Classification of fragile states based on machine learning

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1 Classificatio of fragile states based o machie learig Yuqua Li 1, Hehua Yao 1 1 Departmet of Computer Techology ad Applicatio, Qighai Uiversity, Xiig, Chia Abstract. The study of fragile states has become a sigificat issue i global security, developmet ad poverty at preset. The existig classificatio methods of fragile state, which is a simple additio to the atioal idex ad threshold segmetatio, is ot reasoable eough. We itroduce a ew method based o machie learig. With this method, it will be easier ad more reasoable to classify a coutry. We use two kids of classifier, oe of which is the support vector machie, ad the other is the gradiet boosted regressio trees. Both models have flaws, so we use esemble learig techiques to combie them. First of all, subjective labellig of a part of the atioal data to allows the machie to lear why a coutry becomes vulerable from these data, ad how to classify the vulerability class of a coutry. The, we traied the model with the data, ad divided fragile states ito four categories successfully (Alert, Warig, Stable ad Sustaiable). For the classificatio result, our model got a 93% test error rate, ad a 96% traiig error rate, which is better tha 77% with the threshold segmetatio method. 1 Itroductio At preset the study of fragile states or of the coutry's vulerability research has become a iteratioal academics ad policy makers to discuss i today's global security, developmet ad poverty problems [1~3], as oe of the core issues. Uderstadig the vulerability of the state, ad the cosequeces of its cosequeces, has oly recetly emerged as a field of study [4]. For the past five years, how to classify a fragile state has become a iteratioal group's mai priorities [5~6]. Some wellkow uiversities ad other research istitutes i may coutries have set up research ceters to discuss the issue of "fragile states", ad academic papers are costatly beig rolled out for the grad view [7~9]. I the past, fragile states were simply separated by subjective thresholds [10~11]. First, the staff evaluates ecoomic, evirometal ad other idicators (scores from 0 to 10). The, they simply add up ad choose thresholds accordig to some rules, separatig differet coutries usig these thresholds. I fact, it is ot fair or reasoable for some coutries to do so. A typical example: a coutry with 11 idicators is perfect, but oe of them, huma rights, is very low with oly two poits. At this time, the huma rights idicator will directly affect the coutry's vulerability directly, ad ca affect the coutry's vulerability through idirect ifluece (such as ecoomic iequality, group grievace). This coutry is supposed to be classified as edagered, but it is recogized as excellet by threshold segmetatio method. 2 Support Vector Machie SVM is a ew geeratio machie learig method proposed by Vapik o the basis of statistical learig theory [12]. It has sigificat advatages i solvig small sample, oliear, high dimesio ad other problems. At preset SVM has bee widely used i may fields of classificatio problems ad regressio problems, ad has a good predictio effect. SVC is a abbreviatio of support vector classificatio ad is a importat brach of support vector machie (SVM) [13]. The classificatio schematic diagram is as follows: Figure1. SVC schematic diagram Give traiig vectors x i R p,,,, i two classes, ad a vector y {1, 1}, SVC solves the followig primal problem: The Authors, published by EDP Scieces. This is a ope access article distributed uder the terms of the Creative Commos Attributio Licese 4.0 (

2 mi 1 ω, b, ζ 2 ωt ω + C ζ i Subject to y i (ω T φ(x i ) + b) 1 ζ i ζ i 0, i = 1 Its dual is Subject to (1) (2) mi 1 α 2 αt Q e T α (3) y T α = 0 0 α i C, i = 1 where is the vector of all oes, C > 0 is the upper boud, Q is a by positive semidefiite matrix, Q ij y i y j K(x i, x j ), where K(x i, x j ) = φ(x i ) T φ(x j ) is the kerel. Here traiig vectors are implicitly mapped ito a higher (maybe ifiite) dimesioal space by the fuctio φ. The decisio fuctio is: (4) sg( y i α i K(x i, x) + ρ) (5) 3 Gradiet Boosted Regressio Trees Gradiet Boosted Regressio Trees is a geeralizatio of boostig to arbitrary differetiable loss fuctios [14~16]. GBRT is a accurate ad effective off-the-shelf procedure that ca be used for both regressio ad classificatio problems. Gradiet Tree Boostig models are used i a variety of areas icludig Web search rakig ad ecology [16]. The classificatio schematic diagram is as follows: GBRT cosiders additive models of the followig form: M F(x) = γ m h m (x) m=1 where h m (x) are the basis fuctios which are usually called weak learers i the cotext of boostig. Gradiet Tree Boostig uses decisio trees of fixed size as weak learers. Decisio trees have a umber of abilities that make them valuable for boostig, amely the ability to hadle data of mixed type ad the ability to model complex fuctios. Similar to other boostig algorithms GBRT builds the additive model i a forward stage wise fashio: F m (x) = F m 1 (x) + γ m h m (x) (7) At each stage the decisio tree h m (x) is chose to miimize the loss fuctio L give the curret model F m 1 ad its fit F m 1 (x i ) F m (x) = F m 1 (x) + argmi h (6) L (y i, F m 1 (x i ) + h(x)) (8) The iitial model F 0 is problem specific, for leastsquares regressio oe usually chooses the mea of the target values. Gradiet Boostig attempts to solve this miimizatio problem umerically via steepest descet: The steepest descet directio is the egative gradiet of the loss fuctio evaluated at the curret model F m 1 which ca be calculated for ay differetiable loss fuctio: F m (x) = F m 1 (x) γ m F L(y i, F m 1 (x i )) (9) Where the step legth γ m is chose usig lie search: γ m = argmi LL(y i, F m 1 (x i ) γ L(y i, F m 1 (x i )) ) γ F m 1 (x i ) (10) 4 SVC-GBRT model Whether it is the SVC model or the GBRT model, the expressio of the sigle model may ot be eough, so we itegrate the two usig itegrated learig ad get the fial itegrated learig model. The fial classificatio schematic diagram is as follows: Figure 2. GBRT schematic 2

