An Extended Maritime Domain Awareness Probabilistic Ontology Derived from Human-aided Multi-Entity Bayesian Networks Learning

Abstract

- Ontologies have been commonly associated with representing a domain using deterministic information. Probabilistic Ontologies extend this capability by incorporating formal probabilistic semantics. PR-OWL is a language that extends OWL with semantics based on Multi-Entity Bayesian Networks (MEBN), a Bayesian probabilistic logic. Developing probabilistic ontologies can be greatly facilitated by the use of a modeling framework such as the Uncertainty Modeling Process for Semantic Technology (UMP-ST). An example of using UMPST was the development of a probabilistic ontology to support PROGNOS (PRobabilistic OntoloGies for Net-Centric Operational Systems), a system that supports Maritime Domain Awareness (MDA). The PROGNOS probabilistic ontology provides semantically aware uncertainty management to support fusion of heterogeneous input and probabilistic assessment of situations to improve MDA. However, manually developing and maintaining a probabilistic ontology is a labor-intensive and insufficiently agile process. Greater automation through a combination of reference models and machine learning methods may enhance agility in probabilistic situation awareness (PSAW) systems. For this reason, a process for Human-aided MEBN Learning in PSAW (HMLP) was suggested. In previous work, we used UMP-ST to develop the PROGNOS probabilistic ontology. This paper presents an extended PROGNOS probabilistic ontology developed using HMLP. The contribution of this research is to introduce the extended PROGNOS probabilistic ontology and present a comparison between two processes (UMPST and HMLP).

Keywords

• Probabilistic Ontology
• Maritime Domain Awareness
• Predictive Situation Awareness
• Bayesian Networks
• Multi-Entity Bayesian Networks
• Uncertainty Modeling Process for Semantic Technology
• Human-aided Machine Learning

-

In information science, integration of heterogeneous, distributed, and unstructured information is a difficult and complex challenge. A major issue is ensuring information compatibility, for which ontologies have become a standard solution [ 18 ]. Traditional ontologies are limited to deterministic knowledge. Probabilistic Ontologies (POs) move beyond this limitation by incorporating formal probabilistic semantics. Probabilistic OWL (PR-OWL) [ 19 ] is a probabilistic ontology language that extends OWL with semantics based on Multi-Entity Bayesian Networks (MEBN), a Bayesian probabilistic logic [1]. PR-OWL has been extended to PR-OWL 2 [ 14 ], which provides a tighter link between the deterministic and probabilistic aspects of the Ontologies. MEBN is flexible enough to represent a variety of complex and uncertain situations. MEBN has been applied to systems [2][3][4][5][6][7] for Predictive Situation Awareness (PSAW), providing the ability to estimate and predict aspects of a temporally evolving situation.

Developing probabilistic ontologies can be greatly facilitated by the use of a modeling framework such as the UMP-ST, a modeling process for constructing a probabilistic ontology [ 13 ]. The UMP-ST consists of four main disciplines: (1) Requirement, (2) Analysis & Design, (3) Implementation, and (4) Test. UMP-ST was used to develop a probabilistic ontology to support PROGNOS (PRobabilistic OntoloGies for Net-Centric Operational Systems), a system to support Maritime Domain Awareness (MDA). The existing system for MDA (e.g., US Navy's Net-Centric infrastructure, FORCENet) is used to fuse lower-level multi-sensor data, analyze the fused data by human analysts, and support decision-making for naval operations. However, the era of big data requires greater automation. The PROGNOS probabilistic ontology [7] supports ingestion of lower-level data, fusion of heterogeneous input, and probabilistic assessment of situations to improve MDA. PROGNOS is a prototype system that aims especially to identify threatening targets (e.g., terrorists and terrorist-ships).

Manually developing and maintaining a probabilistic ontology is a labor-intensive and insufficiently agile process. Furthermore, it is important to make use of data when available. Therefore, greater automation through a combination of reference models and machine learning methods has the potential to enhance agility and effectiveness in modeling a probabilistic ontology for PSAW. For this reason, a process for Human-aided MEBN Learning in PSAW (HMLP) has been suggested [ 20 ]. HMLP contains three supporting methodologies, MEBN-RM [ 10 ], a reference MEBN model for PSAW [8], and MEBN learning algorithms [9][ 10 ]. These component methodologies enable efficient and effective modeling. MEBN-RM and the reference model are introduced in Section 2 below.

In previous work, we used UMP-ST to develop the PROGNOS PO. This paper presents an extended PROGNOS PO developed using HMLP. In the following sections, the paper (1) provides background information, (2) introduces the original PROGNOS PO derived from UMP-ST, (3) presents the extended PROGNOS PO derived from HMLP, and (4) compares two processes.

II.

BACKGROUND

This section introduces (1) MEBN, (2) MEBN-RM Mapping Model, (3) A Reference MEBN Model for PSAW, (4) Uncertainty Modeling Process for Semantic Technology (UMP-ST), and (5) Human-aided MEBN learning in PSAW (HMLP). HMLP assumes input data based on the relational model (RM) as its data schema. We choose RM because it is the most popular database model and has the necessary expressive power to represent entities and their relationships. It is necessary to define how to convert elements of RM to elements of MEBN, so a mapping rule between MEBN and RM, called MEBN-RM, was developed. Also, we introduce a reference MEBN model for PSAW which provides a set of basic templates to support the design of a MEBN model for PSAW. HMLP is a modification of UMP-ST, so UMP-ST is introduced in this section. Some of the following background summaries are taken from [ 20 ].

