Professor Anita Layton’s class focused on leading us to understand the world from the perspective of modeling. The class included both mathematical modeling and machine learning modeling, which is extremely versatile today. The former requires specialized mathematical and physical knowledge to model how the world works, while the latter extracts knowledge autonomously by the ability of the algorithms themselves. In any case, both mathematical modeling and machine learning modeling can help us approach complex truths via some simple models, and thus provide a new perspective for understanding the world.
Professor Layton started with mathematical models, including the predator-prey model and the SIR model. The SIR model, for example, can be applied to predicting the spread of disease by dividing people into S (susceptible individuals), I (infected individuals), and R (recovered individuals). This continuous mathematical model is built upon very simple assumptions and can portray the interactions between different groups of people. After the reinforcement of the model assumptions, the SIR model has been able to predict the spread of COVID-19.
Then Professor Layton elaborated on some of the classical algorithms in machine learning, such as linear models, logistic regression models, the KNN model, the SVM model, and today’s highly popular neural network models. By briefly explaining the basic ideas behind these models and showing how to implement them when faced with real-world problems, Professor Layton gave us a quick introduction to these very useful tools for machine learning.
During Professor Layton’s five-day course, we not only learned the methods of mathematical modeling and the tools of machine learning modeling, but also broadened our mind and learned to understand and simplify the world from the perspective of modeling. In addition, we came to understand many applications of modeling in real life, such as drug screening, weather forecasting, etc., which also provided new directions and inspirations for our future study.
