Computational Graph For Logistic Regression

fi(x) = alog 1 1 +e−ΦT_(b)x + (1−a) log 1− 1 1 +e−ΦT_(b)x +µi||x||22

and construct computational graphGgi for directional derivative gi(x) =∇ T_f

i(x)×Yi. Our con-

struction is based on closed form expression forgi(x):

gi(x) = p X j=1 2µi[x]j+ (a−1)[Φ(b)]j+ [Φ(b)]j 1 +e−ΦT_(b)x [yj]i

The input nodesv1, . . . , vp correspond to components [x]1, . . . ,[x]pand the rest nodes are arranged

according to Definition.

Figure 41: Computational graph Ggi for gi(x). Input nodes are marked by green. Last node is marked by red.

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