Statistical Independence and Correlation: Understanding Gauss Functions

This lecture delves into the concepts of statistical independence and correlation, emphasizing the difference between them. Through examples and joint probability calculations, the instructor explains how to determine if two variables are uncorrelated or statistically independent. The lecture also covers linear correlation and explores real and spurious correlations using intriguing examples like arcade revenue and worldwide space launches. Additionally, the lecture discusses marginal and conditional probability density functions of Gauss functions, likelihood estimation, and the application of Gaussian Mixture Models for clustering. The importance of likelihood functions in fitting data distributions is highlighted, along with the challenges posed by non-convexity. The session concludes with a comparison of different solutions using AIC and BIC metrics in Gaussian Mixture Models.