Development of the Non-Iterative Supervised Learning Predictor Based on the Ito Decomposition and SGTM Neural-Like Structure for Managing Medical Insurance Costs †
<p>Dataset visualization using Orange Software, version 3.13.0. The <span class="html-italic">x</span>-axis represents the <span class="html-italic">insurance contractor’s age</span>, and the <span class="html-italic">y</span>-axis is the size of the <span class="html-italic">medical insurance costs</span>. The circles mark <span class="html-italic">women</span>, and the crosses mark <span class="html-italic">men</span>. The blue circles mark the <span class="html-italic">woman-non-smoker</span>, and the red circles mark the <span class="html-italic">woman-smoker</span>. The blue crosses mark the <span class="html-italic">male-smoker</span>, the red crosses mark the <span class="html-italic">male non-smoker</span>. The size of the figures reflects the value of the <span class="html-italic">body mass index</span>. The larger index, the larger shape of the corresponding figure. Shapes and colors were chosen randomly.</p> "> Figure 2
<p>Topology of the common linear neural-like structure of the successive geometric transformations model (SGTM).</p> "> Figure 3
<p>Topology of the proposed model (combining the use of the Ito decomposition and SGTM linear neural-like structure).</p> "> Figure 4
<p>Optimal parameters identification for training and test modes: (<b>a</b>) mean absolute percentage error (MAPE) value according to changing the hidden layer’s neurons number, (<b>b</b>) MAPE value according to changing the training time.</p> "> Figure 5
<p>Topology of the proposed optimized model.</p> "> Figure 6
<p>Mean absolute error (MAE) in training and testing modes for developed and existing methods. On the <span class="html-italic">x</span>-axis, the mean absolute error value for all considered methods is illustrated.</p> "> Figure 7
<p>The training time for all methods.</p> "> Figure 8
<p>Visualization of the methods’ results. On the <span class="html-italic">x</span>-axis, the real values of insurance medical costs are given, and on the <span class="html-italic">y</span>-axis are values obtained by one of the methods: (<b>a</b>) support vector regression with RBF kernel, (<b>b</b>) linear regression, (<b>c</b>) adaptive boosting, (<b>d</b>) multilayer perceptron, (<b>e</b>) linear common SGTM neural-like structure, or (<b>f</b>) proposed method.</p> "> Figure 8 Cont.
<p>Visualization of the methods’ results. On the <span class="html-italic">x</span>-axis, the real values of insurance medical costs are given, and on the <span class="html-italic">y</span>-axis are values obtained by one of the methods: (<b>a</b>) support vector regression with RBF kernel, (<b>b</b>) linear regression, (<b>c</b>) adaptive boosting, (<b>d</b>) multilayer perceptron, (<b>e</b>) linear common SGTM neural-like structure, or (<b>f</b>) proposed method.</p> ">
Abstract
:1. Introduction
2. Data Description
2.1. Data Analysis
- Insurance contractor age (Age). The minimal age of the insurance contractor is 18 years, maximum is 64 years, and the average age of the entire sample is 39.2 years. Insurance contractor age included 574 young insurance contractors (18–35), 548 senior insurance contractors (35–55), and 216 elder insurance contractors (>55).
- Body mass index (BMI). This is the ratio of the person’s height to their weight (kg/m2). Minimal BMI is 15.96, the maximum is 53.12, and the average is 30.66. It is higher than normal.
- The number of dependents (Children). This is the number of children covered by medical insurance. This indicator ranges from 1 to 5, and the average is 1095.
- Smoking (Smoker). The dataset contains 1064 smokers and 274 non-smokers.
- Beneficiary’s residential area in the United States (Area). This column displays four regions of the United States, where the number of observations for each of them is northeast: 324, northwest: 325, southeast: 364, and southwest: 325.
2.2. Data Preparation
3. Predictor Based on the Ito Decomposition and Neural-Like Structure of the Successive Geometric Transformations Model (SGTM)
3.1. Linear Neural-Like Structure of the Successive Geometric Transformations Model
3.2. The Ito Decomposition
3.3. The Composition of the Non-Iterative Supervised Learning Predictor Using Ito Decomposition
4. Modelling and Results
- Mean absolute percentage error (MAPE);
- Sum square error (SSE);
- Symmetric mean absolute percentage error (SMAPE);
- Root mean square error (RMSE);
- Mean absolute error (MAE).
