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REDUCING RISKS THROUGH IMPROVEMENT OF PREDICTION MODELS
Zurab Gasitashvili1, Merab Pkhovelishvili2, Natela Archvadze3
1Georgian Technical University, Tbilisi, Georgia zur_gas@gtu.ge
2Muskhelishvili Institute of Computational Mathematics, Georgian Technical University,
merab5@list.ru
3Ivane Javakhishvili Tbilisi State University, Tbilisi, Georgia natela.archvadze@tsu.ge
Abstract
Management or avoidance of risks or mitigation of undesirable outcomes are linked to specific actions, as well as to prediction models. These prediction models should be improved to obtain "better" predictions and thus, manage risks, and take measures for their reduction. We consider such algorithm of event prediction, which, using parallel data, can obtain prediction with high reliability that, in its turn, helps to reduce risks or completely avoid them
Keywords: Risk management, Parallel data, Prediction models, model improvement algorithm.
I. Introduction
At this point, fundamental research studies on safety theory and risks are very important. They can be practically used for reducing risks in the fields of industry, energy, transport, construction, and agriculture [1].
There are many risks in our world. Some of them impact individuals, others pose danger for the entire society, and some specific risks impact only certain fields and activities. Because of damage caused by risks, protection from them and avoidance of negative outcomes are very important.
Risk management has great importance in the economy, as well as risk reduction. This mainly applies to those risks, which can be identified. These processes should be equipped with the appropriate models and procession of information needed for identification. As it is discussed in [2], systemic use of all existing information is one of the main parts of risk analysis, which allows to evaluate the risks of undesirable accidents and events.
For reduction of risks, we consider the algorithm for prediction improvement built by us, which helps to predict such events, as the risks associated with natural disasters. In particular, we single out prediction of earthquakes, landslides and mudflows.
II. Use of improved algorithm of earthquake prediction models for avoidance of undesirable risks
Let us review several models of earthquake prediction specifically for Georgia. The information was taken from the online map of earthquakes [3], where there are maps, lists, data and information on earthquakes, and a seismic map of the world. In Table 1, the list of earthquakes occurred on the territory of Georgia is given, which belong to the earthquakes with moderate
strength (magnitude 4-5). We took earthquake magnitude, occurrence date, time and name of epicenter as characteristics of each earthquake. The table contains earthquakes occurred in 20202021. UTC means the Coordinated Universal Time.
Table 1: Earthquakes occurred in Georgia in 2020-2021
N Magnitude Date Time Epicenter
1 4.7 16.08.2021 00:49 (UTC) Georgia, Kvemo Kartli region, Dmanisi municipality
2 4.1 15.08.2021 22:36 (UTC) Georgia, region of Samtskhe-
Javakheti, Ninotsminda municipality
3 4 14.07.2021 06:35 (UTC) Georgia, region of Samtskhe-
Javakheti, Ninotsminda municipality
4 4.1 17.04.2021 20:07 (UTC) Georgia, Colchis National Park
5 4.3 13.03.2021 10:00 (UTC) Georgia, region of Racha-Lechkhumi and Kvemo-Svaneti, Onsky municipality
6 4.3 21.04.2020 05:23 (UTC) Georgia ('velo Sak art)
Designate the set of actually occurred earthquakes with pr e a l. Designate the earthquake prediction models with: Mod1Mod2j ... etc. which provide some predictions through their predecessors (for example, for earthquakes - when it would occur, at which location and with which magnitude). We must choose only those models from these models, which satisfy the necessary condition, i.e. Intersection of the set of model predictions with the set of actual events should result in the set of actual events. We call this condition a necessary condition for choosing a prediction model [4]. This condition in case of earthquake means the following: If during the T time there were occurred, for example, six earthquakes (as in our example), only those models should be considered that predicted all these six earthquakes. Assume that such are the following models: . In our case it is not essential, what specifically is each model
and based on which predecessors of the earthquake it makes the prediction.
