nLab supervised learning




Supervised learning is a problem in machine learning in which one infers a correspondence between a distribution of examples and a distribution of labels. More formally, given 𝒟={(x i,y i)} 1in\mathcal{D} = \{(x_i, y_i)\}_{1 \leq i \leq n} where x i d,y i dx_i \in \mathbb{R}^d, y_i \in \mathbb{R}^{d'} such that random samples (x i,y i)(x_i, y_i) (i.i.d.) are realizations of (X,Y)D(X, Y) \sim D an unknown distribution, supervised learning aims to describe a function f^: d d\hat{f}:\mathbb{R}^d \to \mathbb{R}^{d'} such that when given another dataset 𝒟\mathcal{D}' sampled from the same distribution, f^\hat{f} satisfies the optimization objective:

f^=argmin f𝔼[(f,𝒟)]\hat{f} = \argmin_f \mathbb{E}[\mathcal{L}(f, \mathcal{D}')]

where :( d d)×𝒟 +\mathcal{L}: (\mathbb{R}^d \to \mathbb{R}^{d'}) \times \mathcal{D}' \to \mathbb{R}^+ is a loss function that captures some notion of a deviation of a certain estimate ff from the true correspondence between XX and YY.

Last revised on March 4, 2021 at 08:16:10. See the history of this page for a list of all contributions to it.