=Paper=
{{Paper
|id=Vol-2846/paper31
|storemode=property
|title=Using a General Prior Knowledge Graph to Improve Data-Driven Causal Network Learning
|pdfUrl=https://ceur-ws.org/Vol-2846/paper31.pdf
|volume=Vol-2846
|authors=Meghamala Sinha,Stephen A. Ramsey
|dblpUrl=https://dblp.org/rec/conf/aaaiss/SinhaR21
}}
==Using a General Prior Knowledge Graph to Improve Data-Driven Causal Network Learning==
https://ceur-ws.org/Vol-2846/paper31.pdf
Using a General Prior Knowledge Graph to Improve
Data-Driven Causal Network Learning
Meghamala Sinhaa , Stephen A. Ramseya,b
a
School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, OR 97331, United States
b
Department of Biomedical Sciences, Oregon State University, Corvallis, OR 97331, United States
Abstract
We describe a method βKg2Causalβ for using a large-scale, general-purpose biomedical knowledge graph
as a prior for data-driven causal network structure learning. Given a set of observed nodes in a dataset,
and some relationship edges between the nodes derived from a knowledge graph, Kg2Causal uses the
knowledge graph-derived edges to guide the data-driven inference of a causal Bayesian network. We
tested Kg2Causal on several real-world biological datasets with known ground-truth networks and
demonstrate improvement in network learning accuracy, relative to a baseline of an uninformative net-
work structure prior. We also demonstrate the application of our method if data are collected under
different experimental conditions including interventions on the observed variables.
Keywords
Causal inference, Structure learning, Knowledge graph, Informative prior
1. Introduction
Causal modeling is a useful analytical tool in various fields due to its applicability in action
planning, prediction and diagnosis [1, 2, 3, 4, 5]. However, learning a causal Bayesian network
(CBN) solely from data is a challenging task [6, 7, 8]. CBN learning can be thought of as model
selection problem in which model is a directed acyclic graph (DAG), where problem is to find
the graph πΊ that maximizes some objective (score) function of dataset π·. In some CBN learn-
ing methods, score function is likelihood π(π· β£ πΊ) representing overall fit of πΊ to π· in context
of a generative model for the data. For a dataset with π observables (features), the number of
possible DAGsβand thus requirement for dataβgrows super-exponentially with π [9]. In most
network learning applications, prior knowledge exists about causal (or suspected causal) rela-
tionships among the observables; such prior knowledge can be valuable resource for network
structure learning [10]. Supposing that prior knowledge can be represented as prior probability
π(πΊ) on network structure, one can alternatively choose as basis for CBN scoring function, the
posterior probability π(πΊ β£ π·) = π(π· β£ πΊ) π(πΊ)/π(π·). In contrast to substantial amount of work
done on variety of marginal likelihood and scoring methods, less attention has been given to
functional form (and associated parameterization) of the prior π(πΊ) for application contexts
In A. Martin, K. Hinkelmann, H.-G. Fill, A. Gerber, D. Lenat, R. Stolle, F. van Harmelen (Eds.), Proceedings of the AAAI
2021 Spring Symposium on Combining Machine Learning and Knowledge Engineering (AAAI-MAKE 2021) - Stanford
University, Palo Alto, California, USA, March 22-24, 2021.
" sinham@oregonstate.edu (M. Sinha)
Β© 2021 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073 CEUR Workshop Proceedings (CEUR-WS.org)
where structured prior knowledge is available. Without expert knowledge, standard network
inference approaches, by default, assume uniform (uninformative) prior which can lead to er-
roneous relationships or relationship orientations both due to (i) size of space of networks and
(ii) degeneracy of Markov-equivalent networks. Proper incorporation of informative priors can
enhance model efficiency [11] and can also overcome weakness of smaller dataset.
