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Gaussian process latent variable models (GPLVMs) are a versatile family of unsupervised learning models commonly used for dimensionality reduction. However, common challenges in modeling data with GPLVMs include inadequate kernel…
Regression models are popular tools in empirical sciences to infer the influence of a set of variables onto a dependent variable given an experimental dataset. In neuroscience and cognitive psychology, Generalized Linear Models (GLMs)…
Inferring a graphical model or network from observational data from a large number of variables is a well studied problem in machine learning and computational statistics. In this paper we consider a version of this problem that is relevant…
We propose a partially linear additive Gaussian graphical model (PLA-GGM) for the estimation of associations between random variables distorted by observed confounders. Model parameters are estimated using an $L_1$-regularized maximal…
Graphs are a powerful data structure for representing relational data and are widely used to describe complex real-world systems. Probabilistic Graphical Models (PGMs) and Graph Neural Networks (GNNs) can both leverage graph-structured…
Gaussian Graphical Models (GGM) are popularly used in neuroimaging studies based on fMRI, EEG or MEG to estimate functional connectivity, or relationships between remote brain regions. In multi-subject studies, scientists seek to identify…
Probabilistic Graphical Models are often used to understand dynamics of a system. They can model relationships between features (nodes) and the underlying distribution. Theoretically these models can represent very complex dependency…
The marginal correlation between two variables is a measure of their linear dependence. The two original variables need not interact directly, because marginal correlation may arise from the mediation of other variables in the system. The…
Convolutional neural networks (CNNs) provide flexible function approximations for a wide variety of applications when the input variables are in the form of images or spatial data. Although CNNs often outperform traditional statistical…
There remains an open question about the usefulness and the interpretation of Machine learning (MLE) approaches for discrimination of spatial patterns of brain images between samples or activation states. In the last few decades, these…
In genome-wide prediction, independence of marker allele substitution effects is typically assumed; however, since early stages of this technology it has been known that nature points to correlated effects. In statistics, graphical models…
For the problem of inferring a Gaussian graphical model (GGM), this work explores the application of a recent approach from the multiple testing literature for graph inference. The main idea of the method by Rebafka et al. (2022) is to…
Graph Convolutional Network (GCN) has experienced great success in graph analysis tasks. It works by smoothing the node features across the graph. The current GCN models overwhelmingly assume that the node feature information is complete.…
A longstanding problem in machine learning is to find unsupervised methods that can learn the statistical structure of high dimensional signals. In recent years, GANs have gained much attention as a possible solution to the problem, and in…
In most domains of network analysis researchers consider networks that arise in nature with weighted edges. Such networks are routinely dichotomized in the interest of using available methods for statistical inference with networks. The…
Random graphs, where the connections between nodes are considered random variables, have wide applicability in the social sciences. Exponential-family Random Graph Models (ERGM) have shown themselves to be a useful class of models for…
Currently there exists rather promising new trend in machine leaning (ML) based on the relationship between neural networks (NN) and Gaussian processes (GP), including many related subtopics, e.g., signal propagation in NNs, theoretical…
We describe various sets of conditional independence relationships, sufficient for qualitatively comparing non-vanishing squared partial correlations of a Gaussian random vector. These sufficient conditions are satisfied by several…
Graphs are a powerful data structure to represent relational data and are widely used to describe complex real-world data structures. Probabilistic Graphical Models (PGMs) have been well-developed in the past years to mathematically model…
Nonlinear relations, such as the curvilinear relationship between childhood trauma and resilience in patients with schizophrenia and the moderation relationship between mentalizing, and internalizing and externalizing symptoms and quality…