A. MULTI-ENTITY BAYESIAN NETWORKS

MEBN is a compact model combining Bayesian networks (BN) with First-order logic (FOL) to represent repeated structures in a joint distribution representing domain knowledge. MEBN is a highly expressive model for treating uncertainty and complex forms of data and information. A MEBN model, called an MTheory, is composed of fragments, called MFrags. An MFrag consists of a set of resident nodes, a set of context nodes, a set of input nodes, an acyclic directed graph for the nodes, and a set of class local distributions (CLD) for the nodes. A resident node is a random variable which is associated with a function or predicate of FOL and whose class local distribution is resident in an MFrag. A context node is derived from a resident node and determines conditions under which the class local distribution defined in the MFrag is valid. An input node has its distribution defined elsewhere and conditions the class local distribution defined in the MFrag. Nodes for an acyclic directed graph are associated with resident and input nodes. An FOL function or predicate of a resident node contains ordinary variables, which can be replaced with entity identifiers to generate multiple instances of the RVs. MFrags in an MTheory are used to generate instances of fragments of BN. The fragments of BN are combined to form a Bayesian network, called a situation-specific Bayesian Network (SSBN). An MTheory can be used to generate an unbounded number of different SSBNs. Further information about MEBN can be found in [1].

B. MEBN-RM Mapping Model

MEBN-RM [ 10 ] is a mapping model which provides a specification for how to convert relational databases [ 11 ][ 12 ] to MTheories [1]. The relational model (RM) is the most popular database model. MEBN-RM provides an entity mapping between a relation in RM and an entity in MEBN, a resident node mapping between an attribute in RM and a resident node in MEBN, an MFrag mapping between a relation in RM and an MFrag in MEBN, and an MTheory mapping between an RM and an MTheory. An MTheory can be constructed automatically from a relational database by using mapping rules in MEBN-RM. Therefore, MEBN-RM can support a MEBN learning algorithm, which develops an MTheory from a dataset, or an MTheory developer, who aims to develop an MTheory using domain knowledge and MEBN knowledge. HMLP exploits MEBN-RM for efficient development of an MTheory.

C. A Reference MEBN Model for PSAW

A reference model is an abstract framework to which a developer refers in order to develop a specific model. A reference MEBN model for PSAW is a reference model for a PSAW-MTheory which specifies references for MFrags, RVs, relationships of RVs, and entities. The reference MEBN model for PSAW can support the design of a PSAW-MTheory and improve the quality of the PSAW-MTheory. The references for entity are classified into five categories (Time entity T, Observer entity OR, Sensor entity SR, Target entity TR, and Reported target entity RT). Entities derived from these categories describe a situation in which an observer OR observes a target TR and interprets it as a reported target RT using a sensor SR at a certain time T [ 20 ]. The reference MEBN model for PSAW provides some referring random variables (RV), called PSAW-RVs. PSAW-RVs are classified into five categories (Observing condition RV, Reported object RV, Target object RV, Situation RV, and Context RV). These PSAW-RVs are defined in five types of MFrags (Observing condition MFrag, Report MFrag, Target MFrag, Situation MFrag, and Context MFrag). An observing condition RV defined in an observing condition MFrag represents probabilistic knowledge about conditions of a sensor (e.g., maintenance conditions for a sensor). A reported object RV defined in a report MFrag represents probabilistic knowledge about a relation or an attribute of observed targets (e.g., a reported target size). A target object RV defined in a target MFrag represents probabilistic knowledge about a relation or an attribute for actual targets (e.g., an actual target size). A situation RV defined in a situation MFrag represents probabilistic knowledge about situations of targets (e.g., a collaborating situation for targets). A context RV defined in a context MFrag represents probabilistic knowledge about conditions under which the class local distribution defined in the MFrag is valid. For example, an RV Predecessor(pre_t, t) can be a context RV. The context RV Predecessor(pre_t, t) means that the time interval pre_t occurs immediately before the time interval t. More specific information for the reference MEBN model for PSAW can be found in [ 20 ].

D. Uncertainty Modeling Process for Semantic Technology (UMP-ST)

UMP-ST is a framework to support the design of a probabilistic ontology [ 13 ]. The PROGNOS probabilistic ontology was developed using UMP-ST. UMP-ST provides processes for constructing a probabilistic ontology through four disciplines: (1) Requirement, (2) Analysis & Design, (3)

Implementation, and (4) Test.