For most applications of causal modeling, some prior knowledge is available. For example, in
medicine, most cases have prior knowledge about etiology, symptoms, and treatment of under-
lying diseases or conditions which can be obtained from biomedical literature or knowledge-
bases. Although there is in general large scale availability of structured prior knowledge (for
example, ontologies) in various scientific domains, these mostly comprise disparate informa-
tion sources in various standards and formats, which poses a challenge to integrate them into
single structure. These problems motivated building of large multi-graphs called knowledge
graphs (KG) [12] that incorporate structured knowledge from multiple sources within a con-
sistent schema. Knowledge graph is a term of art to mean a large graph-structured model to
store interlinked relationships between nodes representing concepts [13]. These large-scale
networks accommodate structural information which can be leveraged for reasoning, recom-
mendation or decision making. We hypothesized that combining information from structured
databases of general prior knowledge with causal modeling based on context-specific multi-
variate measurements will improve accuracy of learned network compared to result of data-
driven causal modeling without incorporating prior knowledge.
In this work, we propose a method,
βKg2Causalβ, for extracting relations
as pairs of nodes from a knowledge
graph, and for incorporating them as
priors on corresponding edges in a
score-based, data-driven causal network
learning method. In this study, prior
edges from knowledge graph are ac-
Figure 1: (a) A network containing known relationships be- counted for in prior probability of the
tween lungs condition and diseases, (b) correspond- graph, using the method of Castelos
ing sub-graph in a knowledge graph and Siebes [11]. We used a large-scale
biomedical knowledge graph (KG) 1 that
we and collaborators (see Acknowledgments) had previously constructed (see Sec. 2.5) con-
taining millions of nodes representing drugs, genes, diseases, or phenotypes (Fig. 1b), as
well as edges between nodes representing various types of predicate relationships. For
the measurement-based network learning component of KG2Causal, we used an optimizing
method combining Tabu search algorithm [14] with Bayesian Dirichlet uniform (BDeu) [15, 16]
network score. Using five different multivariate molecular biology datasets for which ground-
truth networks were available (see Sec. 4), we empirically analysed network learning accuracy
of βKg2Causalβ along with various types of uninformative prior to test the usefulness of adding
KG-based priors. We provide a comparative benchmark of our methods performance over
five real-world biological datasets and two synthetic datasets of varying sizes where we found
1
https://github.com/RTXteam/RTX/code/reasoningtool/kg-construction
that Kg2Causal had superior network learning accuracy to methods that do not use general
knowledge-base as network structure prior. Finally, we demonstrate (Sec. 4.3) the application
of Kg2Causal if data are collected under different experimental conditions including interven-
tions on the observed variables. We implemented βKg2Causalβ in the R programming language
(leveraging the bnLearn package [17]) and provide the code as open-source software 2 .
2. Related work and Background
In this section, we describe Kg2Causalβs conceptual foundations including CBNs, score-based
causal modeling, interventions, and knowledge graph-based priors in network learning.
2.1. Causal network: Brief Overview
A causal Bayesian Network [1, 2] is a DAG πΊ = (π , πΈ), where π = {π1 , β¦ , ππ } denotes the
set of variables (nodes) and πΈ β π Γ π denotes the causal relationships (edges). For an edge
(ππ , ππ ), we say that ππ is a parent (cause) of ππ , and ππ is a child (effect) of ππ . We will use
Pa(ππ ) to denote the set of parents of ππ . The conditional probability distribution ππ defines
the probability of ππ given the states of its parents Pa(ππ ). A causal network represents a joint
distribution π over variables π as long as it satisfies two main assumptions:
a) Causal Markov: Any given variable ππ is independent of its non-descendants, conditioned
on all of its direct causes. The assumption implies that the joint distribution π(π ) can be fac-
tored as: π(π ) = βππ=1 ππ (ππ β£ Pa(ππ )).
b) Faithfulness: The joint distribution π(π1 , β¦ , ππ ) is faithful to πΊ if every conditional inde-
pendence relation in π is entailed by the causal Markov assumption applied to πΊ [18].
