– Understanding Complex Systems
6.3 Development of ESA Components
l identifies the target variable, while i and j identify the evidence variables.
Vδand
Vγare the variables without parents evolved with time. Equation (6.8) is therefore an important component in the ESA to generate the transition of knowledge. This reveals in-depth awareness of patterns for current situations over time and gives insight into the next likely event. As a proof of concept for our ESA, we integrated the implemented variable elimination algorithm of JavaBayes [77]. It is open-source software. Having presented the mathematical developments, the next section describes the derived ESA paradigm.
6.3 Development of ESA Components
Besides our mathematical analysis in the previous sections, this section presents the ESA paradigm. With reference to the SA (situation awareness) theory [16], which describes a mental model at three hierarchical levels, overall SA can be defined as shown in equation (6.9).
OSA = e3 [+ e4 + e5] (6.9)
where e3 = g (f (e1), f (e2))
e3 is the active SA component obtained as function g(.) from the integration of system knowledge of function f(e1) and interface knowledge of function f(e2). It is the crucial aspect of SA that is often prone to
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errors, as discussed by [16]. Direct observation from real world, e4, and distant observer, e5, provides other sources of information that may probably affect SA and consequently have an impact on decision-making. To interpret these theories, Figure 6.2 shows and simplifies a system model to achieve e3 using the ESA.
6.3.1 The System Model for the ESA
The system model in Figure 6.2, which comprises three essential components, was extracted from our EDBN architecture, which is beyond the scope of this chapter. They are learning algorithms, probabilistic distributions and the trend analysis. The first two components collectively generate the system knowledge f (e1). This is integrated into the third component, which is the interface knowledge f (e2). This is presented in equation (6.9) as it accomplishes e3, the crucial aspect of SA theory. The e4 and e5 are subjective knowledge that may affect decision-making by answering the four ‘W’ questions of SA: What is happening? Why is it happening? What can I do about it? What will happen next? As shown in Figure 6.2, the three components formulate the engine used to reveal specific situations (local dynamics) from frame model (global behaviour) over time, which accurately improves decision-making. There are numerous hidden situational patterns embedded in any DBN. Real-life applications of these situations are presented in the experimental results of section 6.4 as the ESA bridges information gap problems.
In Figure 6.2, the Learning Algorithms dynamically evolve temporal models from multivariate time series (MTS) environments. The time intervals could be weekly, monthly, daily or hourly, observed in the fields of water management, retail, oil production, telecommunications, etc. The MTS is observed as frames and serves as input for learning. The algorithms evolve interlink temporal models from frames 0 to n. The existing learning algorithms, such as hill-climbing and genetic algorithms (GA) [23] [34] [38]
used for learning ordinary BNs from datasets, can fit into Figure 6.2, if upgraded to work over time steps.
Our optimized GA [51] is upgraded to evolve over time and is used as a proof of concept in this system model. The algorithm uses information-theoretic measures (e.g. Minimum Description Length) and mathematical components (e.g. PowerSet in set theory) as genetic operators and as a means of balancing between efficiency and decomposability. The GA is used due to its efficiency as it performed very well when used to learn models from the environments of numerical, nominal and mixed datasets.
The probabilistic distribution integrated into Figure 6.2 is a Bayesian inference of the Variable elimination algorithm, which is used to reason over time. Finding what is needed when it is needed is the result of a probabilistic reasoning from a time slice about a situation. This is otherwise a state of knowledge as described in the SA theory. The component of trend analysis in Figure 6.2 is an interface that constructs a transition matrix of knowledge over time. The nature of knowledge in the patterns
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generated can periodically determine the likely action to be taken on any situation n to arrive at (or avoid) the next situation n+1.
Learning Algorithms
Trend Analysis
Probabilistic Distributions
Frame-t0 Frame-t1 Frame-t2 Frame-tn
Figure 6.2: A System Model for the ESA
In essence, the three components handshake or interchange their outputs and the current situations are made interactive for real-time decision-making. These are basically used to simplify the answers to the Four ‘W’ questions about situations. In applying this technology, we formally develop the ESA algorithm as shown in Figure 6.3.
6.3.2 The ESA Algorithm
An MTS serves as the required schema to Figure 6.2 but the additional capability of the ESA algorithm in Figure 6.3 serves to generate MTS from domain datasets without changing their originalities. Its development is based on the theories, algorithms, models and mathematical analysis, which are used as subroutines as described in the previous sections.
In Figure 6.3, the Dsj is a column of the schema, dt is a frame dataset and bt is a temporal Bayesian Network emerged at time t. As shown in step 1[i], discretization classifies numerical datasets into their corresponding interval values relative to the patterns in the data attributes [40] [42]. Due to the predominance of computational complexity during data-preprocessing, the ESA introduces scalability into the discretization processes by adopting our DMMAL framework. In this scheme, space is shared and
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every used memory is cleared for the next processes. In step 1[v], the Bayesian learners are the algorithms that were recently mentioned [23] [25] [51], whose functionalities are to carry out intra-slice learning over time. They evolve temporal optimal BN at each time step. Likewise, the Bayesian inference, as described in equation (6.8), generates several situational trends as a transition matrix of knowledge, which is consequently used by decision-makers.
INPUT (Ds : Dataset Schema)
1. While Ds = MTS,
[i] If Dsj = Numeric, for j = 0, 1, 2. . . m.
• Call Scalable_Discretizer (Dsj).
[ii] Perform ordering on Ds using t key.
[iii] Set t, the frame count, to 0.
[iv] Let dt є Ds, ∀ t = 0, 1, 2, . . ., n.
[v] For each t <= n,
• Select frame dt for emergence.
• Call Bayesian_Learner (dt).
• Store the emerged temporal BN in matrix B.
• Increment t by 1.
[vi] For Situational Trends, Call Probabilistic Distributions, ∀ bt є B.
[vii] Return the dynamic BNs in B as the frames’
situations, then exit.
2. While Ds <> MTS, [viii] If Dsj = Date,
• Select t.
• Generate MTS from Ds using t.
[ix] Repeat step 1.
Figure 6.3: Emergent Situation Awareness Algorithm
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Decision-making is made simpler with the ESA, as users can now be well acquainted with their current complex domains before projecting into the future. Most of the existing DBN frameworks focus on projecting only into the future with explicit representations. Since the ESA is domain-independent, it not only accommodates highly skilled users, but also allows non-expert practitioners to benefit from DBNs.