In the Requirement discipline, requirement statements are defined. The requirement statements can contain goals, queries, and evidence for a probabilistic ontology. Objectives to be achieved by reasoning with the probabilistic ontology are specified by statements for goals (e.g., detect a ship of interest). To achieve the objectives, specific query statements are specified in this discipline (e.g., what is the type of a ship?). To support the queries, evidence associating with the queries is determined in this discipline (e.g., an appearance of a ship). In the Analysis & Design discipline, entities, attributes, relationships, and probabilistic rules are defined. These are used to support the goals, queries, and evidence. For example, we are developing a probabilistic ontology, which aims to detect a ship of interest (the goals). The goal is achieved by identifying the type of a ship (the queries) given information about the appearance of the ship (the evidence). For this situation, a ship entity is required. Also, type and appearance attributes for the ship entity are required. Suppose that the appearance attribute may depend on the type attribute. This is specified by a probabilistic rule. In the Implementation discipline, a probabilistic ontology is developed using results from the previous disciplines. A probabilistic ontology based on MEBN is used to reason about uncertainty. Therefore, a probabilistic ontology contains OWL classes based on elements from MEBN such as an MFrag, an MTheory, a node, a probability distribution, and an entity. In this step, these OWL classes are defined. For example, the ship entity defined in the previous discipline is mapped to an entity type indicating a ship in the probabilistic ontology. The attributes ship appearance and ship type are mapped to random variables ship appearance and ship type, respectively. The probabilistic rule for the attributes ship appearance and ship type is converted to the joint probability for the random variables ship appearance and ship type. The random variables ship appearance and ship type may belong to an MFrag representing attributes of a ship. The MFrag ship and other MFrags related with a maritime domain may integrate into an MTheory representing a maritime situation. The Test discipline is used to assess the probabilistic ontology developed in the Implementation discipline. More specific information for UMP-ST can be found in [ 13 ].

E. Human-aided MEBN learning in PSAW (HMLP)

HMLP is a framework which aims the development of a probabilistic ontology in PSAW. HMLP provides specific development steps and supporting methods (MEBN-RM, the reference MEBN model for PSAW, and MEBN learning). HMLP improves MEBN learning by providing expert knowledge which is used to limit the search space of parameters, variables, and structures for a probabilistic ontology in PSAW.

Similar to the four disciplines of UMP-ST, HMLP contains four steps (Fig. 1): (1) Analyze Requirements, (2) Design

World Model and Rules, (3) Construct Reasoning Model, and

(4) Test Reasoning Model. (See a full discussion of HMLP in [ 20 ]). A summary of HMLP is presented below.

Stakeholders who request the development of a reasoning model or a probabilistic ontology provide needs and/or missions as inputs of HMLP. An output from the end of HMLP is a reasoning model (in our case, a probabilistic ontology for PSAW). The followings describe the four steps in HMLP. (1) In the Analyze Requirements step, requirements which contain goals to be achieved, queries to answer, and evidence to be used in answering queries are defined. Also, the requirements include performance criteria, which are used in the Test Reasoning Model step, to evaluate the probabilistic ontology. (2) In the Design World Model and Rules step, a world model and rules are developed using the requirements in the previous step. This step contains two sub-steps (Design World Model step and Design Rules step). The Design World Model step defines the world model which may include entities, attributes, and relations (e.g., RM) using the requirements, domain knowledge and/or existing data schemas. The world model is used to identify rules. In the Design Rules step, the rules or influencing relationships between attributes in the world model are defined. (3) In the Construct Reasoning Model step, a probabilistic ontology is constructed using a training dataset, the world model, and the rules. This step includes two substeps (Map to Reasoning Model step and Learn Reasoning Model step). The Map to Reasoning step maps the world model and rules to a candidate probabilistic ontology. The Learn Reasoning Model uses a MEBN learning method to learn the probabilistic ontology from a training dataset. (4) The Test Reasoning Model step evaluates the learned probabilistic ontology in the previous step to determine whether to accept it. The accepted probabilistic ontology is a final result from HMLP.

To develop the PROGNOS PO, three iterations of the four steps in UMP-ST (Requirement, Analysis & Design, Implementation, and Test) were performed [ 14 ]. The following sub-sections summarize the four steps in UMP-ST to develop the PROGNOS PO.

A. Requirements

The Requirement step identifies requirements containing goals, queries, and evidence for a probabilistic ontology. The requirements for the PROGNOS PO were developed gradually over the three iterations. In the first iteration, a simple requirement regarding a ship of interest was identified [7]. In the second iteration, requirements for two types of terroristships were defined. In the third iteration, requirements for crew members in a ship of interest were specified. The following list shows part of the resulting requirements [ 14 ]. 1. Identify if a ship is of interest, 1.1 Is the ship being used to exchange illicit cargo? 1.1.1 Was the ship hijacked?

1.1.2 Does the ship have a terrorist crew member?

1.1.2.1 Is the crew member associated with any terrorist

organization? ...

1.2 Is the ship being used as a suicide ship to bomb a port? ...

The main goal was to identify a ship of interest (i.e., a terrorist-ship). In this requirement, we assumed the ship of interest may exchange illicit cargo and/or be used as a suicide ship to bomb a port. To support this goal, we needed to identify the type of a crew member of a ship. If the type of a crew member is a terrorist, the ship is highly likely to be a terroristship. To identify whether a crew member is a terrorist, we can check whether the crew member is associated with any terrorist organization.

