d1s4: complete chapter pimp

[Goschjann]

• Overview slide: ML: andersrum an lineares Modell rangehen
• simpleste Kiste, SGD als Optimierer,
• Start mit Fehlerminimierung
• Gif für den loop via gradientdescent
• Auflösung: MachLearn-Modell via GD = Limo via Maximum-likelihood
• Lineares Modell: basis-Funktionen = feature Engineering in Machine Learning

[christophM]

you don't have to do it like described, but here is a possible structuring. you can also add more slides if helpful or change stuff:

slide 1: the linear model

• start with the linear equation of a linear model, but without error term and the assumption for its distribution. remove
• the basis functions that are currently on slide 1?
• optional: mention the assumptions or differences in statistics approach ($\epsilon$, y|x ~ N(\mu,\sigma2), )

slide 2: how to linear model with machine learning

• we want to find the optimal weights/coefs using ml approach
• (see also slides-d1s1-intro.pdf, slide 23: learning = repr + eval + optim)
• representation: linear equation
• evaluation: l2 loss (but could also be something different, like R-squared)
• optimization: l2 loss and gradient descent

slide 3:

• empirical risk (currently slide 2)
• differentiation and solving for $\theta$
• optimal $\theta$

slide 4:

• Equivalence to statistical max. likelihood estimator

slide 5: as is slide 6: as is