Related papers: Statistical inference using debiased group graphic…
When a model's performance differs across socially or culturally relevant groups--like race, gender, or the intersections of many such groups--it is often called "biased." While much of the work in algorithmic fairness over the last several…
Quantifying the uncertainty in penalized regression under group sparsity is an important open question. We establish, under a high-dimensional scaling, the asymptotic validity of a modified parametric bootstrap method for the group lasso,…
We study the problem of estimating multiple linear regression equations for the purpose of both prediction and variable selection. Following recent work on multi-task learning Argyriou et al. [2008], we assume that the regression vectors…
The application of the lasso is espoused in high-dimensional settings where only a small number of the regression coefficients are believed to be nonzero. Moreover, statistical properties of high-dimensional lasso estimators are often…
We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…
Classically, statistical datasets have a larger number of data points than features ($n > p$). The standard model of classical statistics caters for the case where data points are considered conditionally independent given the parameters.…
Many theoretical results for the lasso require the samples to be iid. Recent work has provided guarantees for the lasso assuming that the time series is generated by a sparse Vector Auto-Regressive (VAR) model with Gaussian innovations.…
This work performs a non-asymptotic analysis of the generalized Lasso under the assumption of sub-exponential data. Our main results continue recent research on the benchmark case of (sub-)Gaussian sample distributions and thereby explore…
We introduce a generic estimator for the false discovery rate of any model selection procedure, in common statistical modeling settings including the Gaussian linear model, Gaussian graphical model, and model-X setting. We prove that our…
We introduce a flexible framework for making inferences about general linear forms of a large matrix based on noisy observations of a subset of its entries. In particular, under mild regularity conditions, we develop a universal procedure…
The Lasso is an attractive technique for regularization and variable selection for high-dimensional data, where the number of predictor variables $p_n$ is potentially much larger than the number of samples $n$. However, it was recently…
We provide a selected overview of methodology and theory for estimation and inference on the edge weights in high-dimensional directed and undirected Gaussian graphical models. For undirected graphical models, two main explicit…
The popular Lasso approach for sparse estimation can be derived via marginalization of a joint density associated with a particular stochastic model. A different marginalization of the same probabilistic model leads to a different…
The Gaussian graphical model (GGM) incorporates an undirected graph to represent the conditional dependence between variables, with the precision matrix encoding partial correlation between pair of variables given the others. To achieve…
Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…
Sparse regression and classification estimators that respect group structures have application to an assortment of statistical and machine learning problems, from multitask learning to sparse additive modeling to hierarchical selection.…
We consider the problem of estimating multiple related but distinct graphical models on the basis of a high-dimensional data set with observations that belong to distinct classes. A motivating example occurs in the analysis of gene…
We study simultaneous inference for multiple matrix-variate Gaussian graphical models in high-dimensional settings. Such models arise when spatiotemporal data are collected across multiple sample groups or experimental sessions, where each…
We devise a one-shot approach to distributed sparse regression in the high-dimensional setting. The key idea is to average "debiased" or "desparsified" lasso estimators. We show the approach converges at the same rate as the lasso as long…
Gaussian graphical model is one of the powerful tools to analyze conditional independence between two variables for multivariate Gaussian-distributed observations. When the dimension of data is moderate or high, penalized likelihood methods…