B. Analysis & Design

This step defines the types of entities, their properties and relationships, and the rules that apply to them, i.e., the semantics of the domain model. The Unified Modeling Language (UML) diagrams can provide a convenient and understandable visualization of the classes and relationships for the model semantics. The requirements defined in the previous step are used to develop the model semantics. Thus, entities, attributes for the entities, and relationships between the entities were identified. For example, from Requirement 1, an entity was derived (i.e., a ship) and an attribute of the entity was derived (i.e., the type of a ship). From Requirement 1.1.2, a new entity was derived (i.e., a (terrorist) person) and a relationship between the entities was derived (i.e., a ship has a crew (terrorist) member). In the second iteration, Carvalho [ 14 ] developed the model represented by UML as shown in Fig. 2. The classes and relationships form six natural groups (i.e.,

Electronics, Behavior, Ship, Position, Plan, and Social

Network). The ship types are NavyShip, FishingShip, and

MerchantShip. Ship routes are UnusualRoute and UsualRoute.

Two ships can meet each other at a position. A ship can use electronic devices such as Radio, Radar, and AIS (Automatic Identification System). A ship can show behavior such as

Aggressive, Erratic, Evasive, and Normal. A ship can have a

(terrorist) crewmember who may belong to a (terrorist) organization. A ship can have a terrorist plan such as

BombPort and ExchangeIllicitCargo.

After developing the model semantics, conditional rules were identified. There were three iterations of this process. The following list shows a few of the conditional rules from [ 14 ]. 1.(a) If a crew member is a member of a terrorist organization, then it is more likely that he is a terrorist. 1.(b) If an organization has a terrorist member, it is more likely that it is a terrorist organization. ...

4.(a) Research shows that if a crew member has a relationship with terrorists, there is a 68% chance that he has a friend who is a terrorist. ...

These conditional rules were derived from extensive research about terrorism [ 16 ] and from the knowledge provided by a domain expert. These rules were used to develop the PROGNOS PO.

C. Implementation

In the Implementation step, the PROGNOS PO was designed. The PROGNOS PO can be found in [ 14 ][ 15 ]. Fig. 3 shows the PROGNOS PO containing five groups of MFrags.

The first set of MFrags is for a ship of interest. It includes nine MFrags Aggressive Behavior, Terrorist Plan, Evasive

Behavior, Erratic Behavior, Unusual Route, Bomb Port Plan,

Ship Of Interest, Electronics Status, and Exchange Illicit Cargo

Plan. These MFrags are used to reason about properties of a ship (e.g., unusual behavior and an illegal plan). The second set of MFrags is for a person of interest. It includes four MFrags

Person Communications, Person Background Influences,

Person Cluster Associations, and Person Relations. These

MFrags are used to identify a person who may communicate with a terrorist, has a suspicious background and history, and has a relationship with a terrorist. The third set of MFrags is for information of relationships between two ships. It includes two MFrags, Radar and Meeting. These MFrags are used to identify whether one ship is within radar range of another ship and whether two ships are meeting. The fourth set of MFrags is for information about the relationship between a person and an organization. It includes one MFrag Terrorist Person in which a person who belongs to an organization is identified. The last set of MFrags is for information about a relationship between a person and a ship. It includes two MFrags Has Terrorist Crew and Ship Characteristics. These MFrags are used to link a person and a ship, and to identify whether a ship has a terrorist crew member.

The following list shows part of a partial PROGNOS PO containing information about MFrags (F), context nodes (C), resident nodes (R), resident parent nodes (RP), and input parent nodes (IP). Note that a partial probabilistic ontology doesn't contain a class local distribution and domain information for a random variable.

PO 1: Original PROGNOS probabilistic ontology [F: ErraticBehavior_MFrag [C: isA(ship,Ship)] [R: hasErraticBehavior(ship) [IP: hasExchangeIllicitCargoPartition(ship)]] [R: hasEquipmentFailure(ship)] [R: isCrewVisible(ship)[RP: hasErraticBehavior(ship)][RP: hasEquipmentFailure(ship)]] ] [F: TerroristPerson_MFrag [C: isA(person,Person), isA(org,Organization)] [R: isTerroristOrganization(org)[RP: isTerroristPerson(person), isMemberOfOrganization(person, org)]] [R: isTerroristPerson(person)][R: isMemberOfOrganization(person, org)] ] [F: ShipCharacteristics_MFrag [C: isA(ship,Ship), isA(person,Person)] [R: hasCrewMember(ship, person)][R: hasTypeOfShip(ship)][R: isHijacked(ship)] ] [F: EvasiveBehavior_MFrag [C: isA(ship,Ship)] [R: hasEvasiveBehavior(ship)[IP: hasExchangeIllicitCargoPartition(ship)]] ] [F: PersonCommunications_MFrag [C: isA(person,Person)] [R: communicatesWithTerrorist(person)[IP: isTerroristPerson(person)] ] [R: usesChatroom(person) [RP: communicatesWithTerrorist(person)]] [R: usesEmail(person) [RP: communicatesWithTerrorist(person)]] [R: usesCellular(person) [RP: communicatesWithTerrorist(person)]] [R: usesWeblog(person) [RP: communicatesWithTerrorist(person)]] ] [F: PersonBackgroundInfluences_MFrag [C: isA(person,Person)] [R: hasInfluencePartition(person) [IP: isTerroristPerson(person)]] [R: knowsPersonImprisionedInOIForOEF(person) RP: hasOIForOEFInfluence(person)]] [R: hasFamilyStatus(person) [RP: hasInfluencePartition(person)]] [R: hasOIForOEFInfluence(person) [RP: hasInfluencePartition(person)]] [R: knowsPersonKilledInOIForOEF(person) [RP: hasOIForOEFInfluence(person)]] ] [F: AggressiveBehavior_MFrag [C: isA(ship,Ship)] [R: hasAggressiveBehavior(ship) [IP: hasBombPortPlan(ship), hasExchangeIllicitCargoPartition(ship)]] [R: hasWeaponVisible(ship) [RP: hasAggressiveBehavior(ship)]] [R: isJettisoningCargo(ship) [RP: hasAggressiveBehavior(ship)]] [R: speedChange(ship) [RP: hasAggressiveBehavior(ship)]] [R: turnRate(ship) [RP: hasAggressiveBehavior(ship)]] [R: propellerTurnCount(ship) [RP: speedChange(ship)]] [R: cavitation(ship) [RP: speedChange(ship)][RP: turnRate(ship)]] [R: shipRCSchange(ship) [RP: turnRate(ship)]] ] [F: ShipOfInterest_MFrag

