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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Marrying LLMs with Domain Expert Validation for Causal Graph Generation</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Alessandro Castelnovo</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Riccardo Crupi</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Fabio Mercorio</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff3">3</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Mario Mezzanzanica</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff3">3</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Daniele Potertì</string-name>
          <xref ref-type="aff" rid="aff3">3</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Daniele Regoli</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>CRISP Research Centre crispresearch.eu, University of Milano Bicocca</institution>
          ,
          <country country="IT">Italy</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Data Science and Artificial Intelligence, Intesa Sanpaolo S.p.A.</institution>
          ,
          <country country="IT">Italy</country>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>Dept. of Informatics</institution>
          ,
          <addr-line>Systems and Communication, Univ. of Milan-Bicocca</addr-line>
          ,
          <country country="IT">Italy</country>
        </aff>
        <aff id="aff3">
          <label>3</label>
          <institution>Dept. of Statistics and Quantitative Methods, Univ. of Milan-Bicocca</institution>
          ,
          <country country="IT">Italy</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>In the era of rapid growth and transformation driven by artificial intelligence across various sectors, which is catalyzing the fourth industrial revolution, this research is directed toward harnessing its potential to enhance the eficiency of decision-making processes within organizations. When constructing machine learning-based decision models, a fundamental step involves the conversion of domain knowledge into causal-efect relationships that are represented in causal graphs. This process is also notably advantageous for constructing explanation models. We present a method for generating causal graphs that integrates the strengths of Large Language Models (LLMs) with traditional causal theory algorithms. Our method seeks to bridge the gap between AI's theoretical potential and practical applications. In contrast to recent related works that seek to exclude the involvement of domain experts, our method places them at the forefront of the process. We present a novel pipeline that streamlines and enhances domain-expert validation by providing robust causal graph proposals. These proposals are enriched with transparent reports that blend foundational causal theory reasoning with explanations from LLMs.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;Causal Discovery</kwd>
        <kwd>LLMs</kwd>
        <kwd>Human-AI-Interaction</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        In the modern era, the realms of Causality and Artificial Intelligence (AI) are converging to foster
a significant transformation in various sectors, including business and industry. Understanding
causality, a practice deeply rooted in causal inference and causal discovery, has become pivotal in
enhancing decision-making processes and fostering innovation in a data-driven society. Causal
inference, the practice of determining the cause-and-efect relationship between variables [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ],
and causal discovery, the identification of these relationships from observational data [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ], have
taken center stage.
      </p>
      <p>
        In recent years, the push towards explainable AI has garnered significant momentum, with
numerous government initiatives underscoring its importance. Notably, the General Data
Protection Regulation (GDPR) in the European Union [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ], the Defence Advanced Research
Projects Agency (DARPA) XAI program in the United States [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ], and the European Commission’s
proposal for legislation on AI systems (The European Commission 2021) have all been striving to
3rd Italian Workshop on Artificial Intelligence and Applications for Business and Industries - AIABI
co-located with AI*IA 2023
      </p>
      <p>
        © 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
foster the development of AI systems whose outputs are both comprehensible and trustworthy
for end-users. According to [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ], humans perceive an explanation as good when it possesses
certain characteristics. These include being contrastive, concise, selected, social, and causal. In
particular, to ensure the understanding of the underlying causal relationship between data, Direct
Acyclic Graphs (DAGs) emerge as a fundamental tool in the evolution of explainable AI systems.
These graphs, which are pivotal in modeling causal relationships and forming the structural
basis of causal models [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ], represent variables as nodes and causal relationships as edges. This
structure not only eliminates feedback loops but also delineates causal efects with clarity,
facilitating the transparent articulation of causal assumptions. Moreover, DAGs, or Structural
Causal Models (SCMs), play a crucial role in identifying confounding variables, thereby aiding
in the construction of accurate and interpretable models. Through these capabilities, DAGs have
proven to be an indispensable foundation in the creation of AI-driven decision models, aligning
perfectly with the aforementioned government initiatives by contributing to the development
of explanations that can be easily understood and trusted by users [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ]. Thus, the incorporation
of SCMs in AI systems aligns well with ongoing governmental eforts to promote explainable
AI, serving as a vital tool in the realization of this significant objective.
