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.

SettingsComplexityPredictorsphb1b2ρs1s2s3t
iLowestGaussian20220200203
iiMediumGaussian2122015050505
iiiHighestGaussian2222015050505
ivLowestGaussian10000.501505005
vMediumGaussian10010.501505005
viHighestGaussian10020.501505005
viiLowestGaussian10000.50.31505005
viiiMediumGaussian10000.50.61505005
ixHighestGaussian10000.50.91505005
xLowestMixed2010.50200203
xiMediumMixed20110200203
xiiHighestMixed20120200203