- to increase the generalization properties of the method (the difference between the MAPE indicators in the training and testing modes is 2.40% and 1.12%, respectively, for the developed and optimized methods);
- to increase the accuracy of the optimized method by 1.34%.
5. Comparison and Discussion
6. Conclusions
- ―
- the quick, non-iterative training procedure;
- ―
- the increase of generalization properties;
- ―
- the significant increase in the prediction accuracy.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A
Observation/Indicator | Training Errors | Test Errors | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Hidden Layer’s Neurons Number | Training Time | MAPE | SSE | SMAPE | RMSE | MAE | MAPE | SSE | SMAPE | RMSE | MAE |
5 | 0.0328 | 98.0907 | 250,153.1643 | 0.2277 | 7647.4054 | 6017.2457 | 90.4530 | 122,496.0430 | 0.2134 | 7482.6368 | 5799.5606 |
10 | 0.0640 | 29.6955 | 199,827.0208 | 0.1463 | 6108.8903 | 3866.1687 | 30.6628 | 100,543.3525 | 0.1511 | 6141.6628 | 4033.6993 |
15 | 0.0774 | 36.0616 | 192,268.2087 | 0.1466 | 5877.8106 | 3873.7426 | 36.6546 | 96,848.9924 | 0.1486 | 5915.9938 | 3947.6894 |
20 | 0.0940 | 36.1080 | 191,597.2658 | 0.1466 | 5857.2993 | 3875.0551 | 36.3794 | 95,882.4545 | 0.1484 | 5856.9531 | 3937.6843 |
25 | 0.1231 | 37.2211 | 188,909.5383 | 0.1454 | 5775.1331 | 3842.2482 | 38.8044 | 95,367.0315 | 0.1483 | 5825.4686 | 3948.9449 |
30 | 0.1342 | 27.6548 | 156,156.1666 | 0.1085 | 4773.8333 | 2867.1614 | 29.0845 | 83,439.0789 | 0.1190 | 5096.8530 | 3185.9151 |
35 | 0.1476 | 27.0794 | 153,613.4998 | 0.1053 | 4696.1017 | 2783.1433 | 28.2033 | 82,337.1565 | 0.1149 | 5029.5423 | 3077.6321 |
40 | 0.1780 | 27.6964 | 152,671.6923 | 0.1053 | 4667.3098 | 2783.8583 | 30.0943 | 82,309.9318 | 0.1158 | 5027.8793 | 3103.5243 |
45 | 0.2000 | 27.8937 | 152,665.2744 | 0.1054 | 4667.1136 | 2786.0303 | 30.3035 | 82,387.0573 | 0.1161 | 5032.5905 | 3111.7831 |
50 | 0.2079 | 28.5096 | 152,568.5949 | 0.1054 | 4664.1580 | 2785.5579 | 30.6519 | 82,189.3916 | 0.1159 | 5020.5162 | 3107.0487 |
55 | 0.2719 | 28.5293 | 152,511.9680 | 0.1053 | 4662.4269 | 2783.5739 | 30.9454 | 82,394.3576 | 0.1162 | 5033.0364 | 3112.8836 |
60 | 0.2870 | 28.6878 | 152,374.2804 | 0.1053 | 4658.2177 | 2784.8075 | 30.6126 | 82,389.5643 | 0.1155 | 5032.7436 | 3092.6906 |
65 | 0.3159 | 28.6454 | 152,239.3691 | 0.1051 | 4654.0933 | 2779.0867 | 30.7230 | 82,638.1576 | 0.1158 | 5047.9289 | 3098.5853 |
70 | 0.3534 | 28.5060 | 151,938.2782 | 0.1049 | 4644.8887 | 2774.0156 | 30.9568 | 82,804.6760 | 0.1161 | 5058.1006 | 3105.5370 |
75 | 0.3537 | 28.3622 | 151,865.9138 | 0.1048 | 4642.6765 | 2769.1590 | 30.9699 | 82,795.9130 | 0.1160 | 5057.5653 | 3103.7871 |
77 | 0.3632 | 28.4187 | 151,771.1717 | 0.1047 | 4639.7801 | 2767.6075 | 30.8230 | 82,676.2620 | 0.1158 | 5050.2565 | 3099.7172 |
References
- Melnykova, N.; Shakhovska, N.; Sviridova, T. The personalized approach in a medical decentralized diagnostic and treatment. In Proceedings of the 14th International Conference: The Experience of Designing and Application of CAD Systems in Microelectronics (CADSM), Lviv, Ukraine, 21–25 February 2017; Lviv Publishing House: Lviv, Ukraine, 2017; pp. 295–297. [Google Scholar]
- Babichev, S.; Kornelyuk, A.; Lytvynenko, V.; Osypenko, V. Computational analysis of microarray gene expression profiles of lung cancer. Biopolym. Cell 2016, 32, 70–79. [Google Scholar] [CrossRef]
- Medical Cost Personal Datasets. Insurance Forecast by Using Linear Regression. Available online: https://www.kaggle.com/mirichoi0218/insurance/kernels (accessed on 20 September 2018).
