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Implicit Bias of Gradient Descent for Mean Squared Error Regression with Two-Layer Wide Neural Networks

Abstract We investigate gradient descent training of wide neural networks and the corresponding implicit bias in function space. For univariate regression, we show that the solution of training a width-n shallow ReLU network is within n−1/2 of the function which fits the training data and whose difference from the initial function has the smallest 2-norm of the second…

Inference of Media Bias and Content Quality Using Natural-Language Processing

Abstract Media bias can significantly impact the formation and development of opinions and sentiments in a population. It is thus important to study the emergence and development of partisan media and political polarization. However, it is challenging to quantitatively infer the ideological positions of media outlets. In this paper, we present a quantitative framework to…

Local Dependence in Random Graph Models: Characterisation, Properties, and Statistical Inference

Abstract Dependent phenomena, such as relational, spatial and temporal phenomena, tend to be characterized by local dependence in the sense that units which are close in a well-defined sense are dependent. In contrast with spatial and temporal phenomena, though, relational phenomena tend to lack a natural neighbourhood structure in the sense that it is unknown…

Understanding Networks with Exponential-family Random Network Models

Abstract The structure of many complex social networks is determined by nodal and dyadic covariates that are endogenous to the tie variables. While exponential-family random graph models (ERGMs) have been very successful in modeling social networks with exogenous covariates, they are often misspecified for networks where some covariates are stochastic. Exponential-family random network models (ERNMs)…