ROOT: A Data Analysis and Data Mining Tool from CERN
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1. 4 From ROOT console type L Progam File Name where Program File Name is the name of the file including complete folder path in which you saved this program 5 Next still in the ROOT console type SimulateData This will generate the chosen number of simulated observations The resulting ROOT file SimulatedData root will be written in the folder specified by DirName Figure B1 below shows the screen shot of the ROOT console after executing the above steps In this case the name of the file containing the simulation code reproduced below was called SimulateData_Simple cpp and it was located in the folder C Documents and Settings temp Casualty Actuarial Society E Forum Winter 2008 28 ROOT A Data Analysis and Data Mining Tool from CERN ROOT 5 17 02 WELCOME to ROOT Version 5 17702 29 August 2007 You are welcome to visit our Web site http root cern ch KKKKK KKK KKKKK KKK Compiled on 36 August 2007 for win32 with thread support CINT ROOT C C Interpreter version 5 16 24 July 26 2007 Type for help Commands must be C statements Enclose multiple statements between lt gt root L C documents and settings temp SimulateData_Simple cpp root 1 SimulateData gt Generating Event 5666 Generating Event 10000 Total CPU Seconds Consumed 22 5 Total Real Seconds Consumed root 2 Figure B1 Screen shot of the ROOT console after executing the macro to generate 10 000 simulated observa2. ROOT file but in this case we have just one Now right click on the tree icon and a menu appears From this menu select StartViewer A new Tree Viewer window will appear A screen shot of this window is shown in Figure 8 Casualty Actuarial Society E Forum Winter 2008 8 ROOT A Data Analysis and Data Mining Tool from CERN ROOT Browser es crooner ono E af Bela ele a arraes Grot PROOF Sessions Dcaroot ROOT Files S C Documents and Setting Figure 7 Appearance of the ROOT object browser after double clicking on ROOT file icon shown in Figure 3 wr TreeViewer E TreeList E h PolNum Ema dataT reel in EffYear BR EfiMonth J State TotalPremium m E Figure 8 The ROOT tree viewer window displaying the information contained in the sample data tree Notice in Figure 8 the leaf shaped icons in the right panel of the tree viewer These are the leaves of the ROOT tree we created in the sample data load program Next to each leaf is the name of the corresponding variable Casualty Actuarial Society E Forum Winter 2008 9 ROOT A Data Analysis and Data Mining Tool from CERN The ROOT tree viewer is a powerful data exploration tool which can be used for one two and three dimensional data exploration fitting etc In this section we will just see how to quickly generate one and two dimensional histograms from this simple data Suppose we want to see a
3. 70 80 90 100 0 1 2 3 4 5 6 7 8 9 A CreditScore PolicyAge TotalBuildinginsurance Entries 5000000 LossRatio Entries 5000000 Mean 2 03e 005 Mean 0 3986 RMS 1 239 008 RMS 0 09041 F Undertiow o 10E Underflow 0 s0 Overflow o 2 Overflow 0 10 5 Integral Se 006 F Integral 5e 006 FI Skewness 20 34 sL Skewness 4 203 s0 10 E Kurtosis 70 01 10 E f F wE 10 E E E aL 10 10 E 1 E 10 El tok 10 arrears ees re EE EA E E N A A eg el ARA Lr E 0 5 7 6150620025 30 88S s SO 0 0 5 1 15 2 2 5 3 TotalBuildingInsurance LossRatio Figure 17 Raw histograms of the five simulated predictive variables and the loss ratio The figure titles show which figure corresponds to which variable EXPLORATION OF SIMULATED DATA Figure 18 shows several profile histograms plotting LossRatio vs the five predictive variables These profile histograms show the mean value of the loss ratio for a given value of the X axis This is a useful way to visualize the relationship between the target and predictive variables In our simulated data set each of the five predictive variables is correlated by design with the target variable Consequently we should see a non flat pattern in all these profile histograms which we do It may be useful to point out here the time taken to generate the 11 figures shown in Figures 17 and 18 Each of these figures was generated as mentioned earlier from the Casualty Actuarial Society E Forum Winter 2
4. C expression involving one or more of the variables stored in the tree This expression must first be defined using the EQ icons in the tree viewer All these expressions are empty by default In order to achieve our goal of looking at the average premium only in California and New York double click on the first EQ icon in the tree viewer of Figure 10 we will assume that the tree viewer is in the state shown in Figure 10 if not follow the instructions above to bring it this state A dialog appears that allows us to type in the selection criterion and also give it a name Figure 12 shows the screen shot of the tree viewer after double clicking on the EQ icon Casualty Actuarial Society E Forum Winter 2008 12 ROOT A Data Analysis and Data Mining Tool from CERN wr TreeViewer File Edit Run Options Command Option PROF Histogram htemp I Hist l Scan M Rec CurentFolder SurrentTree dataTree E TreeList X State h Polnum Ria data Tree Y TotalPremiur HR EffYear Z empty EffMionth ol empty State FF sean box TotalPremium Jamm R E lt empty Ec empty E lt empty Ec empty E lt empty E lt empty Ec empty E lt empty Ec empty E E e os Figure 12 The tree viewer after double clicking on the E icon Notice the dialog box at left center of the tree viewer Now we can type in our selection criterion a valid C stat
5. delete f1 return Xx void SimulateData Instantiate and start a stop watch TStopwatch StopWatch StopWatch Reset StopWatch Start First open a file to output the data set string OutFileName DirName SimulatedData root TFile fout new TFile OutFileName c_str RECREATE if fout cout lt lt Error opening input file lt lt endl return Next book an ntuple TNtuple nt new TNtuple nt AgeOfBusiness BuildingCount CreditScore PolicyAge TotalBuildingInsur ance PolicyNumber LossRatio Premium Loss EventNum ranl ran2 ran3 Create an array to store the simulated numbers Float_t VarList 13 Now start generating the variables Loop desired number of times int counter 0 for Int_t i 0 i lt Nloop i countert t Casualty Actuarial Society E Forum Winter 2008 30 ROOT A Data Analysis and Data Mining Tool from CERN if counter 5000 0 cout lt lt Generating Event lt lt counter lt lt endl VarList 0 Float_t GetRandomFromLandau 10 0 5 0 0 100 AgeOfBusiness is based on Landau distribution VarList 1 Float_t GetRandomFromLandau 0 4 0 1 0 100 BuildingCount is based on Landau distribution VarList 2 Float_t GetRandomFromUniform 0 100 CreditScore is based on Uniform distribution VarList 3 Float_t GetRandomFromFormula 85 57 7 79
