Table 1.

Abstract representation of the dataset of interest (without asterisk, black) and an additional dataset (with asterisk, grey).^a

$$\begin{array}{ccc}\text{Single-target} \text{learning}& \text{Multi-target} \text{learning}& \text{Transfer} \text{learning}\\ \begin{array}{ccc}\left(\begin{array}{c}{y}_1\\ ⋮\\ y_n\\ y_1^{*}\\ ⋮\\ y_m^{*}\end{array}\right)& \Leftarrow & \left(\begin{array}{ccc}{x}_{11}& \cdots & x_{1p}\\ ⋮& & ⋮\\ x_{n1}& \cdots & x_{np}\\ x_{11}^{*}& \cdots & x_{1p}^{*}\\ ⋮& & ⋮\\ x_{m1}^{*}& \cdots & x_{mp}^{*}\end{array}\right)\end{array}& \begin{array}{ccc}\left(\begin{array}{cc}{y}_1& y_1^{*}\\ ⋮& ⋮\\ y_n& y_n^{*}\end{array}\right)& \Leftarrow & \left(\begin{array}{ccc}{x}_{11}& \cdots & x_{1p}\\ ⋮& & ⋮\\ x_{n1}& \cdots & x_{np}\end{array}\right)\end{array}& \begin{array}{ccc}\left(\begin{array}{c}{y}_1\\ ⋮\\ y_n\end{array}\right)& \Leftarrow & \left(\begin{array}{ccc}{x}_{11}& \cdots & x_{1p}\\ ⋮& & ⋮\\ x_{n1}& \cdots & x_{np}\end{array}\right)\\ & & \Updownarrow \Updownarrow \Updownarrow \\ \left(\begin{array}{c}{y}_1^{*}\\ ⋮\\ y_m^{*}\end{array}\right)& \Leftarrow & \left(\begin{array}{ccc}{x}_{11}^{*}& \cdots & x_{1p}^{*}\\ ⋮& & ⋮\\ x_{m1}^{*}& \cdots & x_{mp}^{*}\end{array}\right)\end{array}\end{array}$$

^aSingle-target learning (left): same targets, same features${}^{*}$, different samples (from one population). Multi-target learning (centre): different targets, same features${}^{*}$, same samples. Transfer learning (right): same or different targets, matched features${}^{*}$, different samples (from one or two populations). ${}^{*}$Partially overlapping feature spaces are also possible. See, for example, Rauschenberger and Glaab (2021) for multi-target learning or Section 2.8 “Extension” for transfer learning.