Undirected graphical models have been widely used to model the conditional independence structure of high-dimensional random vector data for years. In many modern applications such as EEG and fMRI data, the observations are multivariate random …

We study the estimation of the parametric components of single and multiple index volatility models. Using the first- and second-order Stein’s identities, we develop methods that are applicable for the estimation of the variance index in the …

Structural equation models (SEMs) are widely used in sciences, ranging from economics to psychology, to uncover causal relationships underlying a complex system under consideration and estimate structural parameters of interest. We study estimation …

We study accelerated stochastic gradient descent through the lens of the growth condition. Stochastic gradient methods (SGD) with momentum, such as heavy ball (HB) and Nesterov's accelerated methods (NAM), are widely used in practice, especially for …

We consider the problem of estimating the latent structure of a social network based on the observed information diffusion events, or _cascades_. Here for a given cascade, we only observe the times of infection for infected nodes but not the source …

We consider the problem of estimating the difference between two functional undirected graphical models with shared structures. In many applications, data are naturally regarded as high-dimensional random function vectors rather than multivariate …

Density Ratio Estimation has attracted attention from machine learning community due to its ability of comparing the underlying distributions of two datasets. However, in some applications, we want to compare distributions of emphlatent random …