2.2. Constructing a causal network
Let us assume, we have a dataset π· having observations over set of π variables. One of the main
classes of causal learning approaches is the Score-based approach which is derived from classic
Bayesian method where a scoring function evaluates the fit of graph πΊ to data π· [16, 6] with a
higher value indicating better fit. A search algorithm is used to explore the space of all possible
graphs, to maximize the scoring function. Typical heuristic algorithms used for this purpose
include hill-climbing or Tabu search approaches [14]. Other common score based methods are
GDS [19] and Gies [6]. According to standard Bayesian rule, a causal graph πΊ, is a π·π΄πΊ learned
from given data π· as π(πΊ β£ π·) β π(πΊ)π(π· β£ πΊ), where π(πΊ) is prior distribution over space of
all possible DAGs reflecting prior knowledge and π(π· β£ πΊ) is marginal likelihood of the data
π·. As described in Sec. 3, the Kg2Causal method incorporates a score-based approach.
2.3. Learning with interventions
Interventionsβexternal manipulations of nodes (βtargetsβ) in a networkβare important to de-
tect causal relations that can help disambiguate Markov equivalent sub-networks [16]. Let πΌπ
represent set of target nodes that are altered in interventional experiment π and ππ = π \πΌπ be
2
https://github.com/meghasin/Kg2Causal
the complementary set of observational variables. Each intervention can have one or more
targets whose conditional probabilities are changed (so that, conditioned on intervention, tar-
get variableβs distribution may depend only on a (possibly empty) subset of its parent ob-
servables). Hence, each intervention results in deletion of arrows pointing towards the in-
tervened nodes. The joint distribution of π after intervention is π(π1 , ..., ππ ) = βππ βππ ππ (ππ β£
ππ(ππ ))β
βππ βπΌπ ππβ² (ππ β£ ππ(ππ )), where π(ππ β£ ππ(ππ )) is conditional probability similar to ππ , given
that ππ is not a target node, and π β² (ππ β£ ππβ² (ππ )) is post-intervention conditional probability of
ππ given its new set of parents ππβ² (ππ ). For a so-called βperfectβ intervention, one would set
ππβ² (ππ ) = β
[1]. Score-based approaches are well-suited to mixed interventional-observational
datasets, in contrast to constraint-based approaches which are applicable to observational data.
2.4. Incorporation of Priors
In this subsection we introduce three types of uninformative priors on the network structure
π(πΊ), uniform prior, marginal prior, and Bayesian variable selection prior (VSP). We then de-
scribe the knowledge graph-based prior that we use in Kg2Causal method. In cases for lack of
prior knowledge, default choice for prior π(πΊ) is a uniform prior distribution, as follows:
π(πΈ βͺ {ππ , ππ } β£ π·) π(πΈ βͺ {ππ , ππ }) π(π· β£ πΈ βͺ {ππ , ππ })
=
π(πΈ β£ π·) π(πΈ) π(π· β£ πΈ)
where nodes ππ and ππ can have three possible cases ππ βVπ (representing (ππ , ππ ) β πΈ),Vπ βVπ
(representing (ππ , ππ ) β E) or ππ βVπ (no arc) and each have equal probability of occurrence.
So the probability for these edges are assigned as π(ππ βVπ ) = π(ππ βVπ ) = π(ππ β ππ ) =
1/3, since we know that π(ππ βVπ ) + π(ππ β ππ ) + π(ππ β ππ ) = 1. This implies π(ππ β
ππ ) + π(ππ β ππ ) = 2/3, which means a higher promotion for the inclusion of new arcs and
favouring the propagation of false positives in πΊ. Hence, its not always a good idea to use
uniform prior specially for cases where data is not too supportive of the DAG learned and
where π is large. A better version of uniform prior is to use marginal probabilities instead,
where an independent prior can be assumed for each arc with same independent marginal
probabilities as uniform priors, also called marginal uniform [20]. In this case, the probability
of inclusion of each edge is assigned as π(ππ β ππ ) = π(ππ β ππ ) = 1/4 and π(ππ β ππ ) = 1/2.
Compared to the uniform prior, the marginal uniform prior is less prone to false-positive edges
in the posterior-probability-maximizing graph. The Bayesian variable selection prior (VSP)
assigns a probability of inclusion of possible parent nodes, with the default being 1/π.