In Table 2, the numbers of predictions for each of these models, the numbers of successful and failed predictions are given. Let's calculate the probability of success for each model.
It is obvious in this Table, that the sum of successful and failed predictions is equal to the total number of predictions. As for the probability of success [5, 6], it is calculated for each model and determines, how many times earthquake prediction was made and how many times an actual earthquake occurred. Assume that we consider the necessary predecessors and the models created
A A A
for them: 1 2'"' n, where n is the number of considered predecessors. t is the time during which we make the analysis, and the number of actually occurred earthquakes is m. We calculated
the number of earthquakes predicted by each predecessor: Pl''"' ' For example, A the
p
model, which was based on i predecessor, predicted earthquake occurrence i -times.
Table2: The characteristics of "necessary models"
Model Number of Successful Failed Probability of
predictions Number of Number of success
predictions predictions in %
Modx 100 6 94 6.00
Mod2 95 6 89 6.32
Mod3 99 6 93 6.06
Mod4 98 6 92 6.12
Mods 99 6 93 6.06
For each pi let's calculate quotients of the number of actually occurred earthquakes m ,
write it in % and designate with K:
m
K = m 100% Pi
For example, if earthquake actually occurred 4 times, and we calculate the value
4 A
K = —100% = 20°% , then the probability of success for A will be 20%.
'20 !
The probability of success also can be considered the probability of prediction correctness
11
of specific model. Designate this last value with Lm and link the ratio L m = -,*100% to its value, where is a number of actually occurred events, and is a predicted number of event occurrence obtained in the given model.
Table 3: The characteristics of the "necessary models" for the pairs
Model Number of Successful Failed Probability of
predictions Number of Number of success
predictions predictions in %
M o dx n M o d2 17 6 11 35.29
M o dx n M o d3 20 6 14 30.00
M o dx n M o d4 15 6 9 40.00
M o dx n M o d5 13 6 7 46.15
Mo d2 n Mo d3 15 6 9 40.00
Mo d2 n Mo d4 10 6 4 60.00
Mo d2 n Mo d5 16 6 10 37.50
Mo d3 n Mo d4 17 6 11 35.29
Mo d3 H Mod5 8 6 2 75.00
Mo d4 n Mo ds 18 6 12 33.33
The theorem proved in [7]: From the given predictions, always can be chosen at least two such predictions, for which the probability of correctness of simultaneous occurrence is greater or equal than the probability of correctness of the best prediction model: min(Pij) < P^ , wftere = 1. . .n .
In this theorem, P^ designates the probability of correctness of simultaneous occurrence of two prediction models , and designates the set containing the least number of
predictions, which at the same time will be the best prediction model. , where .
According to this theorem, we should consider pairs of models. Let's compose Table 3 with the values corresponding to Table 2, for each possible pair of all five models, considered in the example, whose total number will be 10.
After analysis of Table 3 we see that the best result is obtained from the combination of two models and (although the separate probabilities of success for them are not best,
the combined probability of success is increased up to 75%, even though separately these models have significantly lower values of success: 6.06% and 6.06%. For the considered examples, it is possible that two pairs of the models show the same result. If this is the case, it should be decided by means of expert and material and technical resources needed for work of these models, which one should be used. The diagram corresponding to Table 3 see on Diagram 1:
The "necessary models" for pairs
80 70 60 50 40 30 20 10
1.1
l.ll 1.1
In
1.1
I..
1.1
1.1
II.
I.
Ml M2 M3 M4 M5 M6 M7 M8 M9 M10 ■ Number of predictions ■Successful ■ Failed ■ Probability of success
0
Diagram 1. The characteristics of the "necessary models" for pairs
Keys used in Diagram 1: M1=M od1 n Mod2; M2= Mod1 n Mod3; M3= M o d ! n M o d4; M4=M o d x n M o d 5; M5= Mod2 n Mod3; M6= Mod2 n Mod4; M7= Mod2 n Mod5; M8= Mod3 n Mod4; M9= Mod3 n Mod5; M10= Mod4 n Mod5. The next stages of the prediction algorithm based on parallel data [papers] is consideration of model triples. See Table 4.