[C: isA(ship,Ship)] [R: isShipOfInterest(ship) [IP: hasTerroristPlan(ship)]] ] [F: ExchangeIllicitCargoPlan_MFrag [C: isA(ship,Ship)] [R: hasExchangeIllicitCargoPlan(ship) [IP: hasTerroristPlan(ship)]] [R: hasExchangeIllicitCargoPartition(ship)

[IP: hasTypeOfShip(ship)][RP: hasExchangeIllicitCargoPlan(ship)]] ] [F: PersonRelations_MFrag [C: isA(person,Person)] [R: hasKinshipToTerrorist(person) [RP: hasTerroristBeliefs(person)]] [R: hasFriendshipWithTerrorist(person) [RP: hasTerroristBeliefs(person)]] [R: hasTerroristBeliefs(person) [IP: isTerroristPerson(person)]] ] [F: Meeting_MFrag [C: isA(ship1,Ship), isA(ship2,Ship)] [C: ( ¬ ( ship1 = ship2 ) )] [R: areMeeting(ship1, ship2) [IP: hasExchangeIllicitCargoPartition(ship1)]] [R: areMeetingReport(ship1, ship2) [RP: areMeeting(ship1, ship2)]] ] [F: BombPortPlan_MFrag

[C: isA(ship,Ship)] [R: hasBombPortPlan(ship) [IP: hasTerroristPlan(ship)]] ] [F: HasTerroristCrew_MFrag [C: isA(ship,Ship), isA(person,Person)] [C: hasCrewMember(ship,person)] [R: hasTerroristCrew(ship) [IP: isTerroristPerson(person)]] ] [F: UnusualRoute_MFrag [C: isA(ship2,Ship), isA(ship1,Ship)] [C: ( ¬ ( ship1 = ship2 ) )] [R: hasUnusualRoute(ship1) [RP: hasNormalChangeInDestination(ship1)] [IP: hasBombPortPlan(ship1)][IP: areMeeting(ship1,ship2)]] [R: hasUnusualRouteReport(ship1) [RP: hasUnusualRoute(ship1)]] [R: hasNormalChangeInDestination(ship1) [IP: hasTypeOfShip(ship1)]] contains an isA context node and three resident nodes hasErraticBehavior, hasEquipmentFailure, and isCrewVisible. The resident node hasErraticBehavior is influenced by an input node hasExchangeIllicitCargoPartition. The resident node isCrewVisible is influenced by the resident nodes hasErraticBehavior and hasEquipmentFailure.

This

PROGNOS PO was tested in the next step.

D. Test

In this step, the PROGNOS PO was evaluated to determine whether to accept it. To do this, the case-based evaluation, in which various scenarios were defined and used to examine the reasoning implications of the probabilistic ontology, was used. For example, given a scenario which was developed by a subject matter expert (SME), some information (e.g., history of a target) from the scenario for a target was used as evidence for inference of the PROGNOS PO to identify some properties (e.g., whether the target is a terrorist) of the target. If the result of inference coincided exactly with the scenario from SME, we could think that the probabilistic ontology was reasonable. For this test, three qualitatively different scenarios were used [ 14 ].

After three iterations for UMP-ST, an overall test for the PROGNOS PO was performed using a simulation. In the real world situation, it is very difficult to acquire a real dataset to develop such a probabilistic ontology which contains rare events. For this reason, the simulation was used to produce a test dataset given different scenarios generated randomly. Carvalho [ 14 ] and Costa et al [ 15 ] introduced some results for this test. In such a test, it is important that knowledge used to develop a probabilistic ontology and knowledge used to develop a simulation for testing the probabilistic ontology should not be same. If they are same, the test is meaningless, because the probabilistic ontology and the simulation are same models, but just in different forms.

IV. PROGNOS PO VIA HMLP In this section, we introduce an extended PROGNOS PO derived from the HMLP process. The following shows how the development operates.