The heart of Kg2Causal is the use of an informative prior based on a general-purpose knowl-
edge graph; for this purpose we use an edge decomposition technique described by Castelo
and Siebes [11]. For any pair of vertices (ππ , ππ ) for which an edge ππ βVπ exists in the
general-purpose knowledge graph, we assign a prior probability (π½ = 1/2) on those edges,
with probability 1/4 for ππ βVπ and probability 1/4 for ππ βVπ , since the later two are al-
ternate edges that have no corresponding edge in the general knowledge graph we use the
uniform probability distribution as shown in Fig. 2. In this way we can create a complete
prior probability (from partial knowledge) over the network πΊ; on log scale, we define π(πΊ) as
log π(πΊ) = βππ βππ βπΈ, πβ π log π(ππ β ππ ) + βππ β―ππ βπΈ, πβ π log π(ππ β ππ ).
2.5. Knowledge Graphs
A βknowledge graphβ [13] is a multigraph consisting of
nodes and edges (labeled by relationship type or descrip-
tion of instance attributes) between them. Although most
relationships in knowledge graphs are between entities
and context-based associations, these do not always imply
causal relationship. Nevertheless, such links are strong as-
sociation that can strengthen causal relationships that we
seek to discover. The key idea of Kg2Causal is to use links Figure 2: Complete prior by edge de-
composition technique
from large knowledge graphs as generalised prior informa-
tion to aid in data-driven network learning in highly spe-
cific application contexts. For this work, we leveraged a general biomedical knowledge graph
that we and collaborators (see Acknowledgments) had constructed, KG1 3 . KG1 has 130,443
nodes, 3.5M edges, 11 node semantic types, and 17 edge relation types, and was compiled from
20 different biomedical knowledge-bases (Monarch, COHD, ChEMBL, DGIdb, DisGeNet, Dis-
ease Ontology, GeneProf, HMDB, KEGG, miRBase, miRGate, mychem.info, mygene.info, NCBI
Gene, OMIM, Pathway Commons, Pharos, PubChem, Reactome, and UniprotKB). We hosted
KG1 in a Neo4j database (ver. 3.5.13) and used the Cypher query language to search for concept
mappings between ground-truth network variables and concept nodes in the KG1 knowledge
graph, and for edge connections between mapped concepts within KG1.
3. Our Approach
We developed KG2Causal to leverage a general-purpose biomedical knowledge graph (see
Sec. 2.5) in order to improve context-specific, data-driven network learning from multivariate
observations; such observations could consist of gene expression measurements, proteomics
measurements, or electronic health records. The key ideas of our approach are (i) mapping
each variable in the dataset to a node in the knowledge graph, and querying relationships be-
tween them; (ii) extracting a subgraph containing the connected variables with edges between
them; and (iii) use this edge set as our prior knowledge to guide the optimizing scoring step
for inferring causal network. Mathematically, given a dataset π·, with a set π of observable
variables and given a general-purpose prior knowledge graph Ξ as a multigraph, we want to
learn a causal graph πΊ π = (π , πΈ) that approximately maximizes the posterior probability, i.e.,
argmaxπΊ (π(πΊ β£ π·, Ξ)), given a prior π(πΊ β£ Ξ). As a comparison, we used three uninforma-
tive prior distributions, namely uniform, marginal and Bayesian variable selection priors with
each dataset in order to understand whether or notβand to what extentβusing an informa-
tive network prior improves accuracy of causal network learning in a biomedical context. The
Kg2Causal network discovery workflow, illustrated in Figure 3, consists of the following steps:
β’ Map variables π to nodes in Ξ, and extract a list π½ of edges from Ξ among the nodes
(collapsing same-direction multiedges to single edges).
3
https://github.com/RTXteam/RTX/code/reasoningtool/kg-construction
Figure 3: Workflow of Kg2Causal: Step 1 - Data collection (can be a combination of observational and/or in-
terventional studies). For example, in this figure, we show that node C (in red, top center) has been intervened.
Step 2 - Cleaning and discretizing the data. Step 3 - Generating 100 random DAGs using the observed nodes.
