Table 1. Settings for the prediction example.

The parameterization of the models considered is described where the example in Results is introduced. Complexity identifies the relative size of the models in the multilayer perceptron settings i, ii, and iii, the 10-dimensional generalized linear model settings iv, v, and vi, and the 2-dimensional generalized linear model settings x, xi, and xii. “Gaussian” corresponds to p independent standard normal predictors. “Mixed” correspond to two independent predictors following standard normal and Rademacher distributions. The variable h is the number of hidden layers that the model uses for the E[Y|W] network; b₁ is the bound on the magnitude of the bias in the output node of the network; b₂ is a bound on all other biases and all network weights; ρ is the correlation between the predictors; s₁, s₂, and s₃ are the number of distributions in the random search for an unfavorable distribution that are chosen uniformly from the entire parameter space, uniformly from the boundary, and a mixture of a uniform draw from the entire parameter space and from the boundary (details in the main text); and t is the number of starts used for the shallow interrogation.

Settings	Complexity	Predictors	p	h	b1	b2	ρ	s1	s2	s3	t
i	Lowest	Gaussian	2	0	2	2	0	200	2	0	3
ii	Medium	Gaussian	2	1	2	2	0	150	50	50	5
iii	Highest	Gaussian	2	2	2	2	0	150	50	50	5
iv	Lowest	Gaussian	10	0	0	0.5	0	150	50	0	5
v	Medium	Gaussian	10	0	1	0.5	0	150	50	0	5
vi	Highest	Gaussian	10	0	2	0.5	0	150	50	0	5
vii	Lowest	Gaussian	10	0	0	0.5	0.3	150	50	0	5
viii	Medium	Gaussian	10	0	0	0.5	0.6	150	50	0	5
ix	Highest	Gaussian	10	0	0	0.5	0.9	150	50	0	5
x	Lowest	Mixed	2	0	1	0.5	0	200	2	0	3
xi	Medium	Mixed	2	0	1	1	0	200	2	0	3
xii	Highest	Mixed	2	0	1	2	0	200	2	0	3