What Textbooks Don't Tell You About Curve Fitting

Head to https://squarespace.com/artem to save 10% off your first purchase of a website or domain using code ARTEMKIRSANOV Socials: X/Twitter: https://x.com/ArtemKRSV Patreon: https://patreon.com/artemkirsanov My name is Artem, I'm a graduate student at NYU Center for Neural Science and researcher at Flatiron Institute. In this video we dive deep into a probabilistic interpretation behind the core linear regression algorithm from the ground up. We talk about how the least squares objective naturally arises when we try to maximize the probability of observed data under the model, and how the square is a result of assuming Gaussian distribution of the noise in the samples. We also explore how incorporating prior beliefs about the distribution of model parameters leads to different kinds of regularization in objective functions. Outline: 00:00 Introduction 01:16 What is Regression 02:11 Fitting noise in a linear model 06:02 Deriving Least Squares 07:46 Sponsor: Squarespace 09:04 Incorporating Priors 12:06 L2 regularization as Gaussian Prior 14:30 L1 regularization as Laplace Prior 16:16 Putting all together