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Vector autoregression (VAR) models are widely used for forecasting and macroeconomic analysis, yet they remain limited by their reliance on a linear parameterization. Recent research has introduced nonparametric alternatives, such as…
This study introduces Variational Automatic Relevance Determination (VARD), a novel approach tailored for fitting sparse additive regression models in high-dimensional settings. VARD distinguishes itself by its ability to independently…
We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…
We consider a class of vector autoregressive models with banded coefficient matrices. The setting represents a type of sparse structure for high-dimensional time series, though the implied autocovariance matrices are not banded. The…
Sparse additive modeling is a class of effective methods for performing high-dimensional nonparametric regression. This paper develops a sparse additive model focused on estimation of treatment effect-modification with simultaneous…
Regression models are used in a wide range of applications providing a powerful scientific tool for researchers from different fields. Linear, or simple parametric, models are often not sufficient to describe complex relationships between…
Vector autoregressive (VAR) models have become a staple in the analysis of multivariate time series and are formulated in the time domain as difference equations, with an implied covariance structure. In many contexts, it is desirable to…
Additive models belong to the class of structured nonparametric regression models that do not suffer from the curse of dimensionality. Finding the additive components that are nonzero when the true model is assumed to be sparse is an…
Undirected graphical models are applied in genomics, protein structure prediction, and neuroscience to identify sparse interactions that underlie discrete data. Although Bayesian methods for inference would be favorable in these contexts,…
We propose a Bayesian vector autoregressive (VAR) model for mixed-frequency data. Our model is based on the mean-adjusted parametrization of the VAR and allows for an explicit prior on the 'steady states' (unconditional means) of the…
Lasso-type estimators are routinely used to estimate high-dimensional time series models. The theoretical guarantees established for these estimators typically require the penalty level to be chosen in a suitable fashion often depending on…
Many high-dimensional data sets suffer from hidden confounding which affects both the predictors and the response of interest. In such situations, standard regression methods or algorithms lead to biased estimates. This paper substantially…
The Vector AutoRegressive Moving Average (VARMA) model is fundamental to the theory of multivariate time series; however, identifiability issues have led practitioners to abandon it in favor of the simpler but more restrictive Vector…
High-dimensional vector autoregressive (VAR) models offer a versatile framework for multivariate time series analysis, yet face critical challenges from over-parameterization and uncertain lag order. In this paper, we systematically compare…
Vector autoregression (VAR) is a fundamental tool for modeling multivariate time series. However, as the number of component series is increased, the VAR model becomes overparameterized. Several authors have addressed this issue by…
We consider a flexible semiparametric quantile regression model for analyzing high dimensional heterogeneous data. This model has several appealing features: (1) By considering different conditional quantiles, we may obtain a more complete…
Forward regression is a statistical model selection and estimation procedure which inductively selects covariates that add predictive power into a working statistical regression model. Once a model is selected, unknown regression parameters…
In many problem settings, parameter vectors are not merely sparse but dependent in such a way that non-zero coefficients tend to cluster together. We refer to this form of dependency as "region sparsity." Classical sparse regression…
Spike-and-slab and horseshoe regression are arguably the most popular Bayesian variable selection approaches for linear regression models. However, their performance can deteriorate if outliers and heteroskedasticity are present in the…
Visual Autoregressive (VAR) models have emerged as a powerful paradigm for image synthesis by performing hierarchical next-scale prediction. However, VAR models are inherently prone to cascading error propagation, where subtle coarse-scale…