Window Based Regression

• TIme Series
• input window : $u(t-d+1),u(t-d+2),\dots .,u(t-1),u(t)$
• Require regression function $f:({\mathbb{R}}^k{)}^d\to {\mathbb{R}}^m$
  • $k\times d$ dim matrix
  • Flatten into $d\cdot k$ vector and apply Quadratic Loss

Non Linearity

• Add fixed nonlinear transforms to input arguments : eg polynomials
• Volterra expansion