6. file can be read sequentially if all the information must be processed With no data explosion issues a ROOT file can also be read randomly to process just a few attributes if that is what the analysis requires ROOT is thus able to give us interactive computing capabilities where other solutions fail There are many other reasons why ROOT is an appropriate tool for predictive modeling But efficiency in storing and accessing the data is where ROOT stands out from any other tool that is in the market today Casualty Actuarial Society E Forum Winter 2008 3 ROOT A Data Analysis and Data Mining Tool from CERN HOW TO GET ROOT ROOT can be downloaded under GNU Lesser General Public License 9 from the ROOT download page 10 Installation instructions are also provided there A ROOT uset s guide 11 complete class reference 12 tutorials 13 and useful how to s 14 are also available online A searchable ROOT user forum called Root Talk 15 is a useful resource to find answers to several of the questions an average user might come up with Any references in this paper to the ROOT user s guide correspond to version 5 16 which is the current production version of ROOT as of the writing of this paper Throughout this paper we will sometimes provide the CPU time taken for a given analysis These times were measured on a PC running Windows XP with a 1 73 GHz Intel Pentium M processor and 1 GB of memory Also all these an
7. 008 10 ROOT A Data Analysis and Data Mining Tool from CERN Now suppose we are interested in finding out the average premium collected in each state We can do that in the following manner In the tree viewer Figure 8 drag the leaf labeled TotalPremium to the icon in the same panel labeled Y which is empty by default Then drag the leaf labeled State to the icon labeled X This tells the tree viewer to plot TotalPremium Y axis vs State X axis Next using the Options menu at the top menu bar in the tree viewer set the drawing option to Profile Options gt 2D Options gt Profile This tells the tree viewer to plot a profile histogram which plots the average Y value for each bin on the X axis After these steps the tree viewer window should look like Figure 10 We TreeViewer Eile Edit Run Options Help Command Option PROF Histogram htemp I Hist Scan M Rec CurrentFolder Current Tree dataTree gt O TreeList X State BR PolNum a E e Y TotalPremiur MR Effvear Z empty Effttonth h State MR TotalPremium iList otist Content State KI 4 e r af z RESET Figure 10 The appearance of tree viewer window after preparing it to plot average total premium in each state In Figure 10 notice that the X icon says State next to it and the Y icon says TotalPremium next to it Also notice that the Option is set to PROF in the small Option window below the t
8. 008 18 ROOT A Data Analysis and Data Mining Tool from CERN simulated data set of 5 Million policies It took a total of 50 CPU seconds to generate these 11 figures g Mean 21 73 Mean 1 564 Meany 0 3986 Meany 0 3986 G ie RMS 18 82 o z RM 3 123 3 F RMS y 0 09041 0 655 RMS y 0 09041 oas PE ee g ose Pir sS S e th bet Fane 0 55 oe AE a a E a E 0 56 ee f ee 3 a 0 35 a 0 45 pom E 0 46 0 3 E F 0 356 0 25 Ae F 0 255 0 20 sadassa dasida darsa linsa dasrdliri 0 26 rare arrears re EECA PECEL SY i 27402030 40 50 60 70 80 90 100 210 20 30 40 50 60 70 80 90 100 AgeOfBusiness BuildingCount J Mean 50 02 _ Mean 3 266 Meany 0 3986 Meany 0 3986 o RMS 28 87 o E RM 2 439 vds RMSy 0 09041 F _ RMS y 0 09041 BEERE Torde 8 04E eagle el a E a 0 385 Broren E E a 0 4 E 0 36 z 0 346 E Fes 0 325 sy _ 0o36 E 0 28 o3 Toe 0 26 E Tes 0 24 0 25 0 22E ozen AEn a at iane E Ea A a ata ea i an 2o 20 30 40 50 60 70 80 90 100 2 Peo Carey Danas Pray Wabie DERN Snes L CreditScore PolicyAge TotalBuildinginsurance Entri 5000000 m 2 03e 005 RNS 1 239e 006 Undertiow Overflow 10 Integral ses006 Skewene 20 34 A Kurtosis 534 10 10 LL a gi Ceeeede a a 0 5 10 15 20 25 30 35 40 45 50 TotalBuildingInsurance Figure 18 Profile histograms of LossRatio vs various predictive variables The Y axis in each of these pl
9. 48 x 0 10 PolicyAge is based on a linear distribution VarList 4 Float_t GetRandomFromLandau 3 3736e4 5 4577e2 0 50000000 TotalBuildingInsurance is based on Landau distribution VarList 5 counter PolicyNumber VarList 6 Float_t 0 5 VarList 0 0 0053 0 1 VarList 1 0 025 0 1 VarList 2 0 0057 0 1 VarList 3 0 0227 VarList 4 0 0437 1 0e 6 gRandom gt Gaus 0 0 0 04 LossRatio is a linear combination of VarList 7 Float_t VarList 8 Float_t VarList 9 Float_t VarList 10 Float_t random number VarList 11 Float_t another random number VarList 12 Float_t another random number nt gt Fill VarList End of loop over Nloop Write the ntuple to output file fout gt cd nt gt Write O fo t gt Close Stop the stop watch StopWatch Stop cout lt lt endl cout lt lt endl Total L CPU Seconds Consumed Total Clean up delete fout L Real Seconds Consumed lt lt StopWatch CpuTime lt lt StopWatch RealTime other variables plus an error term gRandom gt Landau 5000 500 Premium VarList 7 VarList 6 Loss counter EventNum 10 0 gRandom gt Rndm ranl is just a 10 0 gRandom gt Rndm ran2 is just 10 0 gRandom gt Rndm ran3 is just and report the time taken to run this macro lt lt lt lt MMMM END of t
10. 500 123456796 2007 02 AZ 1850 123456797 2006 12 CA 2560 123456798 2007 03 KS 1250 The Program to Read the Data This program reads in the above file and stores its contents into a ROOT tree This tree is then written to disk in a ROOT file This ROOT file then can be use for data visualization exploration and analysis This program is a ROOT macro which means it can be executed from the ROOT window It will not run as a stand alone program since it does not contain the main code block In order to see how to generate stand alone compiled ROOT code refer to the ROOT users guide Casualty Actuarial Society E Forum Winter 2008 26 ROOT A Data Analysis and Data Mining Tool from CERN Assuming this program is saved under the name C Documents and Settings temp ReadSampleData cpp on disk the user can run it by typing the following command from the ROOT window x C Documents and Settings temp ReadSampleData cpp This command will execute the program which will result in the input file being read and saved as a ROOT tree on disk The program is reproduced below Reads a simple data file Hinclude lt TFile h gt include lt TTree h gt include lt string gt Hinclude lt iostream gt using namespace std void ReadSampleData Location of the directory for input and output files string dirName C Documents and Settings temp Name of the input and output files string inFile
