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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Improving Probabilistic Rules Compilation using PRM</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Gaspard Ducamp</string-name>
          <email>gaspard.ducamp@ibm.com</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Philippe Bonnard</string-name>
          <email>philippe.bonnard@fr.ibm.com</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Christian De Sainte Marie</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Christophe Gonzales</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Pierre-Henri Wuillemin</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>IBM France Lab</institution>
          ,
          <addr-line>9 rue de Verdun, 94250 Gentilly</addr-line>
          ,
          <country country="FR">France</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>LIP6 (UMR 7606), Sorbonne Universite</institution>
          ,
          <addr-line>4 place Jussieu, 75005 Paris, France https://</addr-line>
        </aff>
      </contrib-group>
      <abstract>
        <p>Widely adopted for more than 20 years in industrial elds, business rules o er the opportunity to non-IT users to de ne decisionmaking policies in a simple and intuitive way. To facilitate their use, systems known as Business Rule Management Systems have been developed, separating the business logic from the application one. While suitable for processing structured and complete data, BRMS face di culties when those are incomplete or uncertain. This study proposes a new approach for the integration of probabilistic reasoning in IBM Operational Decision Manager (ODM), IBMs BRMS, especially through the introduction of a notion of risk, making the compilation phase more complex but increasing the expressiveness of business rules.</p>
      </abstract>
      <kwd-group>
        <kwd>Business Rule Business Rule Management System Decision Making Bayesian Networks Bayesian Inference Object Model Probabilistic Relational Models</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>General presentation</title>
      <p>
        Business Rules Management Systems (BRMS), such as IBM Operational
Decision Manager (ODM), have been introduced in the 90's to facilitate editing,
authoring, deploying and executing business policies by domain users, in the
form of conditions/actions rules. Syntactically close to the business language,
these ease the translation of decision-making and business strategies, making
them accessible to users with no programming experience. Besides the rule set,
an object data model describes the di erent objects concerned by the rules, they
are dynamically instantiated in a working memory during the execution of the
program. The activation/execution of rules is managed by inference algorithms
such as RETE [
        <xref ref-type="bibr" rid="ref13 ref5 ref7">7, 5, 13</xref>
        ].
      </p>
      <p>
        The PhD thesis presented here builds upon work already carried out within
IBM France Lab and the LIP6. It is based on the hybridization of business
rules with probabilistic graphical models such as Bayesian networks [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ] or as
Probabilistic Relational Models [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ].
      </p>
      <p>
        A Bayesian network is a compact representation of a joint probability
distribution over a set of random variables. These appear in the form of nodes in
a direct acyclic graph (DAG) where the absence of arcs represent conditional
independences. This type of structure is used as a decision-making tool in many
expert systems and applications [
        <xref ref-type="bibr" rid="ref10 ref14">10, 14</xref>
        ].
      </p>
      <p>
        Probabilistic Relational Models (PRM), on the other hand, are combining
notions from Bayesian networks and from the paradigm of object-oriented
languages [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ]. The notions of random variables and conditional probabilities are
added to those of classes, relations, interface, inheritance and instantiations.
Such expressiveness makes it possible to answer the problems of reusability and
scalability of graphical models [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ].
      </p>
      <p>
        Several studies including a thesis [
        <xref ref-type="bibr" rid="ref1 ref4">4, 1</xref>
        ] showed that a loose coupling between
IBM's BRMS, on the one hand, and probabilistic graphical models (Bayesian
networks initially, then PRM), on the other hand, allowed reasoning about
uncertain data by introducing the notion of probabilistic production rules.
      </p>
      <p>
        Figure 1 shows how those works t into the ODM toolchain. Several
semantic trees are generated after analyzing and checking the syntax of the user le
describing the rules and the object model (ARL). In addition to producing the
one describing the rules (SemRuleset ) these studies proposed to use the object
model to generate a probabilistic graphical model semantic tree (SemPGM ). The
probabilistic expression of rules are then rewritten to link ODM to an inference
engine (aGrUM1, jSMILE2, ...) using the generated le (PGM le). Once the
rules are rewritten, the models are compiled before being translated into
bytecode in an archive (JAR), facilitating deployment and execution on the target
machines.
1 aGrUM (A GRaphical Universal Modeler) [
        <xref ref-type="bibr" rid="ref15">15</xref>
        ] is an open source C ++ library
for manipulating (learning, modeling, inferring) graphical models and implementing
O3PRM: http: //agrum.gitlab .io
2 SMILE is a reasoning and learning/causal discovery engine for graphical models
https://www.bayesfusion.com/smile-engine
      </p>
      <p>A working example used in those studies is that of a fraud detection
application, an organization being responsible for managing the reimbursement requests
made by its clients according to their nature (type and cost of reimbursement).
For this purpose, a set of healthcare professionals are in charge of validating the
reimbursement requests made by customers.</p>
      <p>Figure 2 shows an example of relation schema for PRM classes of this
problem. A HealthcareProfessional class describes healthcare professionals based on
several characteristics, including their age, location, gender, and the list of clients
they manage (Subscriber), themselves characterized by an age and a list of
reimbursements requests (Reimbursement).</p>
      <p>Generated during compilation, this model allows to answer a rst set of
probabilistic rules. In the example below, we will trigger the action part when
we detect a trusted healthcare professional based in Paris who has a client with
a high risk of fraud.</p>
      <sec id="sec-1-1">
        <title>Ex. 1. An example of probabilistic rule</title>
      </sec>
      <sec id="sec-1-2">
        <title>The previous works raised two major issues:</title>
        <p>{ Business user friendliness: such rules can be di cult to de ne and to
understand by a business user, expressing a probability on particular conditions
requiring a deep level of knowledge of the probabilistic models used.
