Related papers: Relations between networks, regression, partial co…
We develop a framework for derivative Gaussian process latent variable models (DGP-LVMs) that can handle multi-dimensional output data using modified derivative covariance functions. The modifications account for complexities in the…
Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete…
We consider a graphical model where a multivariate normal vector is associated with each node of the underlying graph and estimate the graphical structure. We minimize a loss function obtained by regressing the vector at each node on those…
It is of importance to investigate the significance of a subset of covariates $W$ for the response $Y$ given covariates $Z$ in regression modeling. To this end, we propose a significance test for the partial mean independence problem based…
Multiple-subject network data are fast emerging in recent years, where a separate connectivity matrix is measured over a common set of nodes for each individual subject, along with subject covariates information. In this article, we propose…
Graphical Transformation Models (GTMs) are introduced as a novel approach to effectively model multivariate data with intricate marginals and complex dependency structures semiparametrically, while maintaining interpretability through the…
We propose the Gaussian-Linear Hidden Markov model (GLHMM), a generalisation of different types of HMMs commonly used in neuroscience. In short, the GLHMM is a general framework where linear regression is used to flexibly parameterise the…
Graphical models with bi-directed edges (<->) represent marginal independence: the absence of an edge between two vertices indicates that the corresponding variables are marginally independent. In this paper, we consider maximum likelihood…
We propose NonStGM, a general nonparametric graphical modeling framework for studying dynamic associations among the components of a nonstationary multivariate time series. It builds on the framework of Gaussian Graphical Models (GGM) and…
In image generation, generative models can be evaluated naturally by visually inspecting model outputs. However, this is not always the case for graph generative models (GGMs), making their evaluation challenging. Currently, the standard…
The statistical modeling of random networks has been widely used to uncover interaction mechanisms in complex systems and to predict unobserved links in real-world networks. In many applications, network connections are collected via…
In high-dimensional graph learning problems, some topological properties of the graph, such as bounded node degree or tree structure, are typically assumed to hold so that the sample complexity of recovering the graph structure can be…
The interpretation of complex high-dimensional data typically requires the use of dimensionality reduction techniques to extract explanatory low-dimensional representations. However, in many real-world problems these representations may not…
This paper introduces the Univariate Gaussian Mixture Model Neural Network (uGMM-NN), a novel neural architecture that embeds probabilistic reasoning directly into the computational units of deep networks. Unlike traditional neurons, which…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
Graph-based causal discovery methods aim to capture conditional independencies consistent with the observed data and differentiate causal relationships from indirect or induced ones. Successful construction of graphical models of data…
We propose a novel stochastic network model, called Fractal Gaussian Network (FGN), that embodies well-defined and analytically tractable fractal structures. Such fractal structures have been empirically observed in diverse applications.…
In Gaussian graphical models, conditional independence and partial correlations are natural inferential targets for understanding direct relationships in multivariate data. No comparable framework exists for spatial processes, where…
In many applications, the variables that characterize a stochastic system are measured along a second dimension, such as time. This results in multivariate functional data and the interest is in describing the statistical dependences among…
This paper investigates the statistical properties of non-linear transformations (NLT) of random variables, in order to establish useful tools for estimation and information theory. Specifically, the paper focuses on linear regression…