11. LinearFitter 20 class in ROOT to fit LossRatio with the five predictive vatiables mentioned above We used the first 1 million observations from our simulated data set for the purpose of this fit The total CPU time taken for this analysis was 11 seconds Figure 20 below shows the values of the parameters obtained by the fit and also their true value Since we simulated the relationship between the target variable and the predictive variables we know exactly what the correct parameter estimates should be This allows us to do an absolute end to end calibration verification of the analysis regression chain l Parameter Estimate True Value Variable Name from the Fit of the Parameter Intercept 0 50 0 5 AgeOfBusiness 5 31E 4 5 3E 4 BuildingCount 2 47E 3 2 5E 3 CreditScore 5 70E 4 5 7E 4 PolicyAge 2 27E2 2 27E 2 TotalBuildinglnsurance 4 37E 08 4 37E 08 Figure 20 Results of the fit to the simulated insurance data Also shown are the true values of the parameters Casualty Actuarial Society E Forum Winter 2008 21 ROOT A Data Analysis and Data Mining Tool from CERN In Figure 20 if we compare the parameter estimates from the fit with their true values we see that the two agree quite well This comparison gives us confidence that our analysis chain used here from data preparation to fitting is correct In order to test the performance of TLinearFitter on a much bigger data set we used it to perform a fit on a data se
12. Name dirName SampleData txt string outFileName dirName SampleData root Create a tree to store the data TTree tree new TTree dataTree Sample Data Open the output file to write to TFile fout new TFile outFileName c_str RECREATE fout gt cd Read in the data from the text file int nentries tree gt ReadFile inFileName c_str PolNum T EffY ear T EffMonth I State C TotalPremium D Casualty Actuarial Society E Forum Winter 2008 27 ROOT A Data Analysis and Data Mining Tool from CERN cout lt lt Read lt lt nentries lt lt entries from the input file lt lt inFileName lt lt endl Write the ROOT tree to output file tree gt Write fout gt Close Cleanup delete tree delete fout j Appendix B In this appendix we reproduce the ROOT macro we used to generate the simulated data used in this paper TNtuple class http root cern ch root html516 TNtuple html is used to store the simulated data TNtuple class inherits from TTree class and is useful when one is only storing numeric information In order to run this macro follow these steps 1 Copy the following program see below and save it on your computer 2 Change the value of variable Nloop highlighted in bold face to the number of observations you want to simulate 3 Change the value of the variable DirName highlighted in bold face to the name of folder where you saved this program
13. OOT even from a small PC all the analysis reported in this paper was done on a PC A laptop with ROOT as a data analysis tool may be able to give a better performance than a powerful mainframe using one of the commercially available data analysis tools ROOT can thus be a solution adopted by one person in an insurance company Once proven it can be easily extended to an entire team of data analysts or as a corporate wide solution A ROOT solution is very highly scalable ROOT might be an appropriate solution even for smaller data sets Typically predictive modeling and ad hoc data analysis involve presenting the data in different graphical tabular forms These presentations are best done in a notebook device This is one of the reasons why Excel is very popular among the actuaries Using Excel one can play with the data and once a story emerges from the data it becomes easy to share the story with the rest of the team This concept can be loosely termed as interactive computing When one wants to do analysis on one column in an Excel spreadsheet the entire spreadsheet must be read into memory Like Excel other technologies also suffer similar inefficiencies When data is stored as tables and rows as in a relational database subsets of the data cannot be accessed or modified in an efficient way without touching other parts of the data The design of ROOT allows access to subsets of data without the need to touch the rest of the data An entire ROOT
14. ROOT A Data Analysis and Data Mining Tool from CERN Ravi Kumar ACAS MAAA and Arun Tripathi Ph D Abstract This note briefly describes ROOT which is a free and open source data mining tool developed by CERN the same lab where the World Wide Web WWW was invented Development of ROOT was motivated by the necessity to address the challenges posed by the new generation High Energy Physics experiments which are expected to produce and analyze thousands of terabytes of very complex data every year ROOT is an object oriented data analysis framework written in C It contains several tools designed for statistical data exploration fitting and reporting In addition ROOT comes with powerful high quality graphics capabilities and interfaces including an extensive and self contained GUI development kit that can be used to develop easy to use customized interfaces for the end users This note provides some simple examples of how ROOT can be used in an insurance environment INTRODUCTION In this paper we provide an introduction to some features of ROOT 1 by using it to simulate and analyze the simulated data We also show some very basic but necessary first steps needed for one to become familiar with ROOT Going through this process will hopefully give the reader a flavor of some of the analysis tasks that can be accomplished within ROOT Also hopefully this will provide the reader enough of a familiarity and hands on experience w