- Bodyanskiy, Y.; Vynokurova, O.; Pliss, I.; Setlak, G.; Mulesa, P. Fast learning algorithm for deep evolving GMDH-SVM neural network in data stream mining tasks. In Proceedings of the 2016 IEEE First International Conference on Data Stream Mining & Processing (DSMP), Lviv, Ukraine, 21–25 August 2016; Lviv Publishing House: Lviv, Ukraine, 2016; pp. 257–262. [Google Scholar] [CrossRef]
- Veres, O.; Shakhovska, N. Elements of the formal model big date. In Proceedings of the XI International Conference on Perspective Technologies and Methods in MEMS Design (MEMSTECH), Lviv, Ukraine, 2–6 September 2015; Lviv Publishing House: Lviv, Ukraine, 2015; pp. 81–83. [Google Scholar] [CrossRef]
- Vitynskyi, P.; Tkachenko, R.; Izonin, I.; Kutucu, H. Hybridization of the SGTM Neural-like Structure through Inputs Polynomial Extension. In Proceedings of the 2018 IEEE Second International Conference on Data Stream Mining & Processing (DSMP), Lviv, Ukraine, 21–25 August 2018; Lviv Polytechnic Publishing House: Lviv, Ukraine, 2018; pp. 386–391. [Google Scholar]
- Setlak, G.; Bodyanskiy, Y.; Vynokurova, O.; Pliss, I. Deep evolving GMDH-SVM-neural network and its learning for Data Mining tasks. In Proceedings of the 2016 Federated Conference on Computer Science and Information Systems (FedCSIS), Gdansk, Poland, 11–14 September 2016; pp. 141–145. [Google Scholar]
- Hu, Z.; Bodyanskiy, Y.V.; Tyshchenko, O.K. A Cascade Deep Neuro-Fuzzy System for High-Dimensional Online Possibilistic Fuzzy Clustering. In Proceedings of the XI-th International Scientific and Technical Conference “Computer Science and Information Technologies” (CSIT 2016), Lviv, Ukraine, 6–10 September 2016; Lviv Polytechnic Publishing House: Lviv, Ukraine, 2016; pp. 119–122. [Google Scholar]
- Ganovska, B.; Molitoris, M.; Hosovsky, A.; Pitel, J.; Krolczyk, J.B. Design of the model for the on-line control of the AWJ technology based on neural networks. Indian J. Eng. Mater. Sci. 2016, 23, 279–287. [Google Scholar]
- Gajewski, J.; Valis, D. The determination of combustion engine condition and reliability using oil analysis by MLP and RBF neural networks. Tribol. Int. 2017, 115, 557–572. [Google Scholar] [CrossRef]
- Hu, Z.; Jotsov, V.; Jun, S.; Kochan, O.; Mykyichuk, M.; Kochan, R.; Sasiuk, T. Data science applications to improve accuracy of thermocouples. In Proceedings of the 2016 IEEE 8th International Conference on Intelligent Systems (IS), Sofia, Bulgaria, 4–6 September 2016; pp. 180–188. [Google Scholar] [CrossRef]
- Koprowski, R.; Lanza, M.; Irregolare, C. Corneal power evaluation after myopic corneal refractive surgery using artificial neural networks. BioMed. Eng. Online 2016, 15. [Google Scholar] [CrossRef] [PubMed]
- Glowacz, A. Acoustic based fault diagnosis of three-phase induction motor. Appl. Acoust. 2018, 137, 82–89. [Google Scholar] [CrossRef]
- Deng, L.; Yu, D. Deep Learning: Methods and Applications. Found. Trends Signal Process. 2014, 7, 1–199. [Google Scholar] [CrossRef]
- Bellazzia, R.; Zupan, B. Predictive data mining in clinical medicine: Current issues and guidelines. Int. J. Med. Inform. 2008, 77, 81–97. [Google Scholar] [CrossRef] [PubMed]
- Caruana, R. An empirical comparison of supervised learning algorithms. In Proceedings of the 23rd International Conference on Machine Learning, Pittsburgh, PA, USA, 25–29 June 2006; pp. 161–168. [Google Scholar]
- Medical Cost Personal Datasets. Available online: https://www.kaggle.com/mirichoi0218/insurance (accessed on 9 September 2018).
