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\newcommand{\foldsize}{B} \newcommand{\nriter}{R} [/math]

Consider a hypothesis space [math]\hypospace[/math] constituted by three predictors [math]h^{(1)}(\cdot), h^{(2)}(\cdot),h^{(3)}(\cdot)[/math]. Each predictor [math]h^{(\featureidx)}(\feature)[/math] is a real-valued function of a real-valued argument [math]\feature[/math].

Moreover, for each [math]\featureidx \in \{1,2,3\}[/math],

[[math]] \begin{equation} h^{(\featureidx)}(\feature) = \begin{cases} 0 & \mbox{ if } \feature^2 \leq j \\ j & \mbox{ otherwise.} \end{cases} \end{equation} [[/math]]

Can you tell which of these hypothesis is optimal in the sense of having smallest average squared error loss on the three data points [math](\feature=1/10,\truelabel=3)[/math], [math](0,0)[/math] and [math](1,-1)[/math].