15. al network obtained by training it on the simulated data set The thickness of lines is proportional to the weight for the corresponding connection Figure 22 shows a profile of the residuals for different values of the output LossRatio for the independent test data set The optimized neural network can be automatically exported to a C class to be used elsewhere e g for implementation A output truth vs truth for LossRatio MLP_truthdev_0 Entries 2000 Mean 0 145 Meany 0 0009624 RMS 0 03012 RMS y 0 01521 A output truth for LossRatio 00504 015 02 025 0 3 4035 04 0 45 LossRatio Figure 22 Residual profile for various values of the neural network NN output LossRatio on the test data set The Y axis is the mean value of the NN output minus the true LossRatio for a given value of the true LossRatio The true loss ratio has been normalized so that it takes on values between O and 1 Casualty Actuarial Society E Forum Winter 2008 23 ROOT A Data Analysis and Data Mining Tool from CERN 10 3 Other statistical analysis packages in ROOT The previous two examples use just two of the several statistical analysis classes available in ROOT Here we list some other classes that might be of interest to anyone interested in statistical analysis of data in ROOT The TMinuit 22 and TFumili 23 minimization packages can be used to do either least squares ot maximum likelihood fitting Also see chapter 5
16. alyses were performed using CINT the C interpreter provided by ROOT See chapter 7 of the ROOT users guide to learn about CINT STARTING ROOT If ROOT was installed correctly a tree shaped icon shown in Figure 1 should automatically appear on your Windows desktop ki goot Mol a e 00 Figure 1 The ROOT shortcut icon on Windows desktop In order to start ROOT in Windows just double click on this icon This will start the ROOT console which is shown Figure 2 In Unix Linux environment ROOT can be started by issuing the following command from the command line ROOTSYS bin root ROOTSYS is the environment variable pointing to the directory where ROOT was installed If the directory containing the ROOT executable is already in the system path then Casualty Actuarial Society E Forum Winter 2008 4 ROOT A Data Analysis and Data Mining Tool from CERN one just needs to type root from command line to start ROOT Regardless of the operating system the resulting ROOT console will appear the same as shown in Figure 2 t ROOT 5 16 00 WELCOME to ROOT Version 5 16 66 27 June 2007 You are welcome to visit our Web site http root cern ch KKKKK KKK KKKKKK KX Compiled on 28 June 2007 for win32 with thread support CINT ROOT C C Interpreter version 5 16 21 June 22 2007 Type for help Commands must be C statements Enclose multiple statements between lt gt root 0 Figure 2 The ROOT cons
17. as cache etc adding numerous indices to tables creating additional summaries of the data like OLAP cubes and other similar techniques If one loads a 1 GB text file into a relational database it will take up multiple gigabytes to just store the data When one further tweaks the database for performance with additional indices pre summaries and such the original 1 GB data would have exploded to something very large Most if not all of the commercial software for data analysis is built for accessing data from relational databases These commercial tools cannot overcome the fundamental flaw in the way data is stored tables and rows except by using brute force Casualty Actuarial Society E Forum Winter 2008 2 ROOT A Data Analysis and Data Mining Tool from CERN Some data analysis tools are very memory intensive Some data analysis tools are very I O intensive Some data analysis tools are both memory intensive and I O intensive like most commercial business intelligence tools operating on relational databases In these systems even if the data grows on a linear scale the performance of the system degenerates on an exponential scale Thus these systems are not easily scalable whereas ROOT stores and retrieves data in an optimal way that is conducive for data analysis It avoids most memoty issues and I O performance issues by seamlessly buffering the data between memory and storage One can thus get a very reasonable throughput from R
18. can effectively separate policies with low loss ratio from those with high loss ratio Once we have identified the variables that are most effective in providing this kind of discrimination then we can use them for example in multiple regression to come up with the regression equation that will predict loss ratio from these predictive variables For our analysis we define arbitrarily policies with loss ratio less than 0 4 as good policies signal and those with loss ratio greater than 0 4 as bad policies background Our goal is to find the ranking of predictive variables based on how well they can distinguish between these two kinds of policies Borrowing from high energy physics terminology we will use the words signal loss ratio lt 0 4 and background loss ratio gt 0 4 from now on to represent these two classes of data We fed all the five predictive variables shown in equation 1 and the three random variables ran1 ran2 ran3 to the Fisher classifier The random variables were included to test the effectiveness of the classifier it should be able to identify these as the least predictive The data sample used consisted of 100 000 observations of each type signal and background as defined above for training and testing So a total of 400 000 observations were used in this analysis Rank Variable Discriminating Power 1 PolicyAge 1 20E 01 2 CreditScore 1 51E 02 3 AgeOfBusiness 1 06E 02 4 TotalBuilding
19. cross the whole planet WHY ROOT ROOT is a very appropriate tool for use by actuaries and other insurance analysts who do ad hoc data analysis and predictive modeling type work ROOT is a framework that is specifically designed for large scale data analysis ROOT stores data in a very efficient way in a hierarchical object oriented database This database is machine independent and highly compressed If one loads a 1 GB text file into a ROOT file it will take up much less disk space than the original text file ROOT also has tools to interact with data in a very efficient way It has built in tools to do multi dimensional histograms curve fitting modeling and simulation All these tools are designed to handle large volumes of data Conversely relational databases databases where the data is organized as tables and rows were originally designed for transactional systems and not for data analysis Thus a relational database is very good for use in a policy administration system which looks at one policy at a time or claim administration system which looks at one claim at a time But when one is interested in segmenting the data across all the policies or across all the claims a relational solution falls apart In order to make the relational solution work for large scale data analysis we use the brute force method A typical brute force method will involve adding considerable computing power adding sophisticated I O capabilities such
