entities and relations. [onner et al. (2022) show the existence of popularity bias of entities in biomedical KGs.
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Table 1: Knowledge graph completion results FB15k-237, WNI8RR and YGA03-10 test sets with evaluation metrics W-Metric(-1,, -1, -1).
FB15k-237
WN18RR
YAGO3-10
MRR
H@ 1
H@ 10
MRR
H@
H@ 10
MRR
H@
H@ 10
TransE
0.279
0.168
0,509
0.224
0.061
0.568
0.303
0.205
0,480
UPS-TransE
0.307
0.210
0.512
0.279
0.078
0.566
0.299
0.196
0.498
0.283
0.166
0.514
0.227
0.062
0.565
0.307
0.207
0.488
Causal-TransF-2
0.285
0.175
0.507
0.225
0.058
0.559
0.303
0.203
0.484
RotatE
0.274
0.177
0.477
0.514
0.479
0.581
0.330
0.237
0.496
Ros-RotatE
0.281
0.191
0.470
0.502
0.475
0.553
0.260
0.202
0.385
Causal-RotatF-1
0.288
0.186
0.493
0.525
0.487
0.603
0.364
0.282
0.529
Causal-RotatE-2
0.280
0.189
0,465
0,521
0.485
0.600
0,341
0.264
0.496
DistMult
0,302
0.195
0.514
0.521
0.478
0.607
0,362
0.284
0.535
IPS-DistMull
0.304
0.208
0,501
0,522
0.480
0.611
0.328
0.270
0.445
Gausal-DistMun
0.312
0.206
0.533
0,523
0.478
0.617
0.382
0.295
0.550
Causal-DistMult-2
0.325
0.217
0.553
0.521
0.477
0.608
0.362
0.284
0.537
ComplEx
0.307
0.204
0.517
0.535
0.493
0.619
0.370
0.278
0.573
IPS- Ppsppopp
0.307
0.205
0.511
0.532
0.488
0.623
0.335
0.263
0.473
Dausal-CoplEEx-1
0.330
0.223
0.555
0.535
0.493
0.617
0.386
0.292
0.586
Causal- Mussa--ComplEx22
0.323
0.220
0.541
0.532
0.491
0.611
0.375
0.286
0.567
We utilize causal graphs to make KGC models more explainable. Existing works on explainable KGC models mainly focus on combining embedding with symbolic reasoning (Zhang et al. 2021a), Guo et al. (2016) utilize the logical rules improve the performance of embedding- based methods.
Markov logic network (Richardson & Domingos 2006) designs a probabilistic framework to repre- sent the logical rules features. Neural LP Yang al. (017) derives the logical rules from data and leverages neural networks to deal with the uncertainty and ambiguity of data.
Causal inference techniques have been used to alleviate the data bias issue (Gao et al. 2022 includ- ing SCMs and potential outcome framework. Under SCMs, data bias can be seen as con confounders, then backdoor adjustment (Zhang al.) 2021b) and frontdoor adjustment (Xu al. 2021) are uti- lized to eliminate the confounding effect. Based on the potential outcome framework, Scchabell al. (2016) propose the inverse propensity score (IPS) method, which aims reweight the samples by the chances that they receive the treatments.
EXPERIMENTS
We first introduce the experimental settings. Then, show the results of causal KGC models and compare with other models. Finally, we conduct ablation studies. Please see Appendix A.I for more experimental details.
5.1 EXPERIMENTAL SETTINGS
Datasets We evaluate the models on three popular KGC datasets, FB 5k-233 (Toutanova et al.) 2015), WN18RR (Dettmers et 2018) and YAGO3-10 (Dettmers et al. 2018).
Models We use original TransE (Bordes et al. 2013), RotatE (Sun et al. 2018), DistMult (Yang et al. 2014) and ComplEx (Toutanova al.) 2015) as baselines. We denote TransE with IPS (Schn- abel et al. 2016) method as -rS-TranSE. We denote TransE with our causal method as Causal- TransE. We denote Causal-TrrnsE with artificially designed confounders Causal-Transk and Causal-TrannE-2 2. The notations of RotatE, DistMult and
TransE with learnable confounders as Causal- TransE-2.
