Related papers: Confidence intervals for high-dimensional inverse …
We propose Nodewise Loreg, a nodewise $L_0$-penalized regression method for estimating high-dimensional sparse precision matrices. We establish its asymptotic properties, including convergence rates, support recovery, and asymptotic…
Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for…
The problem of constructing confidence sets in the high-dimensional linear model with $n$ response variables and $p$ parameters, possibly $p\ge n$, is considered. Full honest adaptive inference is possible if the rate of sparse estimation…
We propose a new, computationally efficient, sparsity adaptive changepoint estimator for detecting changes in unknown subsets of a high-dimensional data sequence. Assuming the data sequence is Gaussian, we prove that the new method…
We study frequentist asymptotic properties of Bayesian procedures for high-dimensional Gaussian sparse regression when unknown nuisance parameters are involved. Nuisance parameters can be finite-, high-, or infinite-dimensional. A mixture…
Finite Gaussian mixture models are widely used for model-based clustering of continuous data. Nevertheless, since the number of model parameters scales quadratically with the number of variables, these models can be easily…
Large-scale datasets with count outcome variables are widely present in various applications, and the Poisson regression model is among the most popular models for handling count outcomes. This paper considers the high-dimensional sparse…
Non-parametric inference for functional data over two-dimensional domains entails additional computational and statistical challenges, compared to the one-dimensional case. Separability of the covariance is commonly assumed to address these…
In this paper, we consider the estimation and inference of precision matrices of a rich class of locally stationary and nonlinear time series assuming that only one realization of the time series is observed. Using a Cholesky decomposition…
Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…
While covariance matrices have been widely studied in many scientific fields, relatively limited progress has been made on estimating conditional covariances that permits a large covariance matrix to vary with high-dimensional subject-level…
Hilbert-Schmidt Independence Criterion (HSIC) has recently been used in the field of single-index models to estimate the directions. Compared with some other well-established methods, it requires relatively weaker conditions. However, its…
This paper proposes a new algorithm for multiple sparse regression in high dimensions, where the task is to estimate the support and values of several (typically related) sparse vectors from a few noisy linear measurements. Our algorithm is…
The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the…
We consider the problem of estimating the state of a time-invariant linear Gaussian system in the presence of integrity attacks. The attacker can compromise $p$ out of $m$ sensors, the set of which is fixed over time and unknown to the…
This note studies a method for the efficient estimation of a finite number of unknown parameters from linear equations, which are perturbed by Gaussian noise. In case the unknown parameters have only few nonzero entries, the proposed…
One of the fundamental tasks of science is to find explainable relationships between observed phenomena. One approach to this task that has received attention in recent years is based on probabilistic graphical modelling with sparsity…
This paper proposes a new method of inference in high-dimensional regression models and high-dimensional IV regression models. Estimation is based on a combined use of the orthogonal greedy algorithm, high-dimensional Akaike information…
We study the sparse high-dimensional Gaussian mixture model when the number of clusters is allowed to grow with the sample size. A minimax lower bound for parameter estimation is established, and we show that a constrained maximum…
Missing data occur frequently in a wide range of applications. In this paper, we consider estimation of high-dimensional covariance matrices in the presence of missing observations under a general missing completely at random model in the…