Data Science #17 - The Monte Carlo Algorithm (1949)
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- Опубликовано: 25 ноя 2024
- We review the original Monte Carlo paper from 1949 by
Metropolis, Nicholas, and Stanislaw Ulam. "The monte carlo method." Journal of the American statistical association 44.247 (1949): 335-341.
The Monte Carlo method uses random sampling to approximate solutions for problems that are too complex for analytical methods, such as integration, optimization, and simulation. Its power lies in leveraging randomness to solve high-dimensional and nonlinear problems, making it a fundamental tool in computational science.
In modern data science and AI, Monte Carlo drives key techniques like Bayesian inference (via MCMC) for probabilistic modeling, reinforcement learning for policy evaluation, and uncertainty quantification in predictions. It is essential for handling intractable computations in machine learning and AI systems.
By combining scalability and flexibility, Monte Carlo methods enable breakthroughs in areas like natural language processing, computer vision, and autonomous systems. Its ability to approximate solutions underpins advancements in probabilistic reasoning, decision-making, and optimization in the era of AI and big data.
S. stands, for Stanisław - Ulam was a polish Jew and one of the greatest mathematicians in 20th century. He moved to America just before the war. Before that, he was part of group of great mathematicians from Lwów University (like Stefan Banach). Most of them didn't survive the war. He had very eventful life and worked with all greatest minds of that time. He wrote a book "adventures of a mathematician" where he shares many stories (also about origins of this method). I think there is a movie based on that book, but its not Nolans work and Ive heard its pretty bad - but I recommend the book.
Thank you!
Monte Carlo is not a casino but an administrative part of Monaco.
Isnt it both? from wiki:
"The Monte Carlo Casino, officially named Casino de Monte-Carlo, is a gambling and entertainment complex located in Monaco. It includes a casino..."
@b3k0n then you call it Monte Carlo *casino* and not Monte Carlo. Believe me I lived close for 25 years 😉
My teacher told about this method in 1984. I remembered the name but forgot the details. I haven't watched the video yet so I still don't know the details.
Cool, the authors also barely specify them in the paper, but we are talking about it at the beginning.
@@Datasciencedecodedhistory I did a under graduate study chemical engineering then and I think he used it in the context of simulating the behavior of chemical reactions. But I could be a distorted memory because it is forty years ago. I know that it was some kind of sampling method, as you also describe in your video (which I have watched by now).