ComplEx similar to TransE.
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Table 2: The results on FB15k-237 datasets with different hyper-paramettess.
Causal-ComplEx-1
Causal-ComplExx2
MRR
H@)
H@
MRR
H@]
H@ 10
an
0.307
0.204
0.517
0.307
0.204
0.517
01, * 0, a. 0, a.
0.308
0.210
0.519
0.307
0.204
0.517
QA 0, a, * 0, ar 0
0.308
0.211
0.528
0.308
0.211
0.528
0, 0,
+ 0
0.333
0.227
0.553
0.327
0.218
0.558
# 0, 0,
# 0
0.330
0.223
0.555
0.323
0.220
0.541
0.327
0.222
0,551
0.326
0.222
0.558
aA cze
0.322
0.216
0.553
0.328
0.218
0.557
Evaluation Metries We use W-MRR(-I,-I.-) and W-H@N(-L--1-I)) as evaluation metries and choose the hyper-parameters with the best W-MRR(-1,-I,-I) on the validation set.
5.2
RESULTS
The results show that our causal KGC models achieve improvement on different datasets, different models and different evaluation metrics (MRR, H@ and H@ 10). This demonstrates the effective- ness of our causal KGC models. Models with artificially designed confounders overall is better than models with learnable confounders. The reason is that models with learnable confounders are more difficult to optimize and are more likely to overfit.
Our models are better than the IPS method. IPS method do not achieve consistent performance due to the difficulty of estimating propensity score. The improvement of our causal KGC models is significant FB 15k-237 dataset and YAGO3-10 dataset, and is little on WNI8RR dataset. The reason is that the degree of data bias on WN18RR dataset smaller, as shown in Table
5.3 ABLATION STUDIES
We conduct ablation studies analyze which of the confounders {Zn. Zn. Zr} } influences the models most. We use the models with 0% a, a = 0 as baselines. We train models with only of the hyper-parameters faz, d,, at). We also train models that use fewer typer-parameters by setting Oi Cie and 0% a₂ = dr- Since Za and Z, are similar, one is a confounder of head confounder of tail entities, trained on FB FB15k-20 153-237 dataset with ComplEx model. See Table for the results.
entities and the other
oi Or. All experiments
The results show that ZT influences models most, ZH and ZR influence models little. The reason is that KGC is formulated as predicting the tail entities. The performance of the models have no obvious attenuation if set a₁ a2 or ai a, at+ Thus, we can reduce the computation by using fewer papeeeprraettrrs..
CONCLUSION
Traditional KGC models only consider the correlation in the data and ignore the causation, which leads to the data bias issues. In this paper, we utilize causal inference to alleviate the data bias issues. Some research directions on how to apply causal inference to KGC deserve further thought.
First, we suppose that the confounders {ZH, ZR. Zr} in the causal graph of Figure b)) affect {H, R, T) individually. Confounders that affect at least two of {H, R, T) at the same time other types confounders are worth considering. Second, for the learnable confounders, deeper neural networks are worth exploring. Third, how to use frontdoor adjustment in KGC models also worth exploring. Fourth, counterfactual reasoning is another technique of causal inference, which be used to augment KG data.
backdoor adjustment to get causal KGC models,

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Stephen Bonner, Ian P Barrett, Cheng Ye, Rowan Swiers, Ola Engkvist, Charles Tapley Hoyt, and William L Hamilton. Understanding the performance of knowledge graph embeddings in drug discovery. Artificial Intelligence in the Life Sciences, pp. 100036, 2022.
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Jiawei Chen, Hande Dong, Xiang Wang. Fuli Feng, Meng Wang, and Xiangnan He. Bias and debias in recommender system: A survey and future directions. arXiv preprint arXiv:2010.02240, 2020.
Tim Dettmers, Pasquale Minervini, Pontus Stenetorp, and Sebastian Riedel. Convolutional 2d knowledge graph embeddings. In Thirty-second AAAI conference on artificial intelligence, 2018.
