Mastering Monte Carlo: How To Simulate Your Way to Better Machine Learning Models

In the tumultuous year of 1945, as the world was gripped by what would be the final throes of World War II, a game of solitaire quietly sparked an advancement in the realm of computation. This was no ordinary game, mind you, but one that would lead to the birth of the Monte Carlo method(<a href="https://library.lanl.gov/la-pubs/00326866.pdf" rel="noopener ugc nofollow" target="_blank">1</a>). The player? None other than scientist Stanislaw Ulam, who was also deeply engrossed in the Manhattan Project(<a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2924739/" rel="noopener ugc nofollow" target="_blank">2</a>). Ulam, while convalescing from an illness, found himself engrossed in solitaire. The complex probabilities of the game intrigued him, and he realized that simulating the game repeatedly could provide a good approximation of these probabilities(<a href="https://www.sciencedirect.com/topics/economics-econometrics-and-finance/monte-carlo-simulation" rel="noopener ugc nofollow" target="_blank">3</a>). It was a lightbulb moment, akin to Newton’s apple, but with playing cards instead of fruit. Ulam then discussed these ideas with his colleague John von Neumann, and together they formalized the Monte Carlo method, named after the famed Monte Carlo Casino in Monaco, (portrayed in Edvard Munch’s famous painting shown above), where the stakes are high and chance rules — much like the method itself. Fast forward to the present day, and the Monte Carlo method has become an ace up the sleeve in the world of machine learning, including applications in reinforcement learning, Bayesian filtering, and the optimization of intricate models(<a href="https://link.springer.com/referenceworkentry/10.1007%2F978-0-387-30164-8_525" rel="noopener ugc nofollow" target="_blank">4</a>). Its robustness and versatility have ensured its continued relevance, more than seven decades after its inception. From Ulam’s solitaire games to the sophisticated AI applications of today, the Monte Carlo method remains a testament to the power of simulation and approximation in tackling complex systems. <a href="https://towardsdatascience.com/mastering-monte-carlo-how-to-simulate-your-way-to-better-machine-learning-models-6b57ec4e5514">Read More</a>