Real Time Traffic Monitoring With Bayesian Belief Networks

Transcription

1 Real Time Traffic Monitoring With Bayesian Belief Networks Sicco Pier van Gosliga TNO Defence, Security and Safety, P.O.Box 96864, 2509 JG The Hague, The Netherlands , Paul van Koningsbruggen TNO Defence, Security and Safety P.O.Box 96864, 2509 JG The Hague, The Netherlands , Ronald van Katwijk TNO Environment and Geosciences P.O.Box 49, 2600 AA Delft, The Netherlands , ABSTRACT Modern traffic management systems are, we believe, best implemented as multi-agent systems. When multiple agents have to make decisions on shared knowledge, this knowledge incorporates the uncertainty of underlying information and sensor systems. One approach to deal with uncertainty is the use of probabilistic models called Belief Networks. However, calculating with these models is a NP-hard problem. In order to apply this technology we had to break down its complexity for our specific case. This paper discusses the design choices that we made to boost the performance of our Bayesian belief network and thereby enabling this technique for real-time traffic monitoring in multi-agent systems. INTRODUCTION Traffic management pursues an optimal use of the available infrastructure in terms of traffic flow, safety and quality of life along the road. Over the past decade the number of traffic management instruments has increased rapidly. Ramp metering controls the traffic and throughput at certain hot spots on the road. Variable message signs can instruct drivers to adapt their driving in order to increase safety or lower the level of emissions. The challenge is to select appropriate non-conflicting measures to optimise the quality of the traffic network. Before such decisions can be made, a sound picture of the current traffic situation must be established. Multiple data and information sources are available, but each of them can only partly observe the actual situation and inevitably suffer from some

2 level of inaccuracy. The overall picture inherits this uncertainty, but information systems rarely take this into account explicitly. We envision a hypothesis management system to fuse all sensor data. The method that is discussed in this paper will merge heterogeneous sensor data and other information sources and deal with its uncertainties in a consistent and sound manner. The merging of different types of observations gives the extra opportunity to determine the likelihood of unobserved events that could not have been detected by processing different types of sensors independently from each other. The overall picture that results from this enrichment process will therefore be more reliant and complete. Using this methodology, we want to build a traffic monitoring system to aid decision making for traffic management. The system will be used to recognize the current traffic situation at certain places along a traffic network. The proposed system will function as an intelligent mediator between the sensors and the decision making process. BELIEF NETWORKS The classical approach to reasoning is logical and deterministic. Computers excel in logical reasoning. Rule-based expert systems take this to full advantage. For this reason computer systems have been introduced to substitute and aid human reasoning for many applications. However, not all domains comply with static deterministic rules. Especially traffic networks are highly dynamic and compromise many noisy and partially observable events. Therefore, we need a technology for intelligent transportation systems that can deal with these factors adequately. Amongst systems that are specifically designed for dynamic and chaotic domains, Bayesian belief networks are gaining popularity as de facto standard for reasoning with uncertainty. t=0 (t=0) (t=0) probability (t=0) (t=0) probability good slow 10% good light traffic 50% good normal 90% good dense traffic 50% bad slow 80% bad light traffic 30% bad normal 20% bad dense traffic 70% () (t=0) () probability good light traffic light traffic 70% good dense traffic light traffic 30% bad light traffic light traffic 50% bad dense traffic light traffic 10% (t=0) () probability probability good good 80% good 95% good bad 20% bad 5% bad good 10% bad bad 90% Figure 1: An example of a belief network, on left the graph and on right the corresponding al probability tables.

3 Figure 2: The belief network structure maps onto the topology of the traffic network. Time is modelled by using time-slices. Belief networks are causal models that describe a domain of interest. It uses a visual approach in the form of a graph. In such a structure we can describe variables in our domain and the relations that exist between them. It is a powerful framework for automated reasoning that is capable of dealing with uncertainties in a consistent and mathematically sound manner. It uses the Bayesian view on probability, introduced by Thomas Bayes in the 18 th century [2], which describes the mathematical relation between the probability of an event given knowledge of previous experiences and current observations. There are many proper, but different, ways to design a causal structure for a domain. The topology of the graph should suit the application. In the case of a Traffic Management system, the timing as well as the location of events plays an important role for situational awareness. An elegant way to express these dimensions is the use of time-slices [7]. The graph is built in horizontal layers that consist of variables related to the same moment in time. The arcs visualize a cause and effect relationship between probability variables. For each node (i.e. a probability variable) a table describes how the dependencies with other nodes affect its state. These tables are called al probability tables (CPT) and contain our so-called prior knowledge. For the traffic network model shown in this paper traffic, traffic and