3 Figure3. SVC-GBRT schematic diagram SVC-GBRT is the esemble of SVC ad GBRT. The priciples of SVC ad GBRT are show i the chapter 2 ad 3. Below are the traiig formulas for esemble learig. For i = 1, 2,, : S i = Trai(S i 1 ) G i = Trai(G i ) F i = Esemble(S i, G i ) S: SVC model G: GBRT model F: SVC-GBRT model We trai SVC ad GBRT separately, ad fially use esemble learig to combie them. We use the stackig algorithm to itegrate. First, the sub-classifier is used to calculate the probability distributio of the target i each category. The the probabilities of multiple classifiers are added ad averaged. You get the fial probability distributio. 5 Classificatio of fragile states All the data comes from the World Bak. We wet to their website ad dowloaded the relevat data ad made a lot of aalysis ad processig. We got the followig data (from 2007 to 2015 of every coutry), ad we added the variace ad rage idicators for some ubalaced distributio of idicators. We labelled each coutry year by year, usig huma aotatio. No Table 1. Data features Features 1 Security Apparatus 2 Factioalized Elites 3 Group Grievace 4 Ecoomy 5 Ecoomic Iequality 6 Huma Flight ad Brai Drai 7 State Legitimacy 8 Public Services 9 Huma Rights 10 Demographic Pressures 11 Refugees ad IDPs 12 Exteral Itervetio 13 Variace 14 Rage We split up the data set we previously obtaied, ad we got the traiig set, validatio set, ad test set for cross validatio. The code was writte by Pytho, the the model was traied through cross-validatio, ad the best traiig iteratios was 600. Fially, we obtaied the followig classificatio error curve(figure 5). We used SVC ad GBRT as the compariso, as show i the figure 5, the test error rate of the SVC- GBRT model reached a astoishig 0.07 (while GBRT was 0.12, ad the SVC was 0.14). O the other had, the traiig error rate of the SVC-GBRT model reached a astoishig 0.04 (while GBRT was 0.5 ad SVC was 0.14). 3

4 Figure5. Traiig ad testig error curves After the model traiig was completed, we used the model to predict a typical coutry, the Cetral Africa Republic, ad the results were as follows(figure 6). As we ca see from the figure 6, the probability of Africa beig set for Alert is 0.92, the probability of Africa beig set for Warig is 0.3, the probability of Africa beig set for Stable is 0.1. the probability of Africa beig set for Sustaiable is Fially, the coutry was classified as Alert. 6 CONCLUSIONS Obviously, the traditioal threshold segmetatio method does ot classify the vulerability class of a coutry reasoably ad fairly. Therefore, we itroduce a ew classificatio method, usig machie learig method to classify the vulerability class of a coutry. First of all, subjective labellig of a part of the atioal data to allows the machie to lear why a coutry becomes vulerable from these data. Through model traiig ad testig, we successfully used the model to separate the coutry ito four types (Alert, Warig, Stable ad Sustaiable). Ad the accuracy of the test data set was 93%, which was better tha 77% by the threshold segmetatio method. Figure6. Classificatio result of the Cetral Africa Republic i 2010 Suppose that out aotatio is reasoable eough, we made a compariso betwee machie learig classificatio results ad previous threshold segmetatio results. Table 2. A compariso betwee differet methods of classificatio Method Error rate Accuracy Machie Learig 7% 93% Threshold Segmetatio 23% 77% Fud Qighai uiversity youth research fud Refereces 1. Naude, W. & Satos- Paulio, A. U. Fragile States: Causes, Costs, ad Resposes. Oxford: Oxford Uiversity Press, 2011: Mcloughli, C.. Topic guide o fragile states. Birmigham: Uiversity of Birmigham, UK.2012: Sai, F. G.. Evaluatig State Performace: A Critical View of State Failure ad Fragility Idex. Europea Joural of Developmet Research, 2011, 23(1): Hake, N. &, Messer, J.J. Fragile States Idex2014. Foreig Policy (July -August)2014: 10. 4

5 5. Mekhaus, K.. State Fragility as A Wicked Problem. PRISM, 2010, 1(2): Mata, J. F. & Ziaja S.. Users Guide o Measurig Fragility. Bo: Germa Developmet Isitute, 2009: 24/5 7. Ziaja S.. What Do Fragility Idices Measure? Z Vgl Polit Wiss, 2012, 6: Call, C.. The Fallacy of The Failed States. Third World Quarterly, 2008, (8): Grävigholt, J. & Ziaja S.. State Fragility: To-wards a Multi- Dimesioal Empirical Typology. DIE Discussio Paper, Kapla, S.. Idetify Truly Fragile States. The Washigto Quarterly, 2014, (37)1: Marshall, M. & Cole, B.. Global Report2011: Coflict, Goverace ad State Fragility. Foreig Policy Bulleti, 2011, 18(5). 12. Support-vector etworks, C. Cortes, V. Vapik - Machie Learig, 20, (1995). 13. Scikit-lear: Machie Learig i Pytho, Pedregosa et al., JMLR 12, pp , Breima L, Friedma J, Olshe R. Classificatio ad regressio trees. et al Friedma J H. Greedy fuctio approximatio: A gradiet boostig machie. The Aals of Statistics Stochastic gradiet boostig[j]. Jerome H. Friedma. Computatioal Statistics ad Data Aalysis (4) 5