      </p>
      <p>
        However, modeling causal knowledge is complex and challenging since it requires an actual
understanding of the relations, beyond statistical correlation. Yet, a critical ingredient in this
quest for causality is domain knowledge [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. Nevertheless, in numerous real-world scenarios,
the collaboration between non-technical domain experts and computer scientists in defining a
causal graph can be a challenging and time-consuming process [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ]. This is evident in the work
of [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ], in which is developed a method for counterfactual generation that respects the causal
influence among variables. This application is essential in business and banking contexts, such
as credit lending, where a client who has their loan denied has the right to know what actions
they can take to get the loan approved. These actions must be feasible and take into account
the causal relationships between variables (e.g., the type of job influences income, not the other
way around).
      </p>
      <p>
        LLMs, such as GPT-3.5 and GPT-4, show promise in bridging the gap between computational
eficiency and domain expertise [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ]. They excel in causal reasoning tasks, translating between
natural language and formal methods, generating causal graphs, and identifying background
causal contexts [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ]. LLMs can act as proxies for human domain knowledge, enhancing causal
analysis while reducing human efort [ 10]. Their prowess, mainly when used alongside
existing causal statistical methods [11] holds the potential to revolutionize how we approach
and understand causality. However, despite their benefits, LLMs may misinterpret complex
causal models without deep domain expertise, leading to erroneous decisions [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. Thus, deep
domain knowledge remains crucial and indispensable, acting as a guiding force that enables AI
technologies like LLMs to realize their full potential in causal discovery, thereby contributing to
the ongoing transformative wave in various industries [12].
      </p>
      <p>The primary objective of this work is to harness AI’s transformative power in reshaping
business and industry processes, particularly focusing on the integration of LLMs with causal
discovery techniques. Automating the discovery of causal relationships, allows domain experts
to concentrate solely on validating the proposed causal graph [13], thereby potentially achieving
higher quality and greater eficiency, akin to the revolution AI has brought in other sectors.
This endeavor seeks to significantly reduce the time and human resources traditionally required,
paving the way for a more innovative and eficient approach to business and industrial processes.
Contribution. We present a first attempt at formalizing a causal pipeline to design a causal
graph requiring minimal domain knowledge, that seamlessly combines data-driven statistical
causality techniques with the insights of LLMs, acting as proxies for domain expertise. Moreover,
this comprehensive framework has been encapsulated into an open-source Python package —
that will be available in open source — designed to ease its integration into real-world scenarios.</p>
      <p>As a contribution, this framework aims to be domain-specific, statistically robust,
transparent, and explainable to ensure trust and efective validation by the human-in-the-loop of the
generated causal graph. More in particular:
• domain-specific : among the results generated by the framework is a set of probable
DAGs that optimally depict the causal relationships derived from the given data. Notably,
these graphs are tailored not just to the data, but also to the specific domain, thanks to
the integration of the LLMs with the Causal Discovery theory.
• statistically robust: the framework includes a final statistical sensitivity assessment for
each DAG. This assessment evaluates the causal efect of each edge in accordance with
the literature on causal inference, ensuring the robustness of the results.
• transparent and explainable: for each DAG, a comprehensive report resulting from
rigorous causal theory testing, along with explanations provided by LLMs, either
reinforces or questions the presence of particular edges and directional relationships within
the graph.</p>
      <p>The process concludes with the domain expert making an informed decision to select the
preferred causal graph from among the proposed options. In our implementation, we place
significant emphasis on the aspect of prompt engineering within the overall processing of the
proposed causal pipeline.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Related Works</title>
      <p>In this section, we explore recent developments in the literature on LLMs that (i) focus on their
capabilities in the realm of causal reasoning, and (ii) investigate strategies for integrating LLMs
with causal discovery techniques.</p>
      <p>
        Exploring the Causal Reasoning Abilities of LLMs. Recent advancements indicate that
models like ChatGPT are progressing towards artificial general intelligence (AGI), notably
enhancing causal reasoning and high-precision tasks [14]. There is the potential for a paradigm
shift in machine learning that could harmonize the strengths of AI with human capabilities,
leading to transformative solutions and enhancing human decision-making [15]. Kıcıman et al.
[
        <xref ref-type="bibr" rid="ref8">8</xref>
        ] further explore LLMs capabilities in causal reasoning, illustrating their prowess in tasks
like code generation and complex reasoning. These models demonstrate high performance in
causal discovery, achieving up to 97% accuracy on the Tubingen benchmark and showcasing
versatility across diferent domains. Despite this, they can occasionally falter in basic logic tasks,
raising reliability concerns. Kıcıman et al. [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ] emphasize the importance of incorporating human
domain knowledge into causal analysis, suggesting that LLMs could serve as powerful tools
to enhance this process through dynamic conversational interfaces. Yet, it is vital to remain
cautiously optimistic about their capabilities due to potential erratic performances. Future
research is poised to delve deeper into the capacities and boundaries of LLMs in this domain.