A. Analyze Requirements

This step is not much different from the requirement step in UMP-ST. Therefore, we can reuse requirements developed from the PROGNOS project. The full requirements can be found in [ 14 ]. However, the reference MEBN model for PSAW can provide more items by which a PSAW modeler can consider predefined entities, RVs, and MFrags for PSAW. Recall the four MFrag groups from the reference model:

Reported Object, Observing Conditions, Target Object, and

Situation. The last of these, Situation, is of special note. In PSAW, understanding a situation in which targets operate for their own purposes is one of the important issues. Identifying just the type of a target is an insufficient task for PSAW. The meaning of awareness is not to perceive and estimate actual properties of a target but is to understand, interpret, and explain the relationships between targets. Kokar et al [ 17 ] stated: “The main part of being aware is to be able to answer the question of “what’s going on?””. Awareness of a situation is subjective according to an observer, who is aware of the situation. The modeler, who is developing a probabilistic ontology to support PSAW, should define what situation will be considered and explained through all observation from the world. For the awareness of the PROGNOS situation, we add the following new requirement.

New Goal 1: Recognize emergency situation at sea

Query 1.1: How high is the potential terrorist

threat? Evidence 1.1.1: Ship(s) of interest Evidence 1.1.2: Crew member(s) of

interest

The new goal aims to alert a response team when the threat reaches a certain level. This will be accomplished by estimating potential terrorist attacks in the field given estimation of terrorist ships and terrorist crew members.

In HMLP, a requirement can contain a performance criterion specifying a measure of accuracy (e.g., the mean squared error or the Brier score [ 26 ]). For example, we might require that the mean squared error between ground truth and estimated results from the probabilistic ontology shall be less than a given threshold (e.g., a mean squared error < 0.1).

B. Design World Model and Rules

This step performs two sub-steps (Design World Model and

Design Rules). The Design World Model step is to define a

world model for PROGNOS from the requirements defined in the previous step.

In this step, the reference MEBN model for PSAW can be used to identify possible entities, random variables, and relationships between the random variables. Fig. 4 shows a PROGNOS world model represented in an EER (enhanced entity–relationship) model. We develop the PROGNOS world model using the requirements and the reference model.

The reference model suggests four groups: (1) Reported

Object, (2) Observing Condition, (3) Target Object, and (4)

Situation. A world model for the original PROGNOS PO included the seven relations (e.g., Target, Ship, Person,

Organization, Person_Org, Ship_Person, and Ship_Ship). The

original PROGNOS PO treated only the target object group. In other words, it did not emphasize sensing. We would expect evidence (e.g., reported objects) to be reported to estimate actual targets (e.g., target objects), so relations (i.e.,

Ship_Report, Person_Report, Organization_Report,

Ship_Ship_Report, Person_Org_Report, Ship_Person_Report,

and ReportedTarget) for the reported object group are added in the world model for the extended PROGNOS PO. Observations may contain observation errors influenced by observing conditions (e.g., weather). The observing condition group contains two relations Sensor and SensorProperty. In the previous step, a requirement for the awareness for a situation was added. Therefore, we added a relation Field for the situation group in Fig. 4. Relations (i.e., Location, SensorOf, and ActualTarget) which are not classified in these groups are supporting relations used to join the relations in the four groups.

The reference model provides some rules or relationships between these groups as shown in the arrows (Fig. 4). The observing conditions group and the target object group can influence the reported object group. For example, the attribute sensorPerformance in the relation SensorProperty influenced the report attributes in the report relations Ship_Report,

Person_Report, Organization_Report, Ship_Ship_Report,

Person_Org_Report, and Ship_Person_Report. The arrows in

Fig. 4 indicate these relationships. The following shows a few of these rules.

Rule 1: causal ({hasErraticBehavior, sensorPerformance}, hasErraticBehaviorRPT)

Rule 2: causal ({isShipOfInterest, isTerroristPerson},

PotentialTerroristAttacks)

...

Rule 1 means that two attributes hasErraticBehavior and sensorPerformance cause the attribute hasErraticBehaviorRPT. Rule 2 means that two attributes isShipOfInterest and isTerroristPerson cause the attribute PotentialTerroristAttacks.

C. Construct Reasoning Model

This step performs two sub-steps (Map to Reasoning Model and Learn Reasoning Model) to construct the PROGNOS PO. MEBN-RM provides a converting rule from RM to a probabilistic ontology. Entity relations which contain only one attribute for the primary key of the relation (e.g., ship and person) can be defined as entity types in the probabilistic ontology. Each of the attributes in the relations could be mapped to a resident node in the probabilistic ontology using MEBN-RM. For example, the attribute hasErraticBehavior of the relation Ship became the resident node hasErraticBehavior(ship).

Rules which are defined in the previous step are used to develop relationships between resident nodes in the probabilistic ontology. For example, from Rule 1, we had a conditional dependence P(hasErraticBehaviorRPT(ship_report) | hasErraticBehavior(ship), sensorPerformance(shipSensor, ship)). From Rule 2, we had a conditional dependence

P(PotentialTerroristAttacks(field) | isShipOfInterest(ship), isTerroristPerson(person)).

We could model the extended PROGNOS PO as shown in Fig. 5 using the resident nodes, the relationships between the resident nodes, and the MFrag groups.