20. ement involving variables in the tree in this box and also assign it a name alias We just want to keep California and New York So in the Expression dialog we will type State CA State NY Note that the double quotes are preceded by backslash since the expression itself is a string and within this expression we ate comparing with a string Also keep in mind that both C and ROOT are case sensitive In the alias box we will give it the name Cut1 After these steps the screen shot of the tree viewer is shown in Figure 13 Casualty Actuarial Society E Forum Winter 2008 13 ROOT A Data Analysis and Data Mining Tool from CERN We TreeViewer File Edit Run Options X State PolNum y TotalPremiur Si EffYear Xk EfiMonth RR State JR TotalPremium Figure 13 The tree viewer after typing in the selection criteria in the expression dialog Now click the done button in the selection expression dialog This will close the selection expression dialog The screen shot of the tree viewer after this step is shown in Figure 14 Notice how the appearance of the selection expression icon we just edited has now changed It no longer shows EQ and it is no longer empty Now it contains a valid selection criterion which we can use to filter data Notice how the scissors icon is still empty meaning our selection criterion has not been activated yet In order t
21. es that one can leverage to get started with any kind of analysis 13 REFERENCES AND LINKS 1 Rene Brun and Fons Rademakers ROOT An Object Oriented Data Analysis Framework Proceedings of AITHENP 96 Workshop Lausanne Sep 1996 Nucl Inst amp Meth in Phys Rev A 389 1997 81 86 See also http root cern ch 2 http public web cern ch Public Welcome html 3 http info cern ch 4 http public web cern ch Public Content Chapters AboutCERN Achievements Achievements en html 5 http atlasexperiment org 6 http en wikipedia org wiki ATLAS experiment 7 http lhc web cern ch Ihe 8 http root cern ch root ExApplications html 9 http root cern ch root License html 10 http root cern ch twiki bin view ROOT Download 11 http root cern ch root doc RootDoc html 12 http root cern ch root Reference html 13 http root cern ch root Tutorials html 14 http root cern ch root HowTo html 15 http root cern ch phpBB2 16 http root cern ch root html516 TTreeViewer html 17 http root cern ch root html516 TBrowser html 18 A Hocker et al TMVA Toolkit for Multivariate Data Analysis http arxiv org abs physics 0703039 Also available at http tmva sourceforge net docu TMVA UsersGuide pdf 19 http tmva sourceforge net 20 http root cern ch root htm1514 TLinearFitter html 21
22. have performed so far in the tree viewer can easily be saved as a ROOT macro which is basically a C function using ROOT classes which can be run from the ROOT console to quickly reproduce these steps at a later time The reader is referred to the ROOT user s guide to learn how to accomplish that DATA SIMULATION Complex simulations are a significant part of research in a typical high energy physics experiment and ROOT provides tools to facilitate this process For the purpose of this paper we prepared some simulated insurance like data The code used for this simulation is provided in appendix B For this study we chose to simulate 5 Million BOP policies The loss ratio for each of these policies was generated based on five predictive variables e Age of business Number of years the business has been around e Building Count Number of buildings insured under the policy e Credit score The commercial credit score of the business e Policy Age Number of years the policy has been in force e Total Building Insurance The total amount of building insurance on the policy First for each observation each of these variables was generated independently Age of Business Building Count and Total Building Insurance were generated using Landau distribution Credit Score was simulated using a flat distribution on a scale of 1 100 and Casualty Actuarial Society E Forum Winter 2008 16 ROOT A Data Analysis and Data Mini
23. he Data Simulation Code MIMMMMMMIMMMMMMMII Casualty Actuarial Society E Forum Winter 2008 31
24. histogram of all the states in our data set which will show us the number of policies written in each state In order to get this histogram simply double click the leaf labeled State in the tree viewer A separate window object of type TCanvas appears with this histogram A screen shot of this window is shown in Figure 9 We see that there are four policies in California and two each in New York Kansas and Arizona as expected from our input data The TCanvas object itself is a very complex object which allows the user to interactively explore the data and customize the visual appearance of the graphics that appears on the canvas See chapter 9 of the user s guide for more details DEK File Edit View Options Inspect Classes Entries Mean RMS Figure 9 A histogram of all the states in the data set used by the sample data load program The histogram in Figure 9 can easily be saved to disk in various formats e g gif pdf png etc by using File gt Save or Save As menu in the menu bar at the top of the canvas The reader is encouraged to explore this interactive canvas all the objects on it and the associated context menus Right click on different parts of the canvas e g the title box statistics box the histogram area the lines of the histogram the axes etc and explore the large amount of interactive functionality available in the context menus Casualty Actuarial Society E Forum Winter 2
25. http root cern ch root htmldoc TMultiLayerPerceptron html 22 http root cern ch root html516 TMinuit html 23 http root cern ch root html516 TFumili html 24 http root cern ch root html516 TPrincipal html 25 http root cern ch root html514 TMultiDimFit html 26 http root cern ch root htm1516 TMath html Casualty Actuarial Society E Forum Winter 2008 25 ROOT A Data Analysis and Data Mining Tool from CERN Appendix A SAMPLE DATA LOAD PROGRAM Below is a simple data load program which reads a tab delimited text file and stores them in a ROOT tree This tree is then written to an output ROOT file The contents of the file to be read are produced below This is a simple space delimited file which contains 10 records Each record consists of a Policy Number Policy Effective Year and Month State and the Total Premium collected The purpose of this exercise is to give a simple example of how one can read data into ROOT Note that any line starting with FP is ignored by the ReadFile method which we will use to read the sample data file below Therefore the first line in this sample data set is just for our convenience to tell us what the various fields are PolNum EffYear EffMonth State TotalPremium 123456789 2006 10 CA 5000 123456790 2007 01 NY 6000 123456791 2005 12 KS 1500 123456792 2007 08 CA 3500 123456793 2007 05 AZ 2000 123456794 2006 11 CA 3500 123456795 2006 04 NY 5