Integrating LLMs in Causal Discovery. Long et al. [16] introduced a novel approach
to the challenges of causal discovery by formalizing the use of imperfect experts as an
optimization problem, aiming to minimize the Markov equivalence class (MEC) size while
ensuring the true graph remains included. They proposed a greedy approach reliant on
Bayesian inference to achieve this, incrementally integrating expert knowledge. Empirical
evaluations on real data revealed the efectiveness of their method, especially when the expert
consistently provided correct orientations. However, when using LLMs as the experts, the
results were mixed, suggesting both the potential and the challenges of integrating LLMs
into causal discovery. Ban et al. [17] explore the role of LLMs in Causal Structure Learning
(CSL), focusing on utilizing LLMs to pinpoint direct causal relations in observed data. This
two-stage framework first uses LLMs to identify potential causal connections based on
textual data and then applies these insights as constraints in data-driven CSL algorithms.
The aim is to merge the intuitive causal understanding of LLMs with the detailed causal
analysis found in CSL, potentially increasing its eficiency and accuracy. However, the
study acknowledges the potential errors in the causal statements generated by GPT-4,
indicating room for future improvements in both understanding and quality of causal relationships.
      </p>
      <p>In contrast to existing approaches, our work distinguishes itself by prioritizing human
validation. Unlike conventional methods that aim to autonomously generate causal graphs, we
actively engage domain experts. Our pipeline simplifies their tasks with robust causal graph
proposals, accompanied by a transparent report featuring both causal theory reasoning and
LLM-based explanations.</p>
    </sec>
    <sec id="sec-3">
      <title>3. The causal pipeline with LLM and Human-in-the loop</title>
      <p>Our proposed framework endeavors to deliver DAGs tailored to specific domains, leveraging
an explanation-centric approach and undergoing rigorous statistical testing. This framework
progresses through three essential phases: Causal Discovery, LLM-based Causal Elaboration,
and Causal Inference, as illustrated in Figure 1. Notably, human involvement remains a crucial
element throughout this process. This framework is designed to guide users in selecting the
appropriate Causal Graph, drawing from the Set of Directed Causal Graphs, Causal Relationship
Explanations, and Causal Sensitivity Analysis.</p>
      <p>
        Causal Discovery Step. The causal discovery step begins with a dataset containing the
variables of interest and their observed interactions. We process this dataset using four
distinct causal discovery algorithms: PC (a constraint-based method) [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ], GES (a score-based
method) [18], FCI (an extension of the PC algorithm) [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ], and LiNGAM (a functional causal
model) [19]. Each of these algorithms represents a distinct method within causal discovery.
      </p>
      <p>The output of this process is a set of four Causal Skeletons, each one derived from a causal
discovery algorithm. Each skeleton will be further processed by the LLM in the LLM-based
Causal Elaboration Step.</p>
      <p>LLM-based Causal Elaboration Step. Once we retrieve the sets of Causal Skeletons from
the previous step it is time to determine the direction of the relationships performing the task
of Pairwise Causal Discovery [20]. In this task, the goal is to determine the causal relationship
between two variables. In this stage of the framework, we undertake two primary tasks: initially,
we delve into understanding the inherent nature of the relationships depicted in each Causal
Skeleton, and subsequently, we explore potential additional relationships through conditional
independence tests. One of the fundamental challenges arises from the presumption that the
LLM can infer the domain context purely based on variable values1. In this stage, the success of
the task hinges largely on the quality of the prompt. We are in the process of creating a novel
prompt that aligns with causal theory and maintains consistent performance across various
LLMs, including GPT-3.5, GPT-4, and LLaMA. The outcome of this stage is a set of DAG: a
directional graph where the sequence of cause-and-efect relations is so structured that it never
loops back on itself. Furthermore, in this stage, we generate explanations using carefully crafted
prompts to justify the outputs of the LLMs.</p>
      <p>
        Causal Inference Step. The last phase of our pipeline is designed for the statistical validation
of the obtained DAGs from the preceding step. In pursuit of this objective, we adhere to the
four key steps of causal inference as outlined in [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. To facilitate this process, we leverage the
capabilities of DoWhy, a widely recognized open-source Python library. What distinguishes
DoWhy is its strong foundation in causal assumptions, firmly rooted in the well-established
framework of causal graphs [21].