4 traffic at certain locations where chosen as probability variables. For example, in the traffic model the of vehicles at a certain spot influences traffic further down the route. The relations are expressed in degrees of belief. Figure 3: To test the applicability of our belief network we used the GeNIe modelling environment developed by the Decision Systems Laboratory of the University of Pittsburgh ( When Bayesian networks are applied, we face three technical difficulties: 1. The definition of prior knowledge requires the collection a considerable amount of hard-to-get prior knowledge from domain experts or other sources. 2. The algorithms for reasoning with Bayesian networks are computationally complex [1] and their performance is possibly inadequate for large-scale realtime systems in complex domains. 3. Bayesian reasoning is hard to use in a distributed system. The reasoning process does not solely rely on local knowledge. We will now discuss these issues and propose solutions to solve them. DEFINING PRIOR KNOWLEDGE Often, the process of engineering all the CPT's is a laborious and sometimes infeasible task. Each relation in a belief network should be defined. Doing this manually takes a considerable effort. The validation of this knowledge may become an impossible task. An alternative to manually defined prior knowledge is found in

5 automated learning of the al probability tables. All the probabilities within the CPT's can be learned or trained automatically by simulation and actual sensor data. Figure 4: The Paramics software package was used to learn the al probabilities tables of the belief network, based on simulation. In order to demonstrate this, a simulated traffic network was modelled with the traffic micro simulator Paramics, developed by Quadstone Limited. We ran a simulation for each of the traffic situations that we wanted the system to be able to recognize. The outcomes of these runs were translated to al probabilities by using frequency analysis. Simulation is an effective instrument for deriving CPT values for rare events that do not occur frequently. Domain experts may lack the experience to define accurate probabilities for such events. Real traffic data could also be used. When real traffic data is available, it could be used for on-line training to keep the system up to date with new trends. However, one should be cautious for incomplete and possibly faulty sensor information. These uncertainties should be reflected in the CPT s. On-line learning by using sensor data is an interesting option, when used to update the prior knowledge in the CPT in a balanced manner. REAL-TIME REASONING Reasoning in a belief network can be done in multiple ways. There are in general two approaches to calculating the likelihood of a hypothesis in a belief network. Approximate algorithms are used for estimates of the likelihood. It basically simulates the events in the belief network by repeatedly throwing virtual balls into the belief

6 network that are guided by the arcs. This method is computationally cheap, but is less suitable for determining the likelihood of rare events. Exact reasoning uses Bayes theorem to exactly calculate this likelihood. Calculating the exact likelihood of events is a mathematically complex problem, a so-called NP-hard class problem (e.g. like scheduling or the travellers agent problem). This may result in long computation times. The two main algorithms for exact reasoning are the junction tree method by Spiegelhalter [4] and the lambda-pi message passing method by Pearl [3]. Both algorithms are very efficient. Pearls algorithm is easy to apply in a distributed system, but it has difficulties with some specific types of large networks. Spiegelhalter algorithm can deal with all types of networks in a very efficient way, but is less flexible with respect to distributed systems. algorithm quality drawback Bayes ball very fast makes estimates and ignores unlikely events Pearl exact answers can t be used for large loopy networks Spiegelhalter exact answers is hard to use in distributed systems Table 1: A comparison of various methods to calculate belief networks. Although Bayesian systems are not commonly used for real-time systems, successful applications do exist. A popular application for Bayesian reasoning is the spam filter for as proposed by Heckerman and Horvitz [6]. This system uses a large belief network to calculate the probability of a new message being spam. It uses on-line a learning algorithm based on frequency analysis. Surprisingly, this application works in real time despite the large network that is used. It does not suffer from the NP-hard complexity of the underlying algorithm, because of the special structure of the network. It has a very flat topology that does not have any loops and each node has only one parent. The structure describes the causal dependencies accurately but in a heavily simplified form. Many causal relations that may exist are ignored for the sake of performance. The technique is therefore referred to as a Naive Bayesian Classifier. Nevertheless it is a very effective method and is known to work considerably better than alternative techniques based on (heuristic) rules. The success of this application inspired us to make some drastic design choices. Minimizing the size of CPT's All prior knowledge is used in the calculation, therefore the more knowledge is encoded in the CPT the more computation time is needed. Decreasing the size of CPT s can be done by minimizing the number of possible states for each probability variable. If all probability variables have only two states, then the size of the CPT for that variable will double for each extra al dependency (i.e. parent of a node). Therefore it is wise to limit the number of parents and only include the causal relations that really matter. The negative impact on the outcomes may be marginal, while the performance will significantly improve. By limiting the number of parents for each variable we have greatly reduced the size of the CPT's. Minimizing the presence of loops The structure has a great impact on the performance of reasoning algorithms. This is partly because the structure influences the size of the CPT's. Another important issue on the structure of belief networks is the presence of multiple paths between two nodes. When there are multiple paths of reasoning exist between a common cause and