Table 4: The characteristics of the "necessary models" for triples
Model Number of Successful Failed Probability of
predictions Number of Number of success
predictions predictions in %
Mod1 n Mo d2 n M o d3 10 6 4 60.00
Mod1 n Mod2 n Mod4 9 6 3 66.67
Mod1 n Mod2 n Mod5 11 6 5 54.55
Modi n Mod3 n Mod4 7 6 1 85.71
Mod1 n Mod3 n Mod5 9 6 3 66.67
Mod1 n Mod4 n Mod5 8 6 2 75.00
After analysis of Table 4 we see that the best result is obtained from the combination of three models M o d 1 , M o d 3 , and M o d 5. The combined probability of success for them is increased up to 85.71%.
90 80 70 60 50 40 30 20 10 0
ll.
M1
The "necessary models" for triples
ll. ll. Il_ ll. ll.
M2
M3
M4
M5
M6
Number of predictions Failed number of predictions
I Successful number of predictions I Probability of success
Diagram 2. The characteristics of the "necessary models" for model triples
We introduced the following keys for Diagram 2:
M1=M o dx n M o d2 n Mo d3; M2=Mo dx n Mo d2 n M o d4; M3=M o dx n M o d2 n Mo ds; M4=M o dx n M o d3 n Mo d4; M5=M o dx n M o d3 n Mo ds; M6= Mo dx n Mo d4 n M o ds ;
III. Conclusion
It is obvious that the more is the number of intersections of prediction models, from which we choose the best, the better would be the result, compared to the case of less number of intersections. But we should take into account that greater number of models need greater number of data (predecessors), which can be obtained by spending considerable amount of material resources. Collection and analysis of large amount of data is an unresolved issue for small, low income states. Exactly for these cases it is important to theoretically choose two or three models of prediction, for which intersection of predictions would give best results. While collection of information, in this case, would be needed only for these chosen models, thus sharply reducing the costs of information procession.
References
[1] Gasitashvili, Z., Phkhovelishvili, M., Archvadze, N., Jorjiashvili N. An Algorithm of Improved Prediction from Existing Risk Predictions. / Published by AIJR Publisher in "Abstracts of The Second Eurasian RISK-2020 Conference and Symposium" April 12- 19, 2020, Tbilisi, Georgia. DOI: 10.21467/abstracts.93 pp. 31. 2020.
[2] Aliyev, V., Magerramova, S., Balaeva, A., Azeryar, L. Risk Assessment and Analysis of Accidents of Water Facilities, AIJR Abstracts, pp. 9-10, 2020.
[3] Latest Earthquakes. https://earthquaketrack.ru
[4] Gasitashvili, Z., Phkhovelishvili, M., Archvadze, N. New Algorithms for Improvement of Prediction Models Using Data Parallelism. / 13th International Conference on Computer Science and Information Technologies CSIT 2021. Proceedings. Armenia, Yerevan, September 27 - October 1, 2021. Pp.17-20.
[5] Gasitashvili, Z., Phkhovelishvili, M., Archvadze, N. New algorithm for building effective model from prediction models using parallel data. / Pattern Recognition and Information Processing (PRIP'2021) : Proceedings of the 15th International Conference, 21 -24 Sept. 2021, Minsk, Belarus. - Minsk: UIIP NASB, 2021. - 246 p. - ISBN 978-985-7198-07-8. Pp. 25-28.
[6] Chogovadze, G., Surguladze, G., Topuria, N., Archvadze, N. Implementation of a prediction model with cloud services. // Bulletin of the Georgian National Academy of Sciences, 2020,14(3), pp. 29-35.
[7] Gasitashvili, Z., Phkhovelishvili, M., Archvadze, N. Prediction of events means of data parallelism. Proceedings - Mathematics and Computers in Science and Engineering, MACISE 2019this link is disabled, 2019, pp. 32-35, 8944725.