      </p>
      <p>At the conclusion of the pipeline, we generate a transparent report for the user. This report
includes all the proposed DAGs and the rationale behind their generation. It encompasses the
results of causal discovery tests, LLMs prompt outcomes, and causal inference, empowering
users to make an informed choice regarding their preferred causal graph.
1For the LLM to make meaningful inferences and not merely fabricate a domain, the expert needs to provide at least
some foundational information about the domain.</p>
    </sec>
    <sec id="sec-4">
      <title>4. Conclusion and Next Step</title>
      <p>We presented a novel pipeline for constructing a causal graph that efectively combines
wellestablished causal theory algorithms from the literature with LLMs. While related works focus
on generating a final causal graph without the involvement of domain experts, our approach
is distinct as it places human validation at the core of the process, thereby aligning with the
broader trend where AI aids decision-makers in organizations, enhancing innovation processes
and managerial tasks. Our pipeline is designed to streamline and improve the expert’s work by
providing robust causal graph proposals. It accompanies these proposals with a transparent
report that includes the underlying causal theory reasoning and explanations derived from
LLMs. This approach not only sets us apart from existing methodologies but also aligns with the
ongoing revolution, where AI is a pivotal tool in enhancing business decisions. Our next steps
involve refining our prompts, open-source our code, and enhancing clarity in our LLM-based
Causal Elaboration step through detailed insights and prompt examples. Additionally, we
will further explore the limitations of LLMs, especially in sophisticated domains necessitating
profound expertise, it is also acknowledged that our method could derive further validation
and credibility through a more detailed evaluation segment. This includes highlighting the
pipeline’s eficacy through application on real-world datasets and engaging in a comparative
analysis with alternate methodologies.
Y. Li, S. Lundberg, Sparks of artificial general intelligence: Early experiments with gpt-4,
preprint arXiv:2303.12712 (2023).
[10] A. Radford, J. Wu, R. Child, D. Luan, D. Amodei, I. Sutskever, Language models are
unsupervised multitask learners, OpenAI blog (2019).
[11] M. Hernán, J. Robins, Causal Inference: What If, Chapman &amp; Hall/CRC, Boca Raton, 2020.
[12] D. Danks, Unifying the mind: Cognitive representations as graphical models, Mit Press,
2014.
[13] B. Youngmann, M. Cafarella, B. Salimi, A. Zeng, Causal data integration, arXiv preprint
arXiv:2305.08741 (2023).
[14] Z. C. et al., Understanding causality with large language models: Feasibility and
opportunities, arXiv preprint arXiv:2304.05524 (2023).
[15] C. T. Wolf, Reprogramming the american dream: from rural america to silicon
valley—making ai serve us all by kevin scott and greg shaw, Information &amp; Culture 56 (2021)
113–114.
[16] S. Long, A. Piché, V. Zantedeschi, T. Schuster, A. Drouin, Causal discovery with language
models as imperfect experts, arXiv preprint arXiv:2307.02390 (2023).
[17] T. Ban, L. Chen, X. Wang, H. Chen, From query tools to causal architects: Harnessing large
language models for advanced causal discovery from data, arXiv preprint arXiv:2306.16902
(2023).
[18] D. M. Chickering, Optimal structure identification with greedy search, Journal of machine
learning research 3 (2002) 507–554.
[19] S. Shimizu, P. O. Hoyer, A. Hyvärinen, A. Kerminen, M. Jordan, A linear non-gaussian
acyclic model for causal discovery., Journal of Machine Learning Research 7 (2006).
[20] J. M. Mooij, J. Peters, D. Janzing, J. Zscheischler, B. Schölkopf, Distinguishing cause
from efect using observational data: methods and benchmarks, The Journal of Machine
Learning Research 17 (2016) 1103–1204.
[21] A. Sharma, E. Kiciman, Dowhy: An end-to-end library for causal inference, arXiv preprint
arXiv:2011.04216 (2020).</p>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          [1]
          <string-name>
            <given-names>J.</given-names>
            <surname>Pearl</surname>
          </string-name>
          , et al.,
          <source>Models, reasoning and inference</source>
          , Cambridge, UK: CambridgeUniversityPress
          <volume>19</volume>
          (
          <year>2000</year>
          )
          <article-title>3</article-title>
          .