Step 4 - Optimizing each of the 100 DAGs using Tabu search. In this step, we also extract edges present in the
KG and incorporate them as a prior. Step 5 - Calculating probability of occurrence for each possible arc in the 100
optimized DAGs. Step 6 - Constructing the final network by selecting arc strengths above a threshold.
β’ Generate 100 random DAGs with nodes π . We empirically determined, based on our
previous study [21], that this number is adequate for the medium-to-large datasets 4.
β’ In the score function, we include edge probability contributions from the prior knowl-
edge graph (we assign probability 0.5 for every edge in π½). For each DAG, we used the
stochastic algorithm Tabu [14] to find a DAG that maximizes standard Bayesian Dirichlet
equivalent uniform scoring function (BDeu) [15, 16].
β’ The previous step yields 100 optimized networks. Using these we compute the proba-
bility of each possible directed edge as its empirical frequency of occurrence among the
DAGs. For example, if an edge (π , π ) appears in 80 out of 100 optimized DAGs, we assign
it an empirical probability of 0.80. We store the edge probabilities in a list.
β’ We threshold the edge probabilities in order to obtain the set of edges πΈ for πΊ π . Based
on empirical studies, we chose a threshold of 0.85.
We chose Tabu for its robustness, simplicity (uses few parameters) and history-dependent
(βmemoryβ), although Kg2Causal is in principle compatible with any optimizing method.
3.1. Observational experiment
In the case where the dataset π· is purely observational (i.e., no interventions) from a single
experiment, Kg2Causal can be implemented algorithmically as described above; we provide a
pseudocode description of the βobservationalβ formulation of Kg2Causal in Algorithm 1.
Figure 4: Algorithm 1: Kg2Causal for observational data. We start by creating π random starting DAGs
using procedure createRandomNet and store them as randomDAG. Next, from each DAG in randomDAG, we
learn an optimized network and store the π networks in a list optimizedDAG. In this step, we also pass π½
to createRandomDAG. Next, using the list of networks in optimizedDAG, we compute the probabilistic arc
strength for each ordered pair of nodes as its empirical frequency, using procedure edgeStrength and store
them as edgeProb. Finally, we use learnCausalDAG where we select the edges with weight above a predefined
Threshold. Algorithm 2: Kg2Causal for mixed observational-interventional data.
3.2. Mix of Observational and Interventional experiments
With causal network learning based on a single observational dataset, it is difficult to differen-
tiate between compatible Markov equivalent models [22]. In the simple case of three variables
ππ , ππ and ππ , there are three possible causal models ππ β ππ β ππ , ππ β ππ β ππ , and
ππ β ππ β ππ ; all three structures are Markov equivalent. This ambiguity can be resolved
by incorporating measurements from interventional experiments, causing the Markov equiv-
alent structures to have different likelihoods. However, in real-world settings, it is difficult
to obtain such interventional measurements as compared to observational measurement [23].
Even when interventional datasets are available, learning a causal network from mixed ob-
servational and interventional data is challenging, for two reasons: (i) datasets collected from
different experiments under different environmental conditions or batches are not identically
distributed, in which case their underlying causal structures may differ leading to errors if net-
work inference is applied to the combined set of measurements; and (ii) in real-world settings
interventions are not βperfectβ but rather βuncertainβ (i.e., βimperfectβ or βfat-handβ), mean-
ing that the interventions have other unknown targets, which if ignored would likely yield
spurious interactions in network discovery. To deal with such cases, based on our previous
study demonstrating the effectiveness of the Learn and Vote algorithm [21, 24], we extended
Kg2Causal to include learning from a multi-experiment dataset using a voting-based integra-
tion method where experiment-specific causal networks are learned and combined by weighted
averaging into a consensus causal network. The additional steps in Algorithm 2 are as follows:
1. Let there be π experiments (can be observational and/or interventional) that produced π
datasets with observed variables as (π ) and known intervention targets as πΌ π π , if any.
2. Repeat steps 1-4 (from Sec. 3) for all π experiments.
3. From the π arc-weight lists, average arc strengths and directions over all the π experi-
ments in which the given arc is not intervened.
