Bayesian Networks Modeling for Crop Diseases

Transcription

1 Bayesian Networs Modeling for Crop Diseases Chunguang Bi and Guifen Chen College of nforation & Technology, Jilin gricultural University, Changchun, China bstract. Severe large-scale diseases in agricultural regions have caused significant econoic daage. n order to iprove crop yields, we develop a fraewor to predict the occurrence of crop diseases. n the presence of ris and uncertainty, this paper focuses on finding out the best pest control decisionaing progra which is based on the Bayesian networ. The paper describes the flowchart of a Bayesian networ and the principles used to calculate the conditional probabilities required in it. The practice proves that BN is an effective tool for crop disease. Keywords: Bayesian networ; Modeling; Crop Diseases; nference. 1 ntroduction With the developent of anial husbandry and processing industry, the deand for aize is growing fast. Jilin province is the ain production area of spring aize and the national coodity grain base, with the corn acreage of 2 illion h2, nearly 10% of the national grain acreage. Corn borer is the ost devastating disease in aize production and its occurrence ofte gets affected by lots of factors such as eteorological weather conditions and so on. Bayesian networ is one of the ost effective theoretical odels for uncertainty nowledge expression and reasoning. t has not only a solid basis for probability theory, but also a perfect correspondence with technical nowledge structures. So we use Bayesian networ to odel the crop diseases. 2 Bayesian Networs ntroduction Bayesian networ, also nown as belief networ or directed acyclic graphical odel is a probabilistic graphical odel that represents a set of rando variables and their conditional dependences via a directed acyclic graph (DG). t could represent the probabilistic relationships between diseases and syptos. Given syptos, the networ can be used to copute the probabilities of the presence of various diseases. We ay use atheatical sybols to represent a Bayesian networ odel as follows: B= (V, E, P) aong V= {V1, V2 Vn} set of rando variables E= {ViVj Vi,Vj V} set of directed edge P= {P (Vi V1, V2 Vi-1),Vi V} conditional probability table D. Li, Y. Liu, and Y. Chen (Eds.): CCT 2010, Part, FP CT 344, pp , FP nternational Federation for nforation Processing 2011

2 Bayesian Networs Modeling for Crop Diseases 313 Variables can be the abstraction of any proble, to represent interesting phenoenon, coponents, state or property, etc., with certain physical and practical significance. Directed edges show the dependent or causal relations aong variables, the arrow of the edge representing the direction of causal influence (fro parent node to child nodes), disconnected nodes representing the variables which these nodes corresponding to are conditional independent. Conditional probability table lists all possible conditional probabilities each node related to its parent. Probability shows the strength or confidence between child nodes and the parent. Probability of independent node called prior probability. Bayesian networs can be understood in two ways: first, Bayesian networs express conditional independent relations between each node. We can directly get conditional independent relations and dependent relations fro Bayesian networs; Bayesian networs also express joint probability distribution of events in another for. ccording to the structure of Bayesian networ and condition probability table (CPT), we can get the probability of each basic event (a cobination of all attributes) quicly. Bayesian networ consists of two parts. One part is a directed acyclic graph, in which each node represents a rando variable; each arc (connection of two nodes) represents a probability of dependence. f one arc starts fro node to node B, is the parent node and B is the child node. Given the parent nodes, each variable is independent of the non-subclass nodes in the graph. Variables can tae discrete values or continuous values. They can correspond to the actual variables or hidden variables in the data set to for a relationship. Bayesian networs cobine the dependent relations with the probability, the prior nowledge with the saple inforation; overcoe any conceptual and calculating difficulties in the rule-based syste in graphical way. Cobining with statistical techniques aes Bayesian networs advanced in data analysis. Copared with decision-aing tree, artificial neural networs and the density estiation ethods, the advantages of Bayesian networs are as follows: (1) Once the Bayesian networ is deterined, new variables can be easily added on the basis of the current structure. (2) Bayesian networ is very suitable for handling uncertainty and incoplete data sets. t uses probability theory to express the correlation between the variables, also could learn and reason under a liited, incoplete and uncertain inforation condition. For traditional algorith of supervision, all possible input data ust be clear. f one input data was lost, there would be soe deviation for the odel. n order to solve this proble, Bayesian networs get the su or integration of all the probability of possible values. (3) Bayesian networ itself is a ind of uncertainty causal relationship odel. Bayesian networ is different with other decision-aing odels. Through graphic visualization of nowledge, it is an expression of probability nowledge, also a reasoning odel, with a proper description of the causal relationships between networs variables. (4) s cobination of data and prior nowledge in a probability approach, Bayesian networs better reflect the over-fitting of the odel.