- Demsar, J.; Curk, T.; Erjavec, A.; Gorup, C.; Hocevar, T.; Milutinovic, M.; Mozina, M.; Polajnar, M.; Toplak, M.; Staric, A.; et al. Orange: Data Mining Toolbox in Python. J. Mach. Learn. Res. 2013, 14, 2349–2353. [Google Scholar]
- Tkachenko, R.; Izonin, I. Model and Principles for the Implementation of Neural-Like Structures based on Geometric Data Transformations. In Advances in Computer Science for Engineering and Education; Advances in Intelligent Systems and Computing; Hu, Z.B., Petoukhov, S., Eds.; Springer: Cham, Swizland, 2018; Volume 754, pp. 578–587. [Google Scholar] [CrossRef]
- Tkachenko, R.; Tkachenko, P.; Izonin, I.; Tsymbal, Y. Learning-Based Image Scaling Using Neural-Like Structure of Geometric Transformation Paradigm. In Advances in Soft Computing and Machine Learning in Image Processing; Hassanien, A., Oliva, D., Eds.; Studies in Computational Intelligence; Springer: Cham, Swizland, 2018; Volume 730, pp. 537–567. [Google Scholar] [CrossRef]
- Weierstrass, K. Uber Die Analytische Darstellbarkeit Sogenannter Willkurlicher Funktionen einer Reellen Veranderlichen; Sitzungsberichte der Akademie der Wissenschaften: Berlin, Germany, 1885; pp. 633–639. [Google Scholar]
- Iba, H.; Sato, T. Meta-level Strategy for Genetic Algorithms Based on Structured Representations. In Proceedings of the Second Pacific Rim International Conference on Artificial Intelligence, Seoul, Korea, 15–18 September 1992; pp. 548–554. [Google Scholar]
- Iba, H.; Sato, T.; Garis, H. System Identification Approach to Genetic Programming. In Proceedings of the First IEEE Conference on Evolutionary Computation, Orlando, FL, USA, 27–29 June 1994; Volume I, pp. 401–406. [Google Scholar]
- Ivakhnenko, A.G. Polynomial Theory of Complex Systems. IEEE Trans. Syst. Man Cybern. 1971, 1, 364–378. [Google Scholar] [CrossRef]
- Kargupta, H.; Smith, R.E. System Identification with Evolving Polynomial Networks. In Proceedings of the Fourth International Conference on Genetic Algorithms, San Mateo, CA, USA, 14–17 September 1991; pp. 370–376. [Google Scholar]
- Nikolaev, N.I.; Iba, H. Accelerated Genetic Programming of Polynomials. Genet. Program. Evol. Mach. 2001, 2, 231–257. [Google Scholar] [CrossRef]
- Haykin, S. Neural Networks and Learning Machines, 3rd ed.; Pearson Education, Inc.: London, UK, 2009; p. 904. [Google Scholar]
- Ng, A. Machine Learning. Lecture 7.1 Regularization. The Problem of Overfitting. Available online: https://www.youtube.com/watch?v=u73PU6Qwl1I (accessed on 9 September 2018).
- Korobchynskyi, M.V.; Chyrun, L.B.; Vysotska, V.A.; Nych, M.O. Matches prognostication features and perspectives in cybersport. Radio Electron. Comput. Sci. Control 2017, 95–105. [Google Scholar] [CrossRef]
- Botchkarev, A. Performance Metrics (Error Measures) in Machine Learning Regression, Forecasting and Prognostics: Properties and Typology. 2018. Available online: https://arxiv.org/abs/1809.03006 (accessed on 9 September 2018).