{ Performance: ODM provides the ability for users to de ne di erent types
of conditions (for example, using lters, aggregators, and nested conditions).
Neither these constructions, more complex, nor their impacts on the
performances have been studied.</p>
        <p>
          Incidentally, a new inference algorithm [
          <xref ref-type="bibr" rid="ref3">3</xref>
          ] has been studied during the
previous thesis but:
{ the interest of the use of this algorithm comes from the assumption that the
incremental modi cations of the working memory were not going to have big
impacts on the structure of the junction tree used for the inferences,
important savings of calculations could therefore be realized. It is, consequently,
especially adapted to large connected structures;
{ the algorithm works with PRM, but retranscribed in the form of Bayesian
networks (so-called "grounded"). The interest of PRMs is greatly reduced
since the structural redundancies of these grounded networks, which are
encoded in the PRMs that generated them, are not exploited, which reduces
the e ciency of the inferences;
        </p>
        <p>We notice that the graphical model built during the compilation of ODM
takes into account a probabilized model of the relations between the objects
of the working memory but it does not adapt itself to the probabilistic queries
de ned in the rules.
2</p>
      </sec>
    </sec>
    <sec id="sec-2">
      <title>A new de nition of probabilistic production rules</title>
      <p>To address the business user friendliness issue raised above, we need to rede ne
the treatment of uncertainty in the expression of rules by replacing the
probability thresholds attached to single variables by a notion of acceptable risk on the
evaluation of the conditions of the rule as a whole. The action part of a rule will
therefore be executed only if the set of conditions is veri ed with a probability
greater than the de ned acceptable risk. This will allow our probabilistic rules
to be both more complex and intuitive, but it requires a rede nition of the rules
compilation phase to redistribute the overall risk to each individual condition.</p>
      <p>In the rule below, a rewriting of the previous one, the then part will only
be triggered if the probability that conditions c1 and c2 are true is greater than
80%. Using such kind of formulation will ease the use of probabilistic rules by
business users.</p>
      <sec id="sec-2-1">
        <title>Ex. 2. A new form of probabilistic rule</title>
        <p>To achieve this, it is necessary to generate the PRM not only from the object
models but also from the set of rules (see Figure 3). All the predicates over
attributes of a probabilistic object, such as hp.risk==low, will be added in our
graphical model in an extension of the concerned class (red classes in Figure 3).
This requires studying the di erent forms that conditions can take (aggregations,
lters, nesting, ...) and their predicates. Hence, a feasibility study must be carried
out to de ne the theoretical and practical limits of such a method.
The rules will then be rewritten to take into account our new probabilistic
queries (on the probability attribute of the detectInvoiceAnomaly class, for
example). Such manipulations could, however, change the e ciency of the pattern
matching performed by ODM for the selection of rules to be performed, therefore
their impact should be studied.</p>
        <p>On the PRM side, the dynamic instantiation of classes representing rules (in
green in Figure 3) as well as the simpli cation of the model generated during
compilation will be at the center of the project (by taking into account that
some of the data sources will be deterministic). In our example the location of
a healthcare professional is considered certain, thus we don't need to include it
in our new PRM.</p>
        <p>Due to the highly deterministic aspect of the user models, we will assume that
the instantiation of our PRMs will yield a large number of small disjoint
subgraphs (one per health professional, for example), which would require working
on a new inference algorithm taking advantage of this structural redundancy.</p>
        <p>This development work is based on what has been done in the Bayesian
Insight Service (BIS) plugin developed as part of the previous thesis. The
gure 4 illustrates how our new module, PRIME (Probabilistic Reasoning Insight
ModulE ), ts into the ODM compilation chain. It intervenes directly during the
process of rewriting the semantic tree describing the rules (SemRuleset ) but,
unlike BIS, extends the de nition and optimization of the graphical model from
the rules before rewriting them (via the PRM enhancement process).</p>
        <p>Once the rules are rewritten, the graphical model is serialized in order to be
usable by a probabilistic engine in parallel with ODM.</p>
        <p>As part of our work, ODM uses aGrUM for probabilistic calculations and
manipulation of PRMs. The complexity of the compilation, as well as
performance problems during the execution, might require working on an extension of
this library (advanced aggregations, functional nodes, parametric nodes, ...)</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>Application and extensions</title>
      <p>This work will provide an extension of the ODM business rule de nition
language to probabilistic concepts. Syntactically and semantically close to natural
language, it will allow non-computer scientists to de ne probabilistic business
rules in an non-ambiguous and intuitive way.</p>
      <p>
        A study on the use of temporal models via an extension of the PRM
modeling capabilities in O3PRM3 could be done in a second step, which would allow
a similar reasoning but in the context of the treatment of complex events
(Complex Event Processing, CEP [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ]). The use of rules with temporal expressions
is at the core of the reasoning capabilities of IBM Decision Server Insights, a
CEP application developed by IBM. This study would therefore be useful at the
theoretical as well as the technical and industrial levels.
      </p>
      <p>
        Finally, one of the advantages of the expressiveness of PRM is that it is
possible to take into account the structural uncertainty of a model [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ]. In doing
so, a study on a predictive extension of ODM could be carried out. The system
would then be able to reason beyond the working memory, allowing to de ne
new types of rules (anticipation ones, for example).
3 O3PRM is a framework developed in the framework of aGrUM allowing the
manipulation of PRM: http://o3prm.gitlab.io
      </p>
    </sec>
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