3 314 C. Bi and G. Chen 3 Bayesian Networs Modeling 3.1 Modeling Process The construction of Bayesian networ is a very coplex process, a good Bayesian networ will directly affect the correctness. n building a Bayesian networ, we first need to identify the ain variables and their relationships which lead to the corn borer attac, and on this basis can we build a Bayesian networ odel; then, we specify the conditional probability distribution for each node in the graph. fter we get the preliinary conditional probability table (CPT), the syste can further aend the conditional probability according to experts experience and the actual experiental data. The process of constructing a Bayesian networ is as follows: Select variables Experts fixed Bayesian networ Establish the causal relationship between variables Definition of CPT between variables 3.2 Proble Description Fig. 1. Flowchart of Construct Bayesian networ Corn borer, a ajor corn pest, leads to above 40% rate of corn victiization every noral year with a 10-15% reduction in output, and above 70% rate of corn victiization in serious year with a 20% reduction. Reinforcing the study on eteorological conditions of corn borer, establishing Bayesian networs to predict this attac, will be of great significance for prevention wor. The outbrea of corn borer is affected by following variables: (1) Mar-Jul accuulated teperature (CCT). Corn borer, a ind of cold-blooded anial, with a priitive nervous syste, is less able to regulate the body teperature itself. Therefore, its body teperature basically depends on the teperature of external environent. (2) Mar-Jul average axiu teperature (MXT). n Mar-pr, the average teperature is still low; the overwintering larvae ainly use the highest teperature to get ore calories to accelerate developent process. (3) Mar-Jul average iniu teperature (MNT). The iniu teperature is higher and this is conducive to the growth of corn borer. (4) Mar-Jul 5 CM ground teperatures (GT). (5)Feb-May cuulative sunshine duration (CSD). Corn borer is very sensitive to photoperiod. t does not hibernate or diapause in the long-day. More hours of

4 Bayesian Networs Modeling for Crop Diseases 315 sunshine, higher ground and air teperature will do well to the developent of corn borer. (6) Jan-Jun precipitation (MP). High precipitation, high soil huidity, low teperature is not conducive to the developent of overwintering larvae and worse to their pupation and eclosion. f we can grasp the inner relations of these factors, we can predict the occurrence of core borer ore accurately. Now, we build a Bayesian networ prediction odel. 3.3 Establish Causal Relationships Table First, establish the causal relationship table between variables and the occurrence of core borer. The contents of the table are identified by experts. The arrows to right show that rows attributes are father nodes and the coluns attributes are child nodes. On the contrary, the arrows to left show that coluns attributes are the father nodes and the rows attributes are child nodes. Two-way arrows show the relationship can not be deterined and two-way arrows with a slash show that there is no relationship between the two. Table 1. Deand forecasting of causality CCT MXT MNT GT CSD MP Occur CCT / / / / / MXT / / / / / MNT / / / / / GT / / / CSD / / MP / / / / Occur s we can see fro the table, experts couldn t identify the relations between Feb- May cuulative sunshine duration (CSD) and Mar- pr average axiu teperature (MXT). So we got opinions fro another two experts who suggest adopting evidence synthesis ethod. Evidence synthesis is an effective ethod in dealing with uncertain reasoning proble. Synthesis of evidence, fro the theory, first proposed by Depster, is prooted and developed by Shafer in dealing with uncertainty reasoning theory. The earliest synthesis evidence forula of the data theory is the Depster forula[1]: ( ϕ) = 0 (1) = 1 ) 1 K i j ( ( ) ( ) ( i j = ) (2) K = i j ( ) ( ) ( 1 i 2 j 3... = φ ) (3)

5 316 C. Bi and G. Chen n Depster synthetic forula, 1-K, a noralized factor, copletely abandon the conflict between evidence and distribute all probability related with these conflicts to an epty set. This is a very strict with operations. Therefore, the results often perverse in the synthesis of high degree conflict evidence. n order to solve the proble, Yager proposed a new synthetic forula: ( ϕ) = 0 (4) ) = i j ( 3 X ) = i j ( ) ( ) ( ) φ, X i 2 j... 1 = ( ( ) ( ) i 2 j = φ Through the evidence synthesis ethod above, we got the results: ( ) + K (5) (6) Table 2. Evidence synthesis results CSD MXT CSD MXT CSD / MXT uncertainty E E E copound Synthesis results show that the parent node is SSD and child node is MXT, then we build the Bayesian networ odel as shown in figure2: CSD MP GT CCT MX MNT Occur Fig. 2. Prediction proble of Bayesian networ initial odel 3.4 Deterine Conditional Probability Tables This stage is to deterine each variable s state and qualitative probability inforation. This inforation could be gotten fro experts and relevant literature [2].

