Related papers: A Likelihood Ratio Framework for High Dimensional …
We propose a new method of estimation in high-dimensional linear regression model. It allows for very weak distributional assumptions including heteroscedasticity, and does not require the knowledge of the variance of random errors. The…
Statistical inference on the explained variation of an outcome by a set of covariates is of particular interest in practice. When the covariates are of moderate to high-dimension and the effects are not sparse, several approaches have been…
Many standard estimators, when applied to adaptively collected data, fail to be asymptotically normal, thereby complicating the construction of confidence intervals. We address this challenge in a semi-parametric context: estimating the…
We propose a method for inference in generalised linear mixed models (GLMMs) and several extensions of these models. First, we extend the GLMM by allowing the distribution of the random components to be non-Gaussian, that is, assuming an…
This paper develops a bias correction scheme for a multivariate normal model under a general parameterization. In the model, the mean vector and the covariance matrix share the same parameters. It includes many important regression models…
Covariance estimation for high-dimensional datasets is a fundamental problem in modern day statistics with numerous applications. In these high dimensional datasets, the number of variables p is typically larger than the sample size n. A…
When analyzing empirical data, we often find that global linear models overestimate the number of parameters required. In such cases, we may ask whether the data lies on or near a manifold or a set of manifolds (a so-called multi-manifold)…
Most supervised machine learning tasks are subject to irreducible prediction errors. Probabilistic predictive models address this limitation by providing probability distributions that represent a belief over plausible targets, rather than…
We consider high-dimensional inference for potentially misspecified Cox proportional hazard models based on low dimensional results by Lin and Wei [1989]. A de-sparsified Lasso estimator is proposed based on the log partial likelihood…
This paper concerns the development of an inferential framework for high-dimensional linear mixed effect models. These are suitable models, for instance, when we have $n$ repeated measurements for $M$ subjects. We consider a scenario where…
Heterogeneity is a dominant factor in the behaviour of many biological processes. Despite this, it is common for mathematical and statistical analyses to ignore biological heterogeneity as a source of variability in experimental data.…
Additive regression provides an extension of linear regression by modeling the signal of a response as a sum of functions of covariates of relatively low complexity. We study penalized estimation in high-dimensional nonparametric additive…
Ultra-high dimensional longitudinal data are increasingly common and the analysis is challenging both theoretically and methodologically. We offer a new automatic procedure for finding a sparse semivarying coefficient model, which is widely…
In many real-world applications of regression, conditional probability estimation, and uncertainty quantification, exploiting symmetries rooted in physics or geometry can dramatically improve generalization and sample efficiency. While…
We propose a general method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in a high-dimensional model. It can be easily adjusted for multiplicity taking…
We introduce a novel rule-based approach for handling regression problems. The new methodology carries elements from two frameworks: (i) it provides information about the uncertainty of the parameters of interest using Bayesian inference,…
Parameter estimation connects mathematical models to real-world data and decision making across many scientific and industrial applications. Standard approaches such as maximum likelihood estimation and Markov chain Monte Carlo estimate…
The remarkable generalization performance of large-scale models has been challenging the conventional wisdom of the statistical learning theory. Although recent theoretical studies have shed light on this behavior in linear models and…
Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…
Generalization is a central problem in Machine Learning. Most prediction methods require careful calibration of hyperparameters carried out on a hold-out \textit{validation} dataset to achieve generalization. The main goal of this paper is…