Supervised learning problem statement

Let's denote:

• Training set $\huge \left{(x^{(i)},y^{(i)})\right}_{i=1}^{n}$ , where
  • $\huge x^{(i)}\in\mathbb{R}^{p},y^{(i)}\in\mathbb{R}$ for regression
  • $\huge {x}^{(i)}\in\mathbb{R}^{p},{y}^{(i)}\in{C_{1},\ldots,C_{K}}$ for classification
• Model $f(x)$ predicts some value for every object
• Loss function $L(x, y, f)$ that should be minimized