6 Bayesian Networs Modeling for Crop Diseases 317 fter variables selection, we need to confir each variable s state. n order to reduce the size of Bayesian networs, we should liit the nuber that each variable contains and only select those interesting state that users prefer to. When select the state, ae sure that the selected state is utex to each other. Deterine the scope of variables: (1) Mar-Jul accuulated teperature (CCT). { d, d, d} (2) Mar-Jul average axiu teperature (MXT). { , } (3) Mar-Jul average iniu teperature (MNT). { , } (4) Mar-Jul 5 CM ground teperature (GT). { , , } (5) Feb-May cuulative sunshine duration (CSD). { h, h, h} (6) Jan-Jun precipitation (MP). {51-100, } n ost cases, experts only orally describe the causality. The probability we obtained is usually frequency and soe qualitative but not quantitative ters such as "ay", "often", "very little". Therefore, engineers need to ae the transition fro qualitative to quantitative. Through test, Renooij found that these oral quantifiers have soe relations with actual probability[3]. She created a probability bencharing, as shown in figure3: Fig. 3. Probability bencharing The probability bencharing, aing discrete psychological variables to continuous, help us deterine probability distribution ore accurately. Using this bencharing, experts could clearly get the relationship between psychology and quantitative probability. Experts ae a ar which corresponds to a certain nuber, and this nuber equals to the probability distribution. The average result fro that of different experts is final probability distribution of the node [4]. With probability bencharing, identify the conditional probability of each node in the networ. For exaple as shown in table 3: Table 3. Conditional Probability Table CSD CCT

7 318 C. Bi and G. Chen 3.5 Bayesian Networ Bayesian networ is shown in figure 4 (with conditional probabilities): Fig. 4. Core borer Bayesian networ However, the ost iportant application of Bayesian networ is to reasoning bacward according to actual events. For exaple, if we now the ground teperature is , we can enter the evidence that 'GT' = The conditional probability tables already tell us the probabilities of corn borer s occurrence ( ).s figure 5 shows: Fig. 5. Reverse reasoning

8 Bayesian Networs Modeling for Crop Diseases 319 f we now corn borer breas out, then we can enter the evidence that 'occur' =yes and we can observe the result to get other nodes revised probability. Bayesian networ ae the dependant relations of different variables ore explicit. n general there ay be relatively fewer direct dependencies (odeled by arcs between nodes of the networ) and this eans that any variables are conditionally independent. The existence of unlined (conditionally independent) nodes in a networ drastically reduces the possibility of calculating all the probabilities. Usually, all the probabilities can be calculated by joint probability distribution. However, we need to do soe siple calculation when there are soe independent nodes[5]. fter copleting basic construction of Bayesian networ, we still need to adjust conditional probabilities and revise the odel, then iprove the accuracy. 4 pleentation of Crop Disease Forecast Syste Based on Bayesian Networ Construction of a Bayesian networ needs the counication and cooperation of doain experts and Bayesian networ experts[6]. There are two types of nodes in the Crop Disease forecast syste--- disease nodes and eteorological nodes. The disease nodes are Boolean variables, which contain states of occur and dis-occur, while eteorological nodes ay indicate ultiple states. This BN is a ulti-layer networ. Fig. 6. nference results of the BN 5 Conclusions s Bayesian networ applies probability nowledge with coplex systes reasoning, and experts always supply the probability value we need. So, this paper starts

9 320 C. Bi and G. Chen building BN odel with these experts nowledge. On this basis, we establish the Crop Disease Forecast Syste. There is a large nuber of uncertain nowledge in the diagnosis of crop pests, while Bayesian networ has unique advantage in dealing with uncertain factors. n following study, we found that adopting application of Ontology in building Bayesian networs will ae the whole networ perfect. n addition, Bayesian networ could revise the conditional probability table and ae ore accurate prediction of crop disease for its self-learning function. References 1. Mingzhu, X., Guangju, C.: Modified Cobination Rule of Evidence Theory. Electronic Journals 3(9), (2005) 2. Jensen, F.V., Nielsen, T.D.: Bayesian Networs and Decision Graphs, pp Springer, Heidelberg (2007) 3. Du, T., Zhang, S., Wang, Z.: Learning Bayesian Networs fro Data by Particle Swar Optiization. Journal of Shanghai Jiao Tong University E-11(4) (2006) 4. Friedan, N., Linial, M., Nachan,., Peter, D.: Using Bayesian networs to analyze expression data. Coputational Biology 7, (2000) 5. Friedan, N., Koller, D.: Being Bayesian bout Networ Structure. Bayesian pproach to Structure Discovery in Bayesian Networs. Machine Learning 50 (2003) 6. Guifen, C., Helong, Y.: Bayesian Networ and ts pplication in Maize Diseases Diagnosis. n: Proceedings of First FP TC 12 nternational Conferences on Coputer and Coputing Technologies in griculture (2007)