- Chen, C.; Twycross, J.; Garibaldi, J.M. A new accuracy measure based on bounded relative error for time series forecasting. PLoS ONE 2017, 12, 54–67. [Google Scholar] [CrossRef] [PubMed]
- Molnár, E.; Molnár, R.; Kryvinska, N.; Greguš, M. Web Intelligence in practice. J. Serv. Sci. Res. 2017, 6, 149–172. [Google Scholar] [CrossRef]
- Kryvinska, N. Building Consistent Formal Specification for the Service Enterprise Agility Foundation. J. Serv. Sci. Res. 2012, 4, 235–269. [Google Scholar] [CrossRef]
# | Insurance Contractor Age | Insurance Contractor Gender | Body Mass Index, kg/m2 | Number of Dependents | Smoking | Beneficiary’s Residential Area in the United States | Individual Insurance Costs |
---|---|---|---|---|---|---|---|
1 | 19 | female | 27.9 | 0 | yes | southwest | 16,884.924 |
2 | 18 | male | 33.77 | 1 | no | southeast | 1725.5523 |
3 | 28 | male | 33 | 3 | no | southeast | 4449.462 |
4 | 33 | male | 22.705 | 0 | no | northwest | 21,984.4706 |
5 | 32 | male | 28.88 | 0 | no | northwest | 3866.8552 |
6 | 31 | female | 25.74 | 0 | no | northeast | 3756.6216 |
… | … | … | … | … | … | … | … |
i | 60 | female | 27.9 | 0 | yes | southwest | 16,884.924 |
… | … | … | … | … | … | … | … |
n | 61 | female | 29.07 | 0 | yes | northwest | 29,141.3603 |
# | Age | F | M | BMI, kg/m2 | Children | Smoker | Non-Smoker | Area 1 | Area 2 | Area 3 | Area 4 | IIC |
---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 19 | 1 | 0 | 27.9 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 16,884.924 |
2 | 18 | 0 | 1 | 33.77 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1725.5523 |
3 | 28 | 0 | 1 | 33 | 3 | 0 | 1 | 0 | 1 | 0 | 0 | 4449.462 |
4 | 33 | 0 | 1 | 22.705 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 21,984.471 |
5 | 32 | 0 | 1 | 28.88 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 3866.8552 |
6 | 31 | 1 | 0 | 25.74 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 3756.6216 |
… | … | … | … | … | … | … | … | … | … | … | … | … |
i | 60 | 1 | 0 | 27.9 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 16,884.924 |
… | … | … | … | … | … | … | … | … | … | … | … | … |
n | 61 | 0 | 0 | 29.07 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 29,141.360 |
Method/Indicator | MAPE | SSE | SMAPE | RMSE | MAE |
---|---|---|---|---|---|
Training errors | |||||
Proposed model (SGTM + Ito decomposition) | 28.4187 | 151,771 | 0.1047 | 4639.78 | 2767.61 |
Proposed model with optimal parameters | 27.0794 | 153,613 | 0.10531 | 4696.1 | 2783.14 |
Test errors | |||||
Proposed model (SGTM + Ito decomposition) | 30,823 | 82,676 | 0.1158 | 5050.3 | 3099.7 |
Proposed model with optimal parameters | 28,203 | 82,337 | 0.1149 | 5029.5 | 3077.6 |
© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Tkachenko, R.; Izonin, I.; Vitynskyi, P.; Lotoshynska, N.; Pavlyuk, O. Development of the Non-Iterative Supervised Learning Predictor Based on the Ito Decomposition and SGTM Neural-Like Structure for Managing Medical Insurance Costs. Data 2018, 3, 46. https://doi.org/10.3390/data3040046
Tkachenko R, Izonin I, Vitynskyi P, Lotoshynska N, Pavlyuk O. Development of the Non-Iterative Supervised Learning Predictor Based on the Ito Decomposition and SGTM Neural-Like Structure for Managing Medical Insurance Costs. Data. 2018; 3(4):46. https://doi.org/10.3390/data3040046
Chicago/Turabian StyleTkachenko, Roman, Ivan Izonin, Pavlo Vitynskyi, Nataliia Lotoshynska, and Olena Pavlyuk. 2018. "Development of the Non-Iterative Supervised Learning Predictor Based on the Ito Decomposition and SGTM Neural-Like Structure for Managing Medical Insurance Costs" Data 3, no. 4: 46. https://doi.org/10.3390/data3040046