How ChatGPT Helped Code a Copula Model Without Human Input

Table of Links

Abstract and 1 Introduction

2 Methodology

2.1 The task

2.2 The communication protocol

2.3 The copula family

3 Pair programming with ChatGPT

3.1 Warm up

3.2 The density

3.3 The estimation

3.4 The sampling

3.5 The visualization

3.6 The parallelization

4 Summary and discussion

5 Conclusion and Acknowledgments

Appendix A: The solution in Python

Appendix B: The solution in R

References

5 Conclusion

In a human-AI collaboration, we developed working code that implements sampling from a copula model, estimation of its parameter, visualization suggesting that the last two tasks worked properly, and a parallelization of the code for CPUs as well as for GPUs. To illustrate the coding abilities of the AI part, represented by ChatGPT, all the mentioned tasks were implemented without a single line of code written by the human. In addition to presenting how to achieve a successful solution for a given task, we also showed additional examples demonstrating which modifications of our prompts for ChatGPT turned failed solutions to successful ones. This resulted in a comprehensive list of related pros and cons, suggesting that if typical pitfalls can be avoided, we can substantially benefit from a collaboration with an AI partner like ChatGPT.

Acknowledgments

The author thanks the Czech Science Foundation (GACR) for financial sup- ˇ port for this work through grant 21-03085S. The author also thanks to Martin Holeˇna and Marius Hofert for constructive comments and recommendations that definitely helped to improve the readability and quality of the paper.

Appendix A The solution in Python

An example of a redundant code is n = data.shape[0]. As can be observed, the variable n has no use in ClaytonCopulaMLE.

Appendix B The solution in R

Interestingly, even if this code is a direct transpilation of the code from Appendix A, the redundant code from the Python version of ClaytonCopulaMLE is not present. This hints on the ability of ChatGPT to keep only the code that is relevant.

References

Bang, Y., Cahyawijaya, S., Lee, N., Dai, W., Su, D., Wilie, B., Lovenia, H., Ji, Z., Yu, T., Chung, W., et al. (2023). A multitask, multilingual, multimodal evaluation of chatgpt on reasoning, hallucination, and interactivity. arXiv preprint arXiv:2302.04023.

Boulin, A. (2022). Sample from copula: a coppy module. arXiv preprint arXiv:2203.17177.

Brown, T., Mann, B., Ryder, N., Subbiah, M., Kaplan, J. D., Dhariwal, P., Neelakantan, A., Shyam, P., Sastry, G., Askell, A., et al. (2020). Language models are few-shot learners. Advances in neural information processing systems, 33:1877–1901.

Chen, M., Tworek, J., Jun, H., Yuan, Q., Pinto, H. P. d. O., Kaplan, J., Edwards, H., Burda, Y., Joseph, N., Brockman, G., et al. (2021). Evaluating large language models trained on code. arXiv preprint arXiv:2107.03374.

Chowdhery, A., Narang, S., Devlin, J., Bosma, M., Mishra, G., Roberts, A., Barham, P., Chung, H. W., Sutton, C., Gehrmann, S., et al. (2022). Palm: Scaling language modeling with pathways. arXiv preprint arXiv:2204.02311.

Christiano, P. F., Leike, J., Brown, T., Martic, M., Legg, S., and Amodei, D. (2017). Deep reinforcement learning from human preferences. Advances in neural information processing systems, 30.

Clayton, D. G. (1978). A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika, 65:141–151.

Devlin, J., Chang, M.-W., Lee, K., and Toutanova, K. (2018). BERT: Pretraining of deep bidirectional transformers for language understanding. arXiv preprint arXiv:1810.04805.

Frieder, S., Pinchetti, L., Griffiths, R.-R., Salvatori, T., Lukasiewicz, T., Petersen, P. C., Chevalier, A., and Berner, J. (2023). Mathematical capabilities of chatgpt. arXiv preprint arXiv:2301.13867.

Hobæk Haff, I. (2013). Parameter estimation for pair-copula constructions.

Hofert, M. (2010). Sampling nested Archimedean copulas with applications to CDO pricing.