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          [2]
          <string-name>
            <given-names>P.</given-names>
            <surname>Spirtes</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C. N.</given-names>
            <surname>Glymour</surname>
          </string-name>
          ,
          <string-name>
            <given-names>R.</given-names>
            <surname>Scheines</surname>
          </string-name>
          , Causation, prediction, and search, MIT press,
          <year>2000</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          [3]
          <string-name>
            <given-names>The</given-names>
            <surname>European</surname>
          </string-name>
          <string-name>
            <surname>Union</surname>
          </string-name>
          , EU
          <article-title>General Data Protection Regulation (GDPR): Regulation (EU) 2016/679 of the European Parliament and of the Council of 27 April 2016 on the protection of natural persons with regard to the processing of personal data and on the free movement of such data</article-title>
          ,
          <source>and repealing Directive</source>
          <volume>95</volume>
          /46/EC (
          <article-title>General Data Protection Regulation)</article-title>
          ,
          <source>Oficial Journal of the European Union</source>
          ,
          <year>2016</year>
          . http://data.europa.eu/eli/reg/2016/679/2016-05-04.
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          [4]
          <string-name>
            <given-names>D.</given-names>
            <surname>Gunning</surname>
          </string-name>
          , D. Aha,
          <article-title>Darpa's explainable artificial intelligence (xai) program</article-title>
          ,
          <source>AI</source>
          magazine
          <volume>40</volume>
          (
          <year>2019</year>
          )
          <fpage>44</fpage>
          -
          <lpage>58</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          [5]
          <string-name>
            <given-names>T.</given-names>
            <surname>Miller</surname>
          </string-name>
          ,
          <article-title>Explanation in artificial intelligence: Insights from the social sciences</article-title>
          ,
          <source>Artificial intelligence 267</source>
          (
          <year>2019</year>
          )
          <fpage>1</fpage>
          -
          <lpage>38</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation>
          [6]
          <string-name>
            <given-names>R.</given-names>
            <surname>Crupi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Castelnovo</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D.</given-names>
            <surname>Regoli</surname>
          </string-name>
          , B. San Miguel Gonzalez,
          <article-title>Counterfactual explanations as interventions in latent space, Data Mining and Knowledge Discovery (</article-title>
          <year>2022</year>
          )
          <fpage>1</fpage>
          -
          <lpage>37</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation>
          [7]
          <string-name>
            <given-names>X.</given-names>
            <surname>Xie</surname>
          </string-name>
          ,
          <string-name>
            <given-names>F.</given-names>
            <surname>Du</surname>
          </string-name>
          ,
          <string-name>
            <given-names>Y.</given-names>
            <surname>Wu</surname>
          </string-name>
          ,
          <article-title>A visual analytics approach for exploratory causal analysis: Exploration, validation, and applications</article-title>
          ,
          <source>IEEE Transactions on Visualization and Computer Graphics</source>
          <volume>27</volume>
          (
          <year>2020</year>
          )
          <fpage>1448</fpage>
          -
          <lpage>1458</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref8">
        <mixed-citation>
          [8]
          <string-name>
            <given-names>E.</given-names>
            <surname>Kıcıman</surname>
          </string-name>
          ,
          <string-name>
            <given-names>R.</given-names>
            <surname>Ness</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Sharma</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Tan</surname>
          </string-name>
          ,
          <article-title>Causal reasoning and large language models: Opening a new frontier for causality</article-title>
          ,
          <source>arXiv preprint arXiv:2305.00050</source>
          (
          <year>2023</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref9">
        <mixed-citation>
          [9]
          <string-name>
            <given-names>S.</given-names>
            <surname>Bubeck</surname>
          </string-name>
          ,
          <string-name>
            <given-names>V.</given-names>
            <surname>Chandrasekaran</surname>
          </string-name>
          ,
          <string-name>
            <given-names>R.</given-names>
            <surname>Eldan</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Gehrke</surname>
          </string-name>
          ,
          <string-name>
            <given-names>E.</given-names>
            <surname>Horvitz</surname>
          </string-name>
          , E. Kamar,
          <string-name>
            <given-names>P.</given-names>
            <surname>Lee</surname>
          </string-name>
          ,
          <string-name>
            <given-names>Y. T.</given-names>
            <surname>Lee</surname>
          </string-name>
          ,
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>