Chen Gao, Yu Zheng, Wenjie Wang, Fuli Feng, Xiangnan He, and Yong Li. Causal inference in recommender systems: A survey and future directions. arXiv preprint arXiv:2208. / /2397, 2022.
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Shaoxiong Ji, Shirui Pan, Erik Cambria, Pekka Marttinen, and S Yu Philip. A survey on knowledge graphs: Representation, acquisition, and applications. IEEE Transactions on Neural Networks and Learning Systems, 33(2):494 514, 2021.
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Matthew Richardson and Pedro Domingos. Markov logic networks. Machine learning, 62(1):107- 136. 2006.
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Tobias Schnabel, Adith Swaminathan, Ashudeep Singh, Navin Chandak, and Thorsten Joachims. Recommendations as treatments: Debiasing learning and evaluation. international conference machine learning, pp. 1670-1679. PMLR, 2016.
Zhiqing Sun, Zhi-Hong Deng. Jian-Yun Nie, and Jian Tang. Rotate: Knowledge graph embedding by relational rotation in complex space. In International Conference on Learning Representations, 2018.
Kristina Toutanova, Danqi Chen, Patrick Pantel, Hoifung Poon, Pallavi Choudhury, and Michael Gamon. Representing text for joint embedding of text and knowledge bases. In Proceedings of the 2015 conference on empirical methody in natural language processing, pp. 1499-1509, 2015.
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Théo Trouillon, Christopher R Dance, Éric Gaussier, Johannes Welbl, Sebastian Riedel, and Guil- laume Bouchard. Knowledge graph completion via complex tensor factorization. Journal of Machine Learning Research, 18:1-38, 2017.
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A APPENDIX
A.1 EXPERIMENTAL DETAILS
Datasets We evaluate our models three popular knowledge graph completion datasets, WNI8RR Detimers et al. (018). FB 15k-237 Toutanova et al. (2015) and YAGO3-10 Dettmers al. (2018). WNISRR is subset of WN18, with inverse relations removed. WN18 extracted from WordNet, database containing lexical relations between words. FB15k-237 is subset of FB15k, with inverse relations removed. FB15k extracted from Freebase, a large database of real world facts. YAGO3-I0 is subset of YAGO3 that only contains entities with least 10 relations. The statistics the datasets are shown Table 3
Table 3: The statisties of the datasets.
Dataset
#entity
#relation
#training
#validation
#test
WN18RR
40,943
11
86,835
3,034
3,134
FB 15k-237
14,541
237
272,115
17,535
20,466
YGA03-10
123,188
37
1,079,040
5,000
5,000
Data Bias in Datasets We use the Gini coefficients of d(h))d(r)/d(( to measure the data bias of h/r/t /t in the dataset 2, denote as gh (D)/g- (D) (D). Denote the training set as Dj, validation set as D2, and test set as Dz. The Gini coefficients of WN18RR, FB15k-237 and YAGO3-10 datasets are shown in Table 4 Gini coefficients are not less than 0 and not larger than 1. Larger Gini coefficients mean larger data bias. The results show that the degree of data bias on WN18RR dataset is less than that on FB 15k-237 dataset or YAGO3-10 dataset.
parametrrsss We add the N3 regularization Lacrroxx et al. let the regularization coefficient be X. We set the batch size to 1024, epoch to 50 and embed- ding dimension to 2048 for all models. We use Adam Kingma & Ba (004)) with exponential decay as the optimizer. We search the learning rate in (0.001, 0.003, 0.005, 0.01), decay rate in {0.9, 0.93, 0.95, 1.0), 31, B2, B3g in (0.1, 0.3, 0.5, 0.7, 0.9). X in {0.0, 0.001, 0.003, 0.01, 0.033. We first set 31 = 32 = Bg = A = O and search the learning rate and decay rate. For WN18RR dataset, set learning rate to 0.01 and decay rate 0.9 for all models. For FB dataset, set leamn ing rate to 0.005 and decay rate to 0.93 for all models. For YAGO3-10 dataset, we set learning rate to 0.003 and decay rate 0.9 for all models. We search at most 50 hyrre-pass combinations.