7 a common goal, computation time grows exponentially to the number of paths. An effective way to improve the performance is to get rid of as many multiple paths as possible. This will result in a polytree: a belief network that does not have any loops. We removed all loops, while keeping the causal structure intact for the strongest relations (networks C and D in table 2). Minimizing the depth of the network Bayesian reasoning (independent of the used algorithm) works in two directions: diagnostic reasoning and causal reasoning. Evidence is an observed value for a variable. Diagnostic reasoning searches for causes that may explain the observation, where causal reasoning searches for effects of the observation. When diagnostic reasoning affects the likelihood of unobserved variables, it triggers causal reasoning from those variables. For this reason the location of evidence is of importance to the performance. By limiting the depth of network we reduced the number of possible causes for each variable. belief network A belief network C t=0 t=0 belief network B belief network D t=0 t=0 network complexity nodes length timelayers performance millisec. A ,23 B ,09 C < 0,01 D < 0,01 Table 2: A comparison of various ways to use belief networks.

8 DISTRIBUTED SYSTEMS Instead of sending raw sensor data to a central server, crucial information can already be extracted at the sensor level itself. This information can then be fused with other pieces of information in the network. To accomplish this, each sensor needs to be equipped with a processor and a data-communication facility. Given appropriate design, a sensor can be regarded as an intelligent agent. Hence, a group of sensor nodes can create a multi-agent system in which nodes share a task and cooperate using inter-sensor communication. The advantage of distributed networks is that better extraction of locally available information is obtained. This is because sharing the results of local computations concerning locally available sensor information often strongly reduces the need for further data interpretation. In a distributed system computations can be done parallel to up the calculation. For our research project we have used an implementation of the Spiegelhalters algorithm on a single computer. Because one single agent was used for Bayesian reasoning we did not benefit from parallel processing. Spiegelhalters algorithm is considered to be less suitable for distributed systems, especially when these systems are dynamic. However, by assigning pre-defined overlapping parts of the traffic network to agents, information can be locally processed independently from other parts or agents. When the network changes (e.g. by opening new road segments) one only has to update the agents assigned to that segment. For a standard method to distribute belief networks, using the junction tree method of Spiegelhalter, see [5]. CONCLUSION Belief networks are quickly becoming de facto standard for reasoning with uncertainty. Although various reasons make it difficult to use belief networks for decision aid for complex domains like traffic management, the difficulties that come with the method are solvable. The proposed solutions are simple and practical, but very effective: 1. simulation is used to define al probabilities 2. modest simplifications to the model can boost performance 3. predefined belief networks can be used in distributed systems The software that was developed during the research project shows that a real-time system for traffic monitoring is indeed feasible. Although it was feared that the design choices would have a negative impact on the quality of the system, this is not necessarily the case. Furthermore, by choosing belief networks we benefit from the growing number of tools, techniques and algorithms that are available for this methodology. FURTHER WORK Currently we are working on a pilot project to use this approach to detect traffic incidents in region of Delft in the Netherlands. This is a joint project of Netherlands Organization for Applied Scientific Research TNO, Delft University of Technology and the province South Holland. We are now in the process of testing the algorithm

9 on real sensor data and real incidents, of which we hope to publish the first results in a scientific paper on the next ITS congress in Our experience so far, based on simulated data, is satisfying. Therefore, we would like to take this opportunity to encourage others to consider the same approach for new intelligent transportation systems. REFERENCES [1] G. F. Cooper. Probabilistic inference using belief networks is NP-hard. Technical Report KSL-87-27, [2] Rev. Mr. Bayes, An Essay towards solving a Problem in the Doctrine of Chances. Philosophical Transactions of the Royal Society of London, 53 (1763), [3] J. H. Kim and J. Pearl. A computation model for causal and diagnostic reasoning in inference systems. Proceedings of the 8th International Joint Conference on AI, pages , [4] Lauritzen and Spiegelhalter. Local computations with probabilities on graphical structures and their applications to expert systems. Journal of the Royal Statistical Society (Series B), 50: , [5] Y. Xiang. Probabilistic Reasoning in Multi-agent Systems: A Graphical Models Approach. Cambridge University Press, [6] M. Sahami, S. Dumais, D. Heckerman, E. Horvitz. A Bayesian Approach to Filtering Junk . AAAI Workshop on Learning for Text Categorization, July 1998, Madison, Wisconsin. AAAI Technical Report WS [7] S. Russell, P. Norvig. Artificial Intelligence: A Modern Approach. chapter 15: Probabilistic Reasoning Over Time. Prentice Hall; 2nd edition, 2002