User:Econterms/AU-legal

Cauchy-Schwartz inequality

 * $$\left(\sum_{i=1}^n u_i v_i\right)^2\leq \left(\sum_{i=1}^n u_i^2\right) \left(\sum_{i=1}^n v_i^2\right)$$

Lasso regression equations
Data: y is a vector of dependent variable (industry output), X is set of predictors. Lasso for least-squares linear regression. Add constraint on the magnitude of the $$\beta$$s:


 * $$ \hat{\beta}_{lasso} = \underset{\beta \in \mathbb{R}^p}{\operatorname{arg\,min}} \left\{ \frac{1}{N} (y - X \beta )^2 \right\} \text{ subject to } \sum_{j=1}^p |\beta_j| \leq L $$

See history of this page for efforts on this project with Douglas Scott
 * Fair use / copyrights for education