Hofert, M., Huser, R., and Prasad, A. (2018). Hierarchical Archimax copulas. Journal of Multivariate Analysis, 167:195–211.

Hofert, M., M¨achler, M., and McNeil, A. J. (2013). Archimedean copulas in high dimensions: Estimators and numerical challenges motivated by financial applications. Journal de la Soci´et´e Fran¸caise de Statistique, 154(1):25–63.

Huang, Y., Zhang, B., Pang, H., Wang, B., Lee, K. Y., Xie, J., and Jin, Y. (2022). Spatio-temporal wind speed prediction based on clayton copula function with deep learning fusion. Renewable Energy, 192:526–536.

Joe, H. (2014). Dependence Modeling with Copulas. CRC Press.

Katz, D. M., Bommarito, M. J., Gao, S., and Arredondo, P. (2023). GPT-4 passes the bar exam. Available at SSRN 4389233.

Lample, G. and Charton, F. (2019). Deep learning for symbolic mathematics. arXiv preprint arXiv:1912.01412.

Lewkowycz, A., Andreassen, A., Dohan, D., Dyer, E., Michalewski, H., Ramasesh, V., Slone, A., Anil, C., Schlag, I., Gutman-Solo, T., et al. (2022). Solving quantitative reasoning problems with language models. arXiv preprint arXiv:2206.14858.

Li, Y., Choi, D., Chung, J., Kushman, N., Schrittwieser, J., Leblond, R., Eccles, T., Keeling, J., Gimeno, F., Dal Lago, A., et al. (2022). Competition-level code generation with alphacode. Science, 378(6624):1092–1097.

Liu, Y., Ott, M., Goyal, N., Du, J., Joshi, M., Chen, D., Levy, O., Lewis, M., Zettlemoyer, L., and Stoyanov, V. (2019). RoBERTa: A robustly optimized bert pretraining approach. arXiv preprint arXiv:1907.11692.

Maddigan, P. and Susnjak, T. (2023). Chat2vis: Generating data visualisations via natural language using chatgpt, codex and gpt-3 large language models. arXiv preprint arXiv:2302.02094.

Marshall, A. W. and Olkin, I. (1988). Families of multivariate distributions. Journal of the American Statistical Association, 83(403):834–841.

McNeil, A., Frey, R., and Embrechts, P. (2015). Quantitative risk management: Concepts, techniques and tools. Princeton university press.

Michimae, H. and Emura, T. (2022). Likelihood inference for copula models based on left-truncated and competing risks data from field studies. Mathematics, 10(13):2163.

Nelsen, R. B. (2006). An Introduction to Copulas. Springer-Verlag, 2nd edition.

OpenAI (2023). GPT-4 technical report. arXiv preprint arXiv:2303.08774.

Ouyang, L., Wu, J., Jiang, X., Almeida, D., Wainwright, C. L., Mishkin, P., Zhang, C., Agarwal, S., Slama, K., Ray, A., et al. (2022). Training language models to follow instructions with human feedback. arXiv preprint arXiv:2203.02155.

Peng, S., Yuan, K., Gao, L., and Tang, Z. (2021). Mathbert: A pretrained model for mathematical formula understanding. arXiv preprint arXiv:2105.00377.

Schellhase, C. and Spanhel, F. (2018). Estimating non-simplified vine copulas using penalized splines. Statistics and Computing, 28:387–409.

Sklar, A. (1959). Fonctions de r´epartition a n dimensions et leurs marges. Publications de l’Institut Statistique de l’Universit´e de Paris, 8:229–231.

Stiennon, N., Ouyang, L., Wu, J., Ziegler, D., Lowe, R., Voss, C., Radford, A., Amodei, D., and Christiano, P. F. (2020). Learning to summarize with human feedback. Advances in Neural Information Processing Systems, 33:3008–3021.

Williams, L. (2001). Integrating pair programming into a software development process. In Proceedings 14th Conference on Software Engineering Education and Training. ’In search of a software engineering profession’ (Cat. No. PR01059), pages 27–36. IEEE.