on Gaussian Distribution
The Fundamental Role of Gaussian Distribution in Machine Learning The Gaussian distribution, also known as the normal distribution, stands as a cornerstone in statistical modeling and machine learning. Its mathematical elegance and natural occurrence in real-world phenomena make it an indispensable tool for data scientists and researchers. Mathematical Foundation The univariate Gaussian distribution is characterized by its probability density function: $$ p(x|\mu,\sigma^2) = \frac{1}{\sqrt{2\pi\sigma^2}}\exp\left(-\frac{(x-\mu)^2}{2\sigma^2}\right) $$ ...