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High-dimensional Functional Graphical Model Structure Learning via Neighborhood Selection Approach

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 …

High-dimensional Index Volatility Models via Stein's Identity

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 …

Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approach

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 …

Understanding Accelerated Stochastic Gradient Descent via the Growth Condition

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 …

Estimation of a Low-rank Topic-Based Model for Information Cascades

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 …

FuDGE: Functional Differential Graph Estimation with fully and discretely observed curves

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 …

Posterior Ratio Estimation for Latent Variables

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 …

Recovery of simultaneous low rank and two-way sparse coefficient matrices, a nonconvex approach

Kernel Meets Sieve: Post-Regularization Confidence Bands for Sparse Additive Model

High-dimensional Varying Index Coefficient Models via Stein's Identity