26. ing a GUI builder which can be used to develop customized GUIs for specific tasks See chapter 25 of the user s guide ROOT comes with CINT the C C interpreter which allows one to script an analysis in C and quickly execute it on the command line without having to compile This provides a quick way to prototype an analysis which can later be compiled for better performance See chapter 7 of the user s guide for more details All the libraries available in standard C of course can easily be used and integrated with a ROOT analysis Interfaces to Ruby and Python scripting languages See chapter 19 of the user s guide for details Parallel processing See chapter 24 of the user s guide for details Networking See chapter 22 of the user s guide Automatic HTML documentation generation See chapter 27 of the user s guide for details Casualty Actuarial Society E Forum Winter 2008 24 ROOT A Data Analysis and Data Mining Tool from CERN e Three dimensional graphics package 12 SUMMARY AND CONCLUSIONS In this note we have briefly introduced ROOT via some simple examples Hopefully this will give the reader a feel of how to get started with using ROOT in insurance environment We have also provided links below that a curious reader can follow to get a more detailed and advanced understanding of this tool The users guide online tutorials and the how to s pages provide a wealth of information and several working exampl
27. ith ROOT so that they can start using its more advanced features customized to their own needs We want to emphasize that this is just a preview intended for readers who might not be familiar with ROOT at all The scope of various tasks that can be accomplished using ROOT is much more comprehensive We will provide Web links and references at the end of this paper for the curious reader who wants to learn more about this tool ROOT is a free open source object oriented data analysis framework based on C This tool was developed at CERN 2 which is a particle physics lab located near Geneva Switzerland It is interesting to note that CERN is the same lab where the World Wide Web was born 3 4 Development of ROOT was motivated by the need to address the challenges posed by the experimental high energy physics community where scientists produce and analyze vast amounts of very complex data For example the ATLAS 5 6 experiment at the Large ROOT A Data Analysis and Data Mining Tool from CERN Hadron Collider LHC 7 at CERN will be generating over 1 000 terabytes of data per year And this is just one of the experiments running at LHC ROOT is being used widely by several experiments in high energy physics astrophysics etc 8 In terms of the cost of these research projects and the people involved the ROOT user community comprises a multibillion dollar industry with the labs and the users located pretty much a
28. lnsurance 4 56E 05 5 BuildingCount 2 24E 05 6 ran3 7 15E 06 7 ran2 8 95E 07 8 rant 1 36E 07 Figure 19 The results of variable ranking using Fisher discriminant in TMVA Figure 19 shows the results of this analysis We can see that the classifier has correctly identified ran1 ran2 and ran3 as least predictive This is just a simple example of how Casualty Actuarial Society E Forum Winter 2008 20 ROOT A Data Analysis and Data Mining Tool from CERN TMVA can be used to search for predictive variables The meaning of rankings can be found in the TMVA user s guide From now on we will just keep the five predictive variables for fitting and discard the three random variables FITTING Once we have identified the predictive variables we want to use to make the prediction we need to perform a fit to the data using these variables to come up with the optimal relationship between the target variable and the predictive variables In our case we ate interested in obtaining the relationship between LossRatio and the five predictive variables shown in equation 1 Obviously several techniques can be used to solve this problem depending on the characteristics of the data at hand ROOT provides several tools to achieve this including least squares regression method of maximum likelihood neural networks etc In this section we will show the results from using just a couple of these tools 10 1 The TLinearFitter Class We will use T
29. n DoR Eesen acm dEl ROOT Files SampleData root SampleData root ROOT files root ha Figure 5 Screen shot of the ROOT object browser and file selection window after navigating to the ROOT file generated by the sample data load program Casualty Actuarial Society E Forum Winter 2008 7 ROOT A Data Analysis and Data Mining Tool from CERN After selecting the appropriate ROOT file click the open button in the file selection dialog This will close the file selection window and the object browser will again appear like Figure 4 At this point double click the icon labeled ROOT Files in the right hand panel of the object browser After this action the browser looks like Figure 6 wx ROOT Browser DER File view Options Help gej fe lel al Option Contents of ROOT Files 78 CADocuments and Settingsitemp SampleData root PROOF Sessions C croot SmE Figure 6 Appearance of the ROOT browser after double clicking on the ROOT Files icon Notice that an icon representing the selected ROOT file appears in the right panel of the browser The absolute path indicating the file name and location is also shown Now double click on this ROOT file icon The browser will now look like Figure 7 Notice that a tree icon appears in the right panel of the browser This is the tree that we created using the sample data load program One can create several ROOT trees in a single
