What Textbooks Don't Tell You About Curve Fitting

Explore a deep dive into the probabilistic interpretation of linear regression in this 18-minute video by Artem Kirsanov, a graduate student at NYU Center for Neural Science and researcher at Flatiron Institute. Learn how the least squares objective naturally emerges when maximizing the probability of observed data under a model, and understand that the squared term results from assuming Gaussian noise distribution in samples. Discover how incorporating prior beliefs about parameter distributions leads to different regularization techniques in objective functions. The video covers fundamental concepts including what regression is, fitting noise in linear models, deriving least squares, incorporating priors, L2 regularization as Gaussian prior, L1 regularization as Laplace prior, and concludes by synthesizing these concepts into a comprehensive understanding of curve fitting that goes beyond standard textbook explanations.