Fig. 5 shows a set of MFrags in the extended PROGNOS PO. The list on the left indicates the four MFrag groups. Each group is decomposed into sub-groups. For example, the target object group contains five sets of MFrags (Person MFrags, Ship MFrags, MFrags for the relationship between two ships, MFrags for the relationship between a person and a ship, and MFrags for the relationship between a person and an organization). The following list (PO 2) shows part of new MFrags added into the extended PROGNOS PO.

PO 2: Part of New MFrags added into the original PROGNOS probabilistic ontology 1 [F: Orgainzation_Report_MFrag 2 [C: isA(sr,SENSOR), isA(tr ,ORGANIZATION), isA(rt,REPORTEDTARGET)] 3 [C: SensorOf(sr, tr), tr = ReportedTarget(rt)] 4 [R: isTerroristOrganizationRPT(rt) 5 [IP: isTerroristOrganization(tr)] 6 [IP: performance(sr, tr)] 7 8 9 10 11 12 13 14 ] 15 ...

] ] [F: Situation_MFrag [C: isA(ship,SHIP), isA(person,PERSON), isA(field,FIELD)] [C: field = Location(ship)] [C: hasCrewMember(ship, person)] [R: PotentialTerroristAttacks(field) [IP: isShipOfInterest(ship), isTerroristPerson(person)]]

In PO 2, we added the ship report MFrag which can be used to reason about Rule 1. Also, we added the situation MFrag which can be used to reason about Rule 2.

In the Learn Reasoning Model step, the extended PROGNOS PO can be refined using a MEBN learning algorithm. The goal of MEBN learning is to learn an MTheory from a training dataset. A basic MEBN learning method for relational datasets was suggested [9][ 10 ]. This approach assumes that the training dataset is stored in a relational database based on RM. MEBN learning searches parameters, variables, and structures to find an MTheory that provides a good fit to the training dataset. In our case, the structures are given by the above steps as suggested in the PSAW reference model. Therefore, only parameter learning is required. The goal of parameter learning is to estimate the parameters of a class local distribution L given a training dataset D and the type of distribution being learned, which fit well the training dataset D.

For a discrete random variable case, Dirichlet distribution is commonly used because it is conjugate to the multinomial distribution. With a Dirichlet prior distribution, the posterior predictive distribution has a simple form [ 21 ][ 22 ]. For continuous random variables, multiple regression can be used. Park et al [9] introduced a basic MEBN parameter learning and structure learning for a conditional Gaussian hybrid model in which no discrete random variable may have a continuous parent random variable.

For example, parameters for a conditional Gaussian distribution can be estimated using multiple regression. The following class local distribution (CLD) is an illustrative example of a conditional linear Gaussian CLD for the node Speed_RPT(rt, tr), which means a speed report rt for a target tr. The CLD of the node is a continuous CLD with hybrid parents (Sensor_Condition and Speed). In this case, we assume that the discrete parent node Sensor_Condition(sr, tr), which means a condition of a sensor sr for a target tr, has two states (Good and Bad) and the node Speed (tr), which means an actual speed of a target tr, is continuous.

CLD 1 [Conditional Linear Gaussian]: Speed_RPT(rt, tr) 1 if some sr.tr have (Sensor_Condition = Good) [ 2 Ɵ1.0 + Ɵ1.1*Speed + NormalDist(0, Ɵ1.2) 3 ] else [ 4 Ɵ2.0 + Ɵ2.1*Speed + NormalDist(0, Ɵ2.2) 5 ]

Parameter learning for this CLD estimates the parameters (Ɵ1.0, Ɵ1.1, and Ɵ1.2) in Line 2 and the parameters (Ɵ2.0, Ɵ2.1, and Ɵ2.2) in Line 4 using multiple regression.

D. Test Reasoning Model

This step performs two sub-steps (Experiment Reasoning

Model and Evaluate Experimental Results) to evaluate the

extended PROGNOS PO from the test dataset. In the

Experiment Reasoning Model step, the performance of

estimation and prediction for the extended PROGNOS PO can be assessed using a performance measure (e.g., the mean squared error or the Brier score). Each experiment consists of the following five steps. (1) The test dataset provides entity information (e.g., ship1, person1, and field1) and ground truth information (e.g., isShipOfInterest_ship1 = true, isTerroristPerson_person1 = true) to the extended PROGNOS PO. (2) Given these, the extended PROGNOS PO is used to compute a marginal probability distribution (e.g., P(PotentialTerroristAttacks_field1 | isShipOfInterest_ship1 = true, isTerroristPerson_person1 = true) in response to a query. (3) The test dataset provides ground truth data (e.g., PotentialTerroristAttacks_field1 = High). (4) Steps 1-3 are repeated for all test cases. (5) Finally, for results for all cases, the measures are calculated.

In the Evaluate Experimental Results step, we evaluate the measures using the performance criteria in the requirements defined in the Analyze Requirement step (e.g., a mean squared error < 0.1). If the evaluation is not satisfied (e.g., a mean squared error >= 0.1), we can return to the previous steps to improve the performance of the extended PROGNOS PO. We can investigate the extended PROGNOS PO in the Construct Reasoning Model step. Unsatisfactory performance can be caused by a training database of insufficient size. In this case, we may find more datasets and apply them to the learning process. Also, it is possible that the MEBN learning algorithm which we use is ineffective. In this case, the application of a more effective MEBN learning algorithm is required. The world model in the Construct Reasoning Model step can be incorrect. For this, we may need to conduct a further field investigation and research to develop a more accurate world model. The requirements in the Analyze Requirements step can be impracticable or requires a too high standard to address it. In this case, readjustments for the requirements can be performed by the stakeholders.