30. ng Tool from CERN Policy Age was made to follow a linear distribution subject to the condition that policy age must be less than or equal to the building age In addition to these predictive variables we also generated three random variables called ran1 ran2 and ran3 These variables are uniformly distributed between 0 10 These variables don t have any predictive power by design But we will include them in our list of predictive variables while searching for and ranking the most predictive variable The tools being used to search for the predictive variable should be able to identify these random variables as non predictive This works as a sanity check of the tool The loss ratio from the five predictive variables was generated using the following equation LossRatio 0 5 0 00053 AgeOfBusiness 0 0025 BuildingCount 0 00057 CreditScore 0 0227 PolicyAge 0 0437 TotalBuildingInsurance 1 In addition a random Gaussian noise is added to the LossRatio with mean 0 and standard deviation of 0 04 Roughly speaking this corresponds to smearing the true loss ratio by about 10 Figure 17 shows histograms of all the five predictive variables and the loss ratio We have chosen on purpose to simulate only the lossy policies We would like to point out one thing here Since we simulated our data such that the relationship between the target variable Loss Ratio and the five predictive variables follows equation 1 abo
31. o activate this filter simply drag this selection expression icon Cut1 to the scissors icon After this step the tree viewer should look like Figure 15 Now we are teady to make the plot we need Simply click on the drawing icon near bottom left just left to the STOP icon The canvas will now show the updated plot which is shown in Figure 16 Notice that only the states of California and New York appear on the X axis now according to our selection One can apply any arbitrarily complex filter to the data in this manner Casualty Actuarial Society E Forum Winter 2008 14 ROOT A Data Analysis and Data Mining Tool from CERN Wz TreeViewer DAR M X State BR Polnum Esma dataT reel Y TotalPremiur My Effvear Z empty Eff onth oL empty State TotalPremium adelia Reser Ss temp X State PolNum rt TotalPremiurr St EffYear Z empty EffMonth sl Cutt J State FF Scan box TotalPremium Figure 15 Appearance of the tree viewer after activating the selection criterion Cutt Casualty Actuarial Society E Forum Winter 2008 15 ROOT A Data Analysis and Data Mining Tool from CERN File Edit View Options Inspect TotalPremium State State CA State NY Entries 6 Mean 0 8333 Mean y 4343 RMS 0 4714 RMS 1233 Figure 16 Plot of average total premium vs State after applying the state selection criterion Finally all steps we
32. of the user s guide The TPrincipal 24 class can be used for principal components analysis The TMultiDimFit 25 is another non parametric fitting package which can be used to approximate the relationship between target and predictive variables in terms of simple basis functions The TMath 26 class contains several useful mathematical functions See chapter 13 of the user s guide In addition to some of the algorithms mentioned earlier in this note the TMVA package 18 19 provides several other algorithms for data classification The one dimensional two dimensional three dimensional and Profile histogram classes provide a convenient and interactive way to visualize explore and fit data See chapter 3 of the uset s guide for more detail The linear algebra package See chapter 14 of the user s guide 11 SOME OTHER USEFUL FEATURES OF ROOT Previous sections demonstrated using simple simulated data some simple application of ROOT In this section we will list some more tools available in ROOT that might be relevant to us Animation facilities which can again be used to generate animations of some of the analysis chain to be used in presentations Efficient random number generators with large periodicity 2 1 Also one can easily generate random numbers either following any analytical distribution or following any empirical distribution provided by the data A complete self contained GUI toolkit includ
33. ole LOADING DATA INTO ROOT ROOT provides TTree and TNtuple classes to store and access data efficiently Chapter 12 of the ROOT user s guide provides a detailed discussion of ROOT Trees why one should use them for storing data and how to read data into a ROOT tree ROOT ttees are designed specifically to store large volumes of data very efficiently resulting in much smaller files on disk Also since a tree stores data in hierarchical branches each branch can be read independently from any other branch This can make for a very fast access to the data since only the necessary information is read from disk and not necessarily the whole file A very simple example of how to read data into a ROOT tree is given in appendix A This example converts a space delimited file into a ROOT file which can then be explored manipulated further using ROOT ROOT also provides interfaces using ODBC to relational databases such as ORACLE MYSQL etc EXPLORING A ROOT FILE The TTreeViewer class 16 of ROOT provides a GUI for convenient exploration of data once it has been converted into a ROOT tree In order to illustrate some of its Casualty Actuarial Society E Forum Winter 2008 5 ROOT A Data Analysis and Data Mining Tool from CERN functionality we will use the ROOT file generated by the sample data load program mentioned in the previous section Chapter 12 of the ROOT users guide describes how to start a Tree Viewer First one ha
34. op menu bar Now we are ready to produce the graph we want Just click on the graphing icon near the bottom left corner of the panel on the left of the icon labeled STOP Again a new canvas pops up with the desired graph A screen shot of this canvas is shown in Figure 11 Notice how the average premium as well as RMS root mean square is plotted for each state This allows for a visual exploration of the relationships between any two variables quickly One can also perform fits to this relationship The reader is referred to the ROOT user s guide to learn how to perform interactive fits to the data points on a canvas For example see chapter 5 of the ROOT user manual Casualty Actuarial Society E Forum Winter 2008 11 ROOT A Data Analysis and Data Mining Tool from CERN File Edit View Options Inspect Classes TotaiPremium State Entries 10 Mean 1 7 Meany 3266 RMS 1 166 RMS 1639 H 2 amp S000 e Figure 11 Graph of average premium vs state Now suppose we want to apply filters to our data The tree viewer allows us to do that easily In order to illustrate how to do this we will create the profile histogram of average total premium vs state but this time we only want to look at the states of California and New York There is a scissors shaped icon in the tree viewer just below the Z icon see Figure 10 This is used to apply cuts or selection criteria to the data The cut can be any valid
