Related papers: On the Sample Complexity of Graphical Model Select…

We develop a fast variational approximation scheme for Gaussian process (GP) regression, where the spectrum of the covariance function is subjected to a sparse approximation. Our approach enables uncertainty in covariance function…

We introduce a nonstationary spatio-temporal statistical model for gridded data on the sphere. The model specifies a computationally convenient covariance structure that depends on heterogeneous geography. Widely used statistical models on…

Current causal discovery approaches require restrictive model assumptions in the absence of interventional data to ensure structure identifiability. These assumptions often do not hold in real-world applications leading to a loss of…

Fitting models for non-Poisson point processes is complicated by the lack of tractable models for much of the data. By using large samples of independent and identically distributed realizations and statistical learning, it is possible to…

This paper is concerned with sample size determination methodology for prediction models. We propose combining the individual calculations via a learning-type curve. We suggest two distinct ways of doing so, a deterministic skeleton of a…

This paper investigates the active sampling for estimation of approximately bandlimited graph signals. With the assistance of a graph filter, an approximately bandlimited graph signal can be formulated by a Gaussian random field over the…

Learning precise surrogate models of complex computer simulations and physical machines often require long-lasting or expensive experiments. Furthermore, the modeled physical dependencies exhibit nonlinear and nonstationary behavior.…

We provide a survey of nonstationary surrogate models which utilize Gaussian processes (GPs) or variations thereof, including nonstationary kernel adaptations, partition and local GPs, and spatial warpings through deep Gaussian processes.…

Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…

The graphical lasso is a widely used algorithm for fitting undirected Gaussian graphical models. However, for inference on functionals of edge values in the learned graph, standard tools lack formal statistical guarantees, such as control…

A finite point process is characterized by the distribution of the number of points (the size) of the process. In some applications, for example, in the context of packet flows in modern communication networks, it is of interest to infer…

Many statistical models are given in the form of non-normalized densities with an intractable normalization constant. Since maximum likelihood estimation is computationally intensive for these models, several estimation methods have been…

Graphical models have become a very popular tool for representing dependencies within a large set of variables and are key for representing causal structures. We provide results for uniform inference on high-dimensional graphical models…

We introduce a sufficient graphical model by applying the recently developed nonlinear sufficient dimension reduction techniques to the evaluation of conditional independence. The graphical model is nonparametric in nature, as it does not…

Specify a randomized algorithm that, given a very large graph or network, extracts a random subgraph. What can we learn about the input graph from a single subsample? We derive laws of large numbers for the sampler output, by relating…

In modeling spatial processes, a second-order stationarity assumption is often made. However, for spatial data observed on a vast domain, the covariance function often varies over space, leading to a heterogeneous spatial dependence…

A challenging problem in estimating high-dimensional graphical models is to choose the regularization parameter in a data-dependent way. The standard techniques include $K$-fold cross-validation ($K$-CV), Akaike information criterion (AIC),…

Non-stationary time series with non-linear trends are frequently encountered in applications. We consider here the feasibility of accurately forecasting the signals of multiple such time series considering jointly when the number of…

Sampling is a fundamental technique, and sampling without replacement is often desirable when duplicate samples are not beneficial. Within machine learning, sampling is useful for generating diverse outputs from a trained model. We present…

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…