Related papers: On the Sample Complexity of Graphical Model Select…
Selecting regularization parameters in penalized high-dimensional graphical models in a principled, data-driven, and computationally efficient manner continues to be one of the key challenges in high-dimensional statistics. We present…
Gaussian processes (GPs) are a popular class of Bayesian nonparametric models, but its training can be computationally burdensome for massive training datasets. While there has been notable work on scaling up these models for big data,…
Computer models are used as a way to explore complex physical systems. Stationary Gaussian process emulators, with their accompanying uncertainty quantification, are popular surrogates for computer models. However, many computer models are…
Model selection in Gaussian processes scales prohibitively with the size of the training dataset, both in time and memory. While many approximations exist, all incur inevitable approximation error. Recent work accounts for this error in the…
The sampling of graph signals has recently drawn much attention due to the wide applications of graph signal processing. While a lot of efficient methods and interesting results have been reported to the sampling of band-limited or smooth…
Gaussian process regression is used throughout statistics and machine learning for prediction and uncertainty quantification. A Gaussian process is specified by its mean and covariance functions. Many covariance functions, including…
In Gaussian graphical models, the likelihood equations must typically be solved iteratively. We investigate two algorithms: A version of iterative proportional scaling which avoids inversion of large matrices, and an algorithm based on…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
Estimation of structure, such as in variable selection, graphical modelling or cluster analysis is notoriously difficult, especially for high-dimensional data. We introduce stability selection. It is based on subsampling in combination with…
A famously hard graph problem with a broad range of applications is computing the number of perfect matchings, that is the number of unique and complete pairings of the vertices of a graph. We propose a method to estimate the number of…
We propose a covariate-dependent discrete graphical model for capturing dynamic networks among discrete random variables, allowing the dependence structure among vertices to vary with covariates. This discrete dynamic network encompasses…
We propose a new adequacy test and a graphical evaluation tool for nonlinear dynamic models. The proposed techniques can be applied in any setup where parametric conditional distribution of the data is specified, in particular to models…
In many areas of science one aims to estimate latent sub-population mean curves based only on observations of aggregated population curves. By aggregated curves we mean linear combination of functional data that cannot be observed…
This article proposes methods to model nonstationary temporal graph processes. This corresponds to modelling the observation of edge variables (relationships between objects) indicating interactions between pairs of nodes (or objects)…
In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets…
Structural equation models and Bayesian networks have been widely used to analyze causal relations between continuous variables. In such frameworks, linear acyclic models are typically used to model the datagenerating process of variables.…
Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…
Graphical models are widely used in diverse application domains to model the conditional dependencies amongst a collection of random variables. In this paper, we consider settings where the graph structure is covariate-dependent, and…
We study the optimal sample complexity of learning a Gaussian directed acyclic graph (DAG) from observational data. Our main results establish the minimax optimal sample complexity for learning the structure of a linear Gaussian DAG model…
Gaussian processes are powerful, yet analytically tractable models for supervised learning. A Gaussian process is characterized by a mean function and a covariance function (kernel), which are determined by a model selection criterion. The…