2018 to the loss function and
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Under review as a conference paper at ICLR 2023
The Gini coefficients of WN18RR, FB15K-237 and YAGO3-10 datasets. coefficients mean larger data bias.
Table 4:
Larger Gini
Dataset
9h (Di)
g-(Di)
gr (Di)
(D2)
(D2)
(D2))
(Da)
9r gr(Da)
gt (Ds)
WNISRR
0.453
0.667
0.453
0.136
0.664
0.136
0.139
0.664
0.139
FBI5k-233
0,560
0.679
0,560
0.511
0.718
0.511
0.519
0.718
0.519
YGAO3-10
0.573
0.832
0.574
0.191
0.816
0.191
0.191
0.811
0.191
Learnable Confounders We design the learnable confounders 24 qr (X qn (x..)..)) = vec vec((e...r.reeee. + б and 2e
Wecv X + bи. W vec(X..... (...)) + by. The number of parameters of WH/Wr is the product of the number of entities and the number of relations. The number of parameters of entities, which is too large for large datasets. Thus, we use weight sharing method to reduce the number parameters to reasonable size. The number of parameters of by /b/ by
WR is the square the number
Inverse Propensity Scoring We the inverse propensity scoring (IPS) method baseline method. Thus, we show more detailed statement about IPS. IPS method reweights the weight of the loss function for batch of data (h,, ri, (4), where i S B and B is the batch size, The loss function is defined as L = E/ wel(g Ti,ty Zhe Er,, 2,)), where
Σe d(b:))-
the weight (i.e., the inverse propensity score) and
lig(ti Ehis Zors z()) g(hi, Tis Ehi, Bhis Zras zt:) log(
exp(o(h,, ris Ehe Bhes Zre 24,1)
where ( &r.) 2g} is the value of confounding variables corresponding the triplet (h,, Fas t/)-
Our causal KGC model adds an extra term 24 + a, + a to the traditional KGC model r)) Thus, IPS methods focus on the loss function, our causal KGC model focuses on the scoring function.
Sensitivity Analysis We analysis the sensitivity of our models with respect to the hyper- parameters ay, a, and ag. We run experiments by setting as to {0.0, 0.2, 0.4, 0.6, 0.8. 1.0) and a, 0 0.0 to analysis the sensitivity of models with respect ay,, The hyper-parameter o, and a, are similar to the hyper-parameter ag- All experiments are trained on FB15k-237 dataset with ComplEx model. See Table the results. The results show that models sensitive to the hyper-parane papee-pprramters 0% 0t, and (gz-
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Table 5: The results on FB15k-237 datasets with different ayper-parameters.
Causal-ComplExx
Causal-ComplEis
MRR
H@
H@ 10
MRR
H@!
H@ 10
0h. 0.0, 0.0, 0.0
0.307
0.204
0.517
0.307
0.204
0.517
0h 00.,, a, 0.0, at 0.0
0.318
0.220
0.532
0.303
0.201
0.517
0h = 0.4, a, 0.0, at 0.0
0.306
0.210
0.509
0.310
0.209
0.532
= 0.6, a. D.0, 0.0
0.311
0.207
0.533
0.306
0.200
0.529
0.8, 0.0, 0.0
0.310
0.211
0,512
0.309
0.204
0.520
αд 1.0, 0.0, 0.0
0.298
0.189
0.529
0.305
0.200
0.534
0.0, 0.0, 0.0
0.307
0.204
0.517
0.307
0.204
0.517
α4 0.0, 0.2, 0.0
0.302
0.195
0.536
0.308
0.204
0.527
αg = 0.0, a, 0.4, dx 0.0
0.302
0.200
0.525
0.293
0.186
0.509
Q4 = 0.0, a. 0.6, at 0.0
0,309
0.206
0.524
0.308
0.209
0.522
= 0.0,
0.8, 0.0
0.304
0.204
0.531
0.310
0.208
0.533
Q4 0.0, a, 1.0, 0.0
0.301
0.189
0.529
0.307
0.204
0.516
Qa = 0.0,
0.0, 0.0
0.307
0.204
0.517
0.307
0.204
0.517
Qa. 0.0, a, 0.0, 0.2
0.323
0.208
0.556
0.321
0.220
0.532
a4 0.0, a, 0.0, Q: 0.4
0.329
0,222
0.548
0.322
0.214
0.547
9 = 0.0, a, D.0, at 0.6
0.332
0.229
0.551
0.326
0.220
0.552
Qy = 0.0, 0.0, a 0.8
0.329
0.221
0.552
0.322
0.216
0.546
9y 0.0, 0.0,
1.0
0.323
0.215
0.557
0.323
0.213
0.539
13


Reviews:
[{"review_id": "xvxCWG51xQi", "reviewer": "Reviewer_YGuw", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The paper proposes a novel approach to the task of knowledge graph completion, which draws on insights from the field of causal reasoning to obtain an adjustment that should - in principle - help with bias correction in the data underlying the knowledge graph. It considers two types of artificial confounders, one based on the log-popularity and another one, based on a one-layer neural network (aka a perceptron). ", "summary_of_the_review": "Overall, a decent paper with a moderate advance over the current state-of-the-art; it is a \"one-trick pony\" paper, with a single idea being presented and implemented, and evaluated with a single metric.", "strength_and_weaknesses": "Strengths: The overall presentation is clear, and the method is explained in a logical way that is easy to follow. The abstract sets the stage, the introduction reviews relevant work, and the methods clarify the novelty of the work. The results are presented fairly. The conclusion points out that much future work remains.