Related papers: High-dimensional Simultaneous Inference on Non-Gau…
For predictive modeling relying on Bayesian inversion, fully independent, or ``mean-field'', Gaussian distributions are often used as approximate probability density functions in variational inference since the number of variational…
We examine an analytic variational inference scheme for the Gaussian Process State Space Model (GPSSM) - a probabilistic model for system identification and time-series modelling. Our approach performs variational inference over both the…
Developing efficient solutions for inference problems in intelligent sensor networks is crucial for the next generation of location, tracking, and mapping services. This paper develops a scalable distributed probabilistic inference…
High-dimensional variable selection, with many more covariates than observations, is widely documented in standard regression models, but there are still few tools to address it in non-linear mixed-effects models where data are collected…
Precision matrix, which is the inverse of covariance matrix, plays an important role in statistics, as it captures the partial correlation between variables. Testing the equality of two precision matrices in high dimensional setting is a…
To accurately reproduce measurements from the real world, simulators need to have an adequate model of the physical system and require the parameters of the model be identified. We address the latter problem of estimating parameters through…
We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…
A semi-analytic method is proposed for the generation of realizations of a multivariate process of a given linear correlation structure and marginal distribution. This is an extension of a similar method for univariate processes,…
We consider bootstrap inference for estimators which are (asymptotically) biased. We show that, even when the bias term cannot be consistently estimated, valid inference can be obtained by proper implementations of the bootstrap.…
We propose a new framework for the simultaneous inference of monotone and smoothly time-varying functions under complex temporal dynamics. This will be done utilizing the monotone rearrangement and the nonparametric estimation. We…
Debiasing is a fundamental concept in high-dimensional statistics. While degrees-of-freedom adjustment is the state-of-the-art technique in high-dimensional linear regression, it is limited to i.i.d. samples and sub-Gaussian covariates.…
The steady-state Bayesian vector autoregression (BVAR) makes it possible to incorporate prior information about the long-run mean of the process. This has been shown in many studies to substantially improve forecasting performance, and the…
We propose autoregressive Bayesian semi-parametric models for waiting times between recurrent events. The aim is two-fold: inference on the effect of possibly time-varying covariates on the gap times and clustering of individuals based on…
Several new methods have been proposed for performing valid inference after model selection. An older method is sampling splitting: use part of the data for model selection and part for inference. In this paper we revisit sample splitting…
Statistical inference of the high-dimensional regression coefficients is challenging because the uncertainty introduced by the model selection procedure is hard to account for. A critical question remains unsettled; that is, is it possible…
This paper studies inference for the mean vector of a high-dimensional $U$-statistic. In the era of Big Data, the dimension $d$ of the $U$-statistic and the sample size $n$ of the observations tend to be both large, and the computation of…
Deep Gaussian Processes (DGPs) are hierarchical generalizations of Gaussian Processes that combine well calibrated uncertainty estimates with the high flexibility of multilayer models. One of the biggest challenges with these models is that…
Gaussian processes (GPs) are Bayesian nonparametric models for function approximation with principled predictive uncertainty estimates. Deep Gaussian processes (DGPs) are multilayer generalizations of GPs that can represent complex marginal…
The reduced-rank vector autoregressive (VAR) model can be interpreted as a supervised factor model, where two factor modelings are simultaneously applied to response and predictor spaces. This article introduces a new model, called vector…
We propose a flexible yet interpretable model for high-dimensional data with time-varying second order statistics, motivated and applied to functional neuroimaging data. Motivated by the neuroscience literature, we factorize the covariances…