4. Per our earlier work [21], we used a threshold of 0.5 for the average arc probability.
4. Analysis and Results
In this section, we describe the observational datasets and ground-truth networks (Sec. 4.1)
and the simulated mixed interventional-observational datasets (Sec. 4.2) that we analyzed. We
present (Sec. 4.3) the results of empirical studies of network learning performance of Kg2Causal
on these datasets in comparison to other types of network structure priors.
4.1. Observational datasets that were analyzed
To assess performance of Kg2Causal on biological network inference problems, we empirically
analyzed five real world datasets for which published ground-truth networks were available:
Hepatic encephalopathy: This is a clinical study about a serious liver complication called
hepatic encephalopathy (HE) [25] with conditions like electrolyte disorders, infections, poor
spirits. It is a categorical dataset with eight nodes and ground-truth containing ten edges.
Sachs et al. T cell signaling: This is a study on mixed observational and interventional
experiments to infer causal connections between eleven protein and phospholipids in the in-
tracellular signaling network of individual human CD4+ T-cells [26]. The dataset contains
measurement of gene expressions with ground truth network containing twenty edges.
Hematopoietic Stem Cell Differentiation (HSC): This is a real-world gene regulatory
network to study underlying myeloid differentiation from multipotent myeloid progenitors to
megakaryocytes, erythrocytes, granulocytes and monocytes [27] in mammals [28]. The dataset
contains measurement of gene expressions with ground-truth network having thirty edges.
Gonadal Sex Determination (GSD): This a real-world model which represents the go-
nadal differentiation circuit which monitors the transformation of the bipotential gonadal pri-
mordium (BGP) into either female or male gonads [29]. The network consists of eighteen genes
and one node for the urogenital ridge. The dataset contains measurement of gene expressions
with ground-truth network containing seventy nine edges [28].
Yeast cell cycle: This is a dataset derived from a network model of thirty genes participating
in cell-cycle regulation of yeast [30]. The dataset was created by integrating gene expression
data with transitive protein-protein interaction. The ground-truth network has 317 edges.
4.2. Mixed observational-interventional datasets
We tested Kg2Causal using Sachs et al. interventional dataset and simulated observational and
interventional measurement data from synthetic networks using the bnlearn package. For
observational data, we drew random samples and for interventional data, we set some target
nodes in the network to fixed values in order to create mutilated networks [31] before drawing
samples from them. To simulate an uncertain intervention (or βfat-handβ) [32] we intervened
one or more of child nodes of the interventionβs target node.
Cancer: This is a synthetic network [33] on causes and consequences of lung cancer. We
simulated data from one observational and one interventional experiment with equal num-
ber of samples (500) from each experiment to avoid bias. For interventional experiment we
generated a mutilated network: cancer_mut with one intervention (node Smoker).
Asia: This is a synthetic network [34], about occurrence of lung disease and their epidemio-
logical connection a prior visit to Asia. We simulated one observational and two interventional
ROC curve PR curve F-1 score Accuracy
HE
Sachs
HSC
GSD
Yeast
Figure 5: Empirical performance (ROC, precision-vs-recall, F1 vs. cutoff, and accuracy vs. cutoff) of Kg2Causal
in each of five datasets compared to learning with uninformative priors (uniform, marginal, and Bayesian VSP).
experiment from the synthetic network with equal number of samples (500) from each experi-
ment to avoid bias. For the interventional experiments we conducted experiments to generate
two mutilated networks: asia_mut1 with one intervention (node βLung Cancerβ) and asia_mut2
with two intervention (at nodes βLung Cancerβ and βTuberculosisβ).
4.3. Analysis of results
In this section we present results of empirical studies of network learning performance on the
five observational datasets (see Sec. 4.1) and three mixed observational-interventional datasets
(see Sec. 4.2), for Kg2Causal in comparison with three other types of network structure priors.
