We believe that an environmental event captured in multivariate time series (MTS) continually changes in unforeseen situations differently from how some other situations change another set of environmental Temporal Probabilistic Modelling FrameworkDMMAL Framework
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events. For instance, in retail, situations driving sales of toiletries are definitely different from the driving situations of beverages. These hidden and multifold situations, which are continually changing the events, mingle together as they are embedded in the MTS. The basic idea here is to clarify and understand the situations well in order to facilitate efficient decision-making and drastically reduce possible risks.
Achieving this will enable decision-makers to carry out anticipatory planning for good management strategies.
Figure 5.3: An Example of Temporal Probabilistic Model (or Global Dynamics) for Botswana Rainfall Distribution over Time Steps January (or Frame 1) to December (Frame 12) for a Current Year 2000 using the EDBN Architecture.
Since a DBN that is first evolved from an MTS is a temporal probabilistic model or global dynamics of knowledge, the hidden situations revealed from it is the local dynamics, which gives the smallest pieces of information required to understand the environments. Consider a rainfall distribution described by
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weather and climate attributes, which is captured locally as an MTS from the Botswana environment. It is used by the EDBN to reveal the onsets of rainfall to determine farmers’ planting dates. Figures 5.3 and 5.4 are examples of the global and local dynamics (a revealed hidden situation from the complex rainfall environment) respectively. Some of these attributes presented as nodes on the model in Figure 5.3 are:
Atl_SST_Anom - Atlantic Ocean Sea Surface Temperature Anomalies (0C), Ind_SST_Anom -Indian Ocean Sea Surface Temperature Anomalies (0C), Mthly_RR - Monthly Rainfall (in mm), Onset types - false, early, normal, late or failed, Station of rainfall observations, etc.
Figure 5.4: A Revealed Hidden Situation (or local dynamics) for normal onsets of the Rainfall Distribution for a Current Year 2000 at Station 69, using the EDBN Architecture. The situational awareness result of this normal onset is conditioned on parameters: Atl_SST_Anom and Ind_SST_Anom.
For the purpose of interpreting the complex relationships within the attributes of the model, an example of possible situations affecting the ever-changing normal onset event in the model is first predicted over current time steps, as shown in Figure 5.4. The temporal pattern of this situation shows that there are irregular normal onsets in the year 2000 which may not be an excellent signal for farmers’ planting dates.
It is obvious that good anticipatory planning is associated with a detailed understanding of situations that are currently occurring in one’s domain of interest. By first understanding and separating current situations from any anticipation, there is a good contribution to the efficiency of the temporal probabilistic framework. Having established the current situations of events, their future behaviour is then projected to assess the entire behaviour of such complex environment. Before describing the second framework of the
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EDBN, the ESA and the EFSA technologies derived from the temporal probabilistic framework are first introduced with minimal technicalities.
The ESA is an innovative technology, which completely evolves temporal models and reveals the hidden behaviour of what is currently happening over time in any domain of interest. One of its powerful strategies is its emergence from multivariate time series (MTS) data in the absence of domain experts.
Formally, let {V t, E t}represent the set of state and observed DBN variables in ESA at time t. The DBNs are emerged over all the non-negative current time steps t є T, such that T = {t1, t2… tn} and the interlinked probabilistic relationships at each time step t is shown as an example in Figure 5.3. ESA extends the algorithms of ordinary Bayesian networks to truly evolve dynamically as it changes its network and the probabilistic distributions with time. The part of the temporal probabilistic framework shown in Figure 5.2 has three components: the learning algorithms, the probabilistic reasoner and the trend analyzer. The learning component uses genetic algorithms [51] to evolve temporal Bayesian Network models, called frames, over the time steps from the MTS environments. A number of other BN learning algorithms such as [23] [38] can also be adopted herein, as long as they can evolve dynamic models across the time steps.
The probabilistic reasoner is the Bayesian inference engine, which handles the necessary possible forward and backward propagations through the links of the frames and generates probable results through collective intelligence. The trend analyzer is an interface engine that generates n-dimensional transition matrices of knowledge, where n corresponds to the pieces of hidden knowledge to be revealed, e.g. a transition matrix of target probabilities of situations, a transition matrix of target parameter values of events, etc.
Once the ESA technology has automatically modelled, revealed, and guided users to being well acquainted with the current situations of a complex environment, the problems of how to choose the most suitable model for specific real-life applications, especially by non-expert practitioners, are almost solved.
The EFSA completes the process of finding a solution as it takes this technology further, projecting the situations of the environment into the future and avoiding convergence problems when predicting over wider time steps. Its prediction strategy is based on the automatic emergence of temporal models which spans two-dimensional (2D) orthogonal time space from historical Multivariate Time Series (MTS), using some mathematical and algorithmic developments not presented in this chapter. However, models that are to be evolved from massive datasets are sent to the DMMAL framework for scalability.
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