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The topic of deep learning has seen a surge of interest in recent years bothwithin and outside of the field of Statistics. Deep models leverage bothnonlinearity and interaction effects to provide superior predictions in manycases when compared to linear or generalized linear models. However, one of themain challenges with deep modeling approaches is quantification of uncertainty.The use of random weight models, such as the popularized "Extreme LearningMachine," offer a potential solution in this regard. In addition to uncertaintyquantification, these models are extremely computationally efficient as they donot require optimization through stochastic gradient descent, which is what istypically done for deep learning. We show how the use of random weights in adeep model can fit into a likelihood based framework to allow for uncertaintyquantification of the model parameters and any desired estimates. Furthermore,we show how this approach can be used to account for informative sampling ofsurvey data through the use of a pseudo-likelihood. We illustrate theeffectiveness of this methodology through simulation and with a real surveydata application involving American National Election Studies data.

Computationally Efficient Deep Bayesian Unit-Level Modeling of Survey Data under Informative Sampling for Small Area Estimation