Supervised Learning
The goal of supervised learning is to predict target using
input / features, and a model is learned to do so. This can be sufficiently summarized as
\[target = f(features)\]
How to find $f$? Among all possible choices of $f$, choose the one that fits the data the best. That is, solve optimization
\[
\text{Minimize} \sum_{i=1}^{N} \text{loss}\big(y_i, f(x_i)\big) \ \text{over all possible } f
\]
For classification tasks, the target is categorical or takes discrete values (e.g. hot or cold). For regression tasks, the target takes any real value (e.g. temperature). The model type reflects our belief about the reality and different model leads to different algorithm. The philosophy of supervised learning is: future of the past equals future of the future
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