V.

COMPARING UMP-ST AND HMLP

HMLP is a modification of UMP-ST that specifies some detailed sub-steps and uses two reference models (the reference MEBN model for PSAW and MEBN-RM). These reference models can support efficient modeling for a probabilistic ontology in PSAW. The first steps (Requirement) for both processes are same. In the case of HMLP, the reference MEBN model for PSAW provides some guidance on groups of entities to be defined (i.e., Reported Object, Observing Condition, Target Object, and Situation). In the second step of HMLP, the reference model also supports developing a world model in terms of PSAW by providing candidate entities (i.e., T, OR, SR, TR, and RT), attributes, and relationships. In the third step of HMLP, MEBN-RM supports the development of entities, random variables, and MFrags from a relational schema. HMLP also makes use of MEBN learning algorithms, so given a training dataset, a probabilistic ontology can be efficiently constructed. The second and third steps are mainly different with UMP-ST. These steps in HMLP can accelerate the modeling for probabilistic ontologies in PSAW and produce more comprehensive models.

Table 1 shows feature comparison between the original PROGNOS PO and the extended PROGNOS PO. Each number in the table means the number of the features (entities, random variables, relationships between random variables, and MFrags). For example, the number of entities in the original model is three (Ship, Person, and Organization), while the number of entities in the extended model is ten (Field, Ship,

Person, Organization, ShipSensor, PersonSensor,

OrganizationSensor, ReportedShip, ReportedPerson, and

ReportedOrganization). Table 1 shows that the feature of the extended PROGNOS PO is more comprehensive than the feature of the original PROGNOS PO. The original PROGNOS PO contains 51 RVs, while the extended PROGNOS PO contains 115 RVs. This means that the extended PROGNOS PO can answer more various questions. For example, a reasoning about potential terrorist attacks in a field can be performed using the extended PROGNOS PO, but the original PROGNOS PO can’t. Also, the extended PROGNOS PO contains observing conditions for sensors, so this may enable us to perform more accurate reasoning.

If we assume that there is a training dataset for MEBN learning, the development period for the PROGNOS PO can be reduced. Usually, to develop an RV and its parameter, we study literature related to the RV and find possible parameters for the RV. Another way for the development of such an RV is to use domain expert knowledge. A subject matter expert (SME) may provide values and parameters for the RV, and relationships between RVs. In the PROGNOS project, to develop one RV, we used the following steps: (1) an SME in the maritime domain explained domain knowledge to an RV developer, (2) the RV developer developed the RV using the MEBN/PR-OWL software [ 27 ], and (3) the RV in the MEBN/PR-OWL software was evaluated by the SME. These steps were implemented with at least one day per RV. If we assume that for each RV, one day may be required to develop it by one RV developer and one SME, then the original PROGNOS PO requires around 51 days. On the contrary, if we assume that all datasets are available, the development with MEBN learning may require around one day for setting the datasets and learning a PO using a MEBN learning algorithm.

UMP-ST was applied for construction of a probabilistic ontology to support PROGNOS including the PROGNOS PO. The PROGNOS PO played an important role in the operation of PROGNOS. However, manually developing and maintaining a probabilistic ontology is a labor-intensive and insufficiently agile process. Therefore, HMLP containing the reference models and machine learning methods was introduced. In the previous work for PROGNOS, UMP-ST was applied to develop the PROGNOS PO. This paper applied HMLP to develop the extended PROGNOS PO which was more comprehensive than the original model and was developed more quickly.

The following summarizes future research issues. (1) HMLP in this research was not fully applied with MEBN learning from a training dataset. Evaluation of effectiveness (i.e., reasoning accuracy) of reasoning models learned from MEBN learning is required. (2) A probabilistic ontology can contain MFrags, context nodes, resident (or inputs) nodes, graphs, FOL formula for nodes, and class local distributions for nodes. These elements can be subject to MEBN learning. Especially, FOL formula learning in a probabilistic ontology is a difficult topic relative to the others. In our approach, a dataset for learning is given from a relational database. Because we rely on MEBN-RM, we do not need to perform the complicated task of FOL formula learning from text data. FOL formula learning in a probabilistic ontology can be supported by Inductive Logic Programming [ 23 ][ 24 ] and Statistical Natural Language Processing [ 25 ]. (3) Also, future steps for the extended PROGNOS PO are to apply it to a realistic reasoning system for Maritime Domain Awareness.

ACKNOWLEDGMENTS

We appreciate Dr. K. C. Chang, Dr. W. Sun, Dr. R. Carvalho, Dr. R. Haberlin, Mr. S. Matsumoto, and Mr. A. Mugali for their efforts in the previous PROGNOS research. The research was partially supported by the Office of Naval Research (ONR), under Contract#: N00173-09-C-4008.

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