35. ots shows the average loss ratio for the corresponding value of the X variable SEARCHING FOR PREDICTIVE VARIABLES The first step in building a predictive model is to identify which variables to use as predictors The TMVA 18 19 package provides tools to facilitate this process TMVA is an acronym for Toolkit for Multivariate Data Analysis It provides several classification algorithms mainly designed to tackle the task of separating signal from background in complex high energy physics data However it can be used in any environment where classification of data is needed TMVA already comes bundled with ROOT Several of the algorithms in TMVA also provide the ranking of the predictive variables in terms of their discriminating power These algorithms are Likelihood H Matrix and Casualty Actuarial Society E Forum Winter 2008 19 ROOT A Data Analysis and Data Mining Tool from CERN Fisher discriminants Neural Network Boosted Decision Trees and RuleFit The reader is referred to the TMVA user s guide 18 19 for more details of TMVA and the available classification algorithms For our simulated data we will use Fisher Discriminants as an example to find out the ranking of the discriminating power of the various variables First we need to determine the classification we ate interested in A natural classification of interest for us is based on loss ratio we would like to use as predictors the variables that
36. s to start a ROOT object browser TBrowser class 17 from the ROOT console root TBrowser b Figure 3 shows a screen shot of the ROOT console with this command ROOT session Oo x WELCOME to ROOT Version 5 17702 29 August 2007 You are welcome to visit our Web site http root cern ch KKKKKK KX KKKKKKK XK Compiled on 30 August 2007 for win32 with thread support CINT ROOT C C Interpreter version 5 16 24 July 26 2007 Type for help Commands must be C statements Enclose multiple statements between lt gt root TBrowser b Figure 3 A screen shot of the ROOT console with the command to start the ROOT browser This will start the ROOT object browser which looks like figure 4 Casualty Actuarial Society E Forum Winter 2008 6 ROOT A Data Analysis and Data Mining Tool from CERN ROOT Browser erma A of E ol Al Folders O Groot E Ciroot QIPROOF Sessions ROOT Files root PROOF Sessions esroot ROOT Files Figure 4 A screen shot of ROOT object browser Now one can use this object browser to open a ROOT file by using File gt Open menu In this case we will navigate to the ROOT file generated by the sample data load program of Appendix A Using the File menu open the root file called SampleData root Figure 5 shows a screen shot of the file selection dialog used to open the file if ROOT Browser ol af elas Lol al AI Folders O Eo Sessions L Ope
37. t consisting of 49 variables and 9 Million 9E6 observations This analysis took 16 3 CPU Minutes and 20 5 Real Minutes 10 2 Non parametric Fitting Neural Network In the previous section we fit the simulated data using a linear relationship between the target variable LossRatio and the five predictive variables This was appropriate since the simulated data indeed follows such a linear relationship In several real life situations we don t know beforehand what the true functional form of the relationship between the target variable and the predictive variables is In such situations non parametric fitting techniques might be more effective In this section we will use ROOT s neural network package 21 to fit the data already simulated The network used in this analysis consisted of five input nodes the five predictive variables used to simulate the data two hidden layers with 8 and 5 nodes respectively and a single output node LossRatio The network was trained on 2000 data points from the simulated data set over 300 epochs All the input and output nodes were normalized so that they take on values between 0 and 1 Figure 21 shows the structure of the network with the thickness of the connecting lines synapses being proportional to the corresponding weights Casualty Actuarial Society E Forum Winter 2008 22 ROOT A Data Analysis and Data Mining Tool from CERN Figure 21 The structure of the neur
38. tions MMMM Beginning of the Data Simulation Code MIMMMMMMINMIMIII This is a ROOT macro to generate simulated data for a simple model This model relates the loss ratio to five independent variables include TRandom2 h include TStopwatch h include TFile h include TNtuple h include lt string gt using namespace std How many events do we want to generate Int_t Nloop 10 000 Directory where we will be writing to or reading from string DirName C Documents and Settings temp Generate a random number from a Landau distribution Double_t GetRandomFromLandau Double_t mean Double_t sigma Double_t xmin Double_t xmax Double_t x 999 0 while x lt xmin x gt xmax x gRandom gt Landau mean sigma Peturi x Casualty Actuarial Society E Forum Winter 2008 29 ROOT A Data Analysis and Data Mining Tool from CERN Generate a random number from a Uniform distribution Double_t GetRandomFromUniform Double_t xmin Double_t xmax Double_t x 999 0 while x lt xmin x gt xmax x xmin gRandom gt Rndm xmax xmin return x Generate a random number based on any formula Double_t GetRandomFromFormula const char formula Double_t xmin Double_t xmax TF1 f1 new TF1 f1 formula xmin xmax Double_t xx 999 0 while xx lt xmin xx gt xmax xx f1 gt GetRandom
39. ve we know exactly what results to expect from a correctly done regression analysis of this simulated data The regression should give us back within statistical uncertainties the relationship defined in equation 1 above otherwise something is wrong with the analysis Casualty Actuarial Society E Forum Winter 2008 17 ROOT A Data Analysis and Data Mining Tool from CERN AgeOfBusiness Entries 5000000 BuildingCount Entries 5000000 5 Mean 21 73 Mean 1 564 RMS 3 123 Underflow o Overflow 58 RMS 18 82 Underflow 0 Overflow J 400 x 350 Integral 5e 006 10 Integral 5e 006 E Skewness 1 685 Skewness 16 09 300 E Kurtosis 2 855 40 Kurtosis 333 250 E H 10 200 E Hi 10 F 1505 E E 10 1005 so 10 E ara Fr OF FP OPP Pr a I TE i 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 AgeOfBusiness BuildingCount CreditScore Entries 5000000 PolicyAge Entries 5000000 10 Mean 50 02 T0 Mean 3 266 RMS 28 87 on RMS 2 439 100 Underflow J Underflow 0 K Overflow 0 220 Overflow 0 k Integral 5e 006 Integral 5e 006 F Skewness 0 001416 200 Skewness 0 6748 80 Kurtosis 1 202 4 oE Kurtosis __ 0 4466 E 160 60 140F L 120F Age 1005 E 80 gt L 60 Gde 4oE E 20 ne eee eee cee dissila Sere ere err rere re losrsi hirsi lissi lisilo lissi 0 10 20 30 40 50 60
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