To quantify the performance, we considered presence of an edge in the ground truth network
as a βtrue positiveβ and absence of an edge as a βtrue negativeβ causal arc. For the observational
datasets, we used Algorithm 1 with indicated prior (KG, uniform, marginal, or Bayesian VSP)
as described in Sec. 3. For mixed interventional-observational datasets, we used Algorithm 2
with the indicated prior. For each dataset, we found (Fig. 5) that using general knowledge graph
Table 1
Performance of βKg2Causalβ versus three uninformative priors, for network learning from observa-
tional data: Each row represents a specific real-world dataset (see Sec. 4.1) with corresponding ground-truth
network and is split by performance metric (AUROC, AUPR). Rows are ordered by network size (# of nodes).
Dataset Size Metric Uniform Marginal Bayesian VSP Kg2Causal
AUROC 0.800 0.789 0.800 0.842
HE 8 AUPR 0.810 0.799 0.812 0.854
AUROC 0.857 0.854 0.849 0.879
Sachs 11 AUPR 0.732 0.729 0.718 0.800
AUROC 0.705 0.702 0.701 0.745
HSC 11 AUPR 0.547 0.542 0.543 0.564
AUROC 0.656 0.660 0.656 0.676
GSD 18 AUPR 0.457 0.460 0.458 0.473
AUROC 0.569 0.556 0.537 0.623
Yeast 30 AUPR 0.619 0.606 0.581 0.662
Table 2
Performance of βKg2Causalβ versus three uninformative priors, for network learning from mixed
interventional-observational data: Rows correspond to datasets and columns correspond to types of priors,
split into analyses where data are pooled (per Algorithm 1) or voting is used (per Algorithm 2).
Dataset Size Metric Uniform Marginal Bayesian VSP Kg2Causal
Pooling Voting Pooling Voting Pooling Voting Pooling Voting
AUROC 0.750 0.700 0.750 0.740 0.750 0.780 0.813 0.833
Cancer 5 AUPR 0.776 0.677 0.776 0.690 0.776 0.720 0.809 0.738
AUROC 0.878 0.944 0.878 0.944 0.887 0.884 0.903 0.956
Asia 8 AUPR 0.711 0.902 0.711 0.905 0.736 0.852 0.817 0.940
AUROC 0.857 0.873 0.854 0.867 0.849 0.855 0.879 0.883
Sachs 11 AUPR 0.732 0.777 0.729 0.739 0.718 0.728 0.800 0.812
as prior improves performance, by ROC, precision/recall, F1, and accuracy. Quantitatively,
Kg2Causal had higher area under ROC curve (AUROC) and area under precision-recall curve
(AUPR) scores than network learning with three non-KG priors tested, for the five observa-
tional (Table 1) and three mixed interventional-observational (Table 2) datasets. Moreover, the
results of comparative analysis of Kg2Causal performance on mixed datasets (Table 2) show
effect of pooling data from different experiments (Algorithm 1) as compared to voting (Al-
gorithm 2) for such cases: pooling is better for small network (Cancer) (consistent with our
previous findings [21]), whereas voting is better for medium-sized networks (Asia and Sachs).
5. Discussion and Conclusion
A limitation of this study is that due to lack of availability large ground-truth causal networks,
all datasets analyzed in this work are for small to medium sized networks (8-30 nodes); due to
scalability issue of score-based methods, Kg2Causal method as described here would be chal-
lenging to apply to larger networks (many hundreds to thousands of nodes and beyond), which
is an area of future work. Further, we plan to explore ways to incorporate a network structure
prior in constraint based algorithms (for example, PC algorithm [2]), given (in general) more
favorable scalability of constraint-based algorithms and given the overwhelming preponder-
ance of observational-only datasets that are available. We also want to evaluate alternative
methods (other than the method [11] that we are using) for incorporating priors and compare
them. Present work clearly demonstrates, for the case of causal network learning from small- to
medium-sized biomedical or biological datasets, the importance of aggregating and leveraging
structured prior knowledge in order to maximize network learning accuracy.
6. Acknowledgments
This work was supported in part by the National Center for Advancing Translational Sciences
(NCATS) through the Biomedical Data Translator program (OT2TR002520 & OT2TR003428 to
SAR). We thank David Koslicki, Eric Deutsch, Yao Yao, Zheng Liu, Deqing Qu, Finn Womack,
and Ujjval Kumaria for their work on constructing the KG1 knowledge graph.
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