Related papers: Learning Gaussian Graphical Models with Latent Con…
We introduce a Gaussian Prototype Layer for gradient-based prototype learning and demonstrate two novel network architectures for explainable segmentation one of which relies on region proposals. Both models are evaluated on agricultural…
Gaussian graphical models provide a powerful framework to reveal the conditional dependency structure between multivariate variables. The process of uncovering the conditional dependency network is known as structure learning. Bayesian…
Modern generative models are usually designed to match target distributions directly in the data space, where the intrinsic dimension of data can be much lower than the ambient dimension. We argue that this discrepancy may contribute to the…
Variational autoencoders (VAEs) and other generative methods have garnered growing interest not just for their generative properties but also for the ability to dis-entangle a low-dimensional latent variable space. However, few existing…
In this tutorial we explain the inference procedures developed for the sparse Gaussian process (GP) regression and Gaussian process latent variable model (GPLVM). Due to page limit the derivation given in Titsias (2009) and Titsias &…
The Gaussian process latent variable model (GP-LVM) provides a flexible approach for non-linear dimensionality reduction that has been widely applied. However, the current approach for training GP-LVMs is based on maximum likelihood, where…
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…
We present the Mixed Likelihood Gaussian process latent variable model (GP-LVM), capable of modeling data with attributes of different types. The standard formulation of GP-LVM assumes that each observation is drawn from a Gaussian…
Functional Gaussian graphical models (GGM) used for analyzing multivariate functional data customarily estimate an unknown graphical model representing the conditional relationships between the functional variables. However, in many…
Images encode both the state of the world and its content. The former is useful for tasks such as planning and control, and the latter for classification. The automatic extraction of this information is challenging because of the…
The existence of latent variables in practical problems is common, for example when some variables are difficult or expensive to measure, or simply unknown. When latent variables are unaccounted for, structure learning for Gaussian…
The edge structure of the graph defining an undirected graphical model describes precisely the structure of dependence between the variables in the graph. In many applications, the dependence structure is unknown and it is desirable to…
Through recognizing causal subgraphs, causal graph learning (CGL) has risen to be a promising approach for improving the generalizability of graph neural networks under out-of-distribution (OOD) scenarios. However, the empirical successes…
Graphical models serve as effective tools for visualizing conditional dependencies between variables. However, as the number of variables grows, interpretation becomes increasingly difficult, and estimation uncertainty increases due to the…
Gaussian graphical models are used throughout the natural sciences, social sciences, and economics to model the statistical relationships between variables of interest in the form of a graph. We here provide a pedagogic introduction to…
Motivated by modern applications in which one constructs graphical models based on a very large number of features, this paper introduces a new class of cluster-based graphical models, in which variable clustering is applied as an initial…
Learning parameters of latent graphical models (GM) is inherently much harder than that of no-latent ones since the latent variables make the corresponding log-likelihood non-concave. Nevertheless, expectation-maximization schemes are…
The PC algorithm uses conditional independence tests for model selection in graphical modeling with acyclic directed graphs. In Gaussian models, tests of conditional independence are typically based on Pearson correlations, and…
We study causal discovery from observational data in linear Gaussian systems affected by \emph{mixed latent confounding}, where some unobserved factors act broadly across many variables while others influence only small subsets. This…
Deep learning models, such as convolutional neural networks, have long been applied to image and multi-media tasks, particularly those with structured data. More recently, there has been more attention to unstructured data that can be…