Lecture 14: Review Models and Loss

• Response var you want to estimate

• Model, summarizes with parameter w

• w is an estimator

Loss

• $$L(w)=\frac{1}{n}$$ # sum n i
• sum of each $$y_i$$

• We compare the red value vs the purple value. The green value is the best w, it minimizes loss.

Minimizing Loss

• L(w*) ?

• What is your 1. data, 2. model, 3. parameters, 4. loss, (also optimization method)

• From 1-d (best avg) to 2-d, best func

• $$w*$$ is w that minimizes L(w). The best estimator is $$\hat{y}(w^*)$$

• Can generalize our optimization to 3d! (3 weight params)
• Can't plot our loss in 3d (cause it's 4d with 3 dim and loss dim)

• One option is calculus set deriv of loss to 0
• Can actually do brute force. do np.linspace and try all values. O(N^2)?