Generalized Linear Regression for Multiple Targets

Learn multitarget linear regression with simple examples and code comparison (custom vs. sklearn) by comparing loss.

Multiple targets

Consider a regression dataset D={(x1,y1),(x2,y2),,(xn,yn)}D=\{(\bold x_1,\bold y_1),(\bold x_2,\bold y_2),\dots,(\bold x_n,\bold y_n)\}, where xiRd\bold x_i \in \R^d and yiRm\bold y_i \in \R^m. A function fW(x)=WTϕ(x)f_W(\bold x) = W^T\phi(\bold x) is a generalized linear model for regression for any given mapping ϕ\phi of the input features x\bold x, and WW is a matrix with mm columns, one for each target. Note that fW(x)Rmf_W(\bold x) \in \R^m.

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