\n\nWeaknesses: These are easier to list for specific sections, which I have done below.\n\nAbstract: \"our causal KGC models achieve better performance than traditional KGC models\" - on what inputs?\n\nIntro: \"the world is driven by causality rather than correlation\" - over-generalisation, especially as causality is often more difficult to observe\n\nBackground: the embedding isn't motivated or explained; is it externally specified? learned in the graph construction process? In the tensor representation of the causal graph each entity and relation is an element of a set, not a vector, so this needs a clear explanation/illustration.\n\nMethods: \n\n1) While the entire process is motivated by causal inference and the removal of confounders, the simplifying assumptions ultimately amount to a. a frequency penalty and b. a learned entity-specific or relationship-specific penalty. Would it not have been easier to present the entire approach as a penalty-based one, and then provide the motivating causal inference-based derivation in the appendix?\n\n2) The group-theoretic view does not provide any additional value or insight to the paper; I say this despite being a big fan of group theory myself. I recommend removing this section altogether.\n\n3) A clearer differentiation from inverse propensity scoring should be provided by explicitly showing how IPS does something different from the frequency penalty introduced in the method.\n\nResults: \"different evaluation metrics\" - it seems that you only used a single evaluation metric in the end, namely, Metric(-1,-1,-1)?\n\nDiscussion: \"our model is [...] model-agnostic\" is confusing; perhaps \"our approach is [...]\" instead?\n\nAppendix: the standard deviation of frequency is not a great way to quantify bias; perhaps fitting a modified Zipf's law or computing a Gini coefficient could be more useful?", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "u4PAO4dMwk", "reviewer": "Reviewer_v6Kd", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper proposed a causal KGC model to alleviate the data bias issues that come from the data collection process, and further proposed an evaluation method to evaluate the causal KGC models on observation datasets. Moreover, the authors also provided a different perspective of viewing KGC from group theory. Numerical experiments showcased that the causal KGC models outperform traditional KGC models in most cases. ", "summary_of_the_review": "Based on my comments in the previous sections, even though this paper has certain merit of introducing causal model into KGC, but overall I do not think the contribution is significant enough to make this paper be accepted as the ICLR conference proceeding. ", "strength_and_weaknesses": "Strength: It's an interesting ideal of trying to incorporate causal inference techniques into traditional KGC models, and the group theory perspective of KGC is quite novel.\n\nWeakness: 1.I agree that in some sense, data bias can be treated as confounders in the causal model, however, I do not think it's appropriate to simply define the confounders as the \"artificially designed confounders\" and \"learnable confounders\" in this paper. Confounders are the type of variables that have causal impact over both treatment and outcome variables, but in the definition of \"artificially designed confounders\" in this paper, they are essentially treated as the variables that are impacted by treatment variables. In other words, the directions of certain arcs in the causal graph changed.    \n2. I appreciate the attempt of explaining KGC from the group theory perspective. However, I cannot see if there's an potential application or new insights from such explanation. \n\nOther comments: 1. Too much identical sentences in Abstract, Introduction and Conclusion.      \n2. In multiple places, you wrote \"In this paper, we propose causal KGC models to alleviate the issues ...\" Here you should be more specific by saying \"data bias issues\".   \n3. You mentioned \"causal graph\" is multiple places of this paper. However, in the causal KGC model, all causal graphs are essentially identical and they have the same topology as the graph (b) in Figure 1. The reason why causal graph in traditional causal inference is important is because, it gives people a direct way of viewing the relationship between variables, which can help people identify what are confounders, what are instrumental variables etc. By introduction causal model into KGC, here different triplets (h,r,t) will still have no connecting arcs between them, except the newly added confounder variables $(Z_h, Z_r, Z_t)$. For that reason, I do not think you should highlight the concept of \"causal graph\" in this paper at all.   \n4. You mentioned a few times that \"the main feature of causal is invariance and symmetry (Arjovsky et al., 2020)\". However, I did not see that from your cited literature. Why is the main feature of causal is symmetry? A causes B means something totally different from B causes A.    \n5. First sentence in Section 2.1, \"let $\\epsilon$ denote(s) and ... denote(s)\".  \n6. Bottom of page 4: \"$P(y \\mid h, \\ldots, z_t)$ evaluates...\" this is an incomplete sentence.   \n7. Bottom of page 4: \"confounders (is)\" should be \"are\".   \n8. When constructing the \"learnable confounders\", how to learn those neural networks?   \n9. On page 5, $z_t'$ should be $z_{t'}$.  \n10. Please add references to those ranking metrics $MRR$ and $H@N$.  \n11. Should not use the word $Metric$ as the name of your evaluation metric.   \n12. In Section 3.3, \"should invariant\" -> \"should be an invariant\".  \n13. In Section 3.3, \"which may (do) not match ...\"  \n14. Last sentence of Section 5.2: I cannot see the reason from the degree of data bias. Please explain more. ", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "A0HBjAlz13", "reviewer": "Reviewer_L8AG", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The knowledge graph completion is a key to studying the correlations in data. This paper proposes to study the causality of the KGC from a causal graph point of view. The method is evaluated by empirical experiments. However, in total, the novelty of the approach and the profound impact are both limited. \n\n", "summary_of_the_review": "The paper studies the causality of KGC and uses numerical experiments to justify the proposed method. However, the development of the method is not clear and the paper is not well-presented. This limits the potential impact of the paper. ", "strength_and_weaknesses": "Strength: The authors evaluate the proposed causal KCG by relatively comprehensive empirical experiments. \n\nWeaknesses: \n\n1. The preliminaries and background introduction for the SCM models should be more comprehensive, as this is the fundamental point for the later KGC model development. \n\n2. The logarithmic function definition for designed confounders is restrictive. Otherwise, the author should refer to the existing literature for such definition and evidence. \n\n3. In the one-layer neural network, is it able to approximate the complex confounder? This seems to disobey the universal approximation theorem in DNN. \n\n4. The score function $f(h,r,t)$ is not clear how affect the conditional probability $P(y|h,r,t,z_h,z_r,z_t)$. In addition, the linear decomposition might require the $g$ function is soothing. However, the authors seem not to address or mention this part in the paper.\n\n5. The balancing of $\\alpha_{h}, \\alpha_{r}$ and $\\alpha_{t}$ is crucial to balance the bias-variance tradeoff, the authors might be better to discuss this. \n\n6. The authors define a novel metric for evaluation purposes. I was wondering if is there any existing metric for better comparison.\n\n7. The causal-distmult-2 outperforms the competing methods in FB15k-237. But other ones, like causal TransE-1, RotatE-1, and ComplEX-1 are best. Could the authors give some analysis of this phenomenon? ", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}]

Author rebuttal:

Decision: Reject