相关论文: Learning Gaussian Graphical Models with Observed o…

This work proposes an algorithmic framework to learn time-varying graphs from online data. The generality offered by the framework renders it model-independent, i.e., it can be theoretically analyzed in its abstract formulation and then…

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…

We show that a collection of Gaussian mixture models (GMMs) in $R^{n}$ can be optimally classified using $O(n)$ neurons in a neural network with two hidden layers (deep neural network), whereas in contrast, a neural network with a single…

We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be…

We consider structure discovery of undirected graphical models from observational data. Inferring likely structures from few examples is a complex task often requiring the formulation of priors and sophisticated inference procedures.…

Graph Neural Networks (GNNs) have shown superior performance in node classification. However, GNNs perform poorly in the Few-Shot Node Classification (FSNC) task that requires robust generalization to make accurate predictions for unseen…

Restricted Boltzmann Machines (RBMs) are a common family of undirected graphical models with latent variables. An RBM is described by a bipartite graph, with all observed variables in one layer and all latent variables in the other. We…

The Gaussian graphical model (GGM) incorporates an undirected graph to represent the conditional dependence between variables, with the precision matrix encoding partial correlation between pair of variables given the others. To achieve…

3D Gaussian Splatting (3DGS) has demonstrated impressive novel view synthesis performance. While conventional methods require per-scene optimization, more recently several feed-forward methods have been proposed to generate pixel-aligned…

Generative adversarial networks (GANs) learn the distribution of observed samples through a zero-sum game between two machine players, a generator and a discriminator. While GANs achieve great success in learning the complex distribution of…

Graph Convolutional Networks (GCNs) are extensively utilized for deep learning on graphs. The large data sizes of graphs and their vertex features make scalable training algorithms and distributed memory systems necessary. Since the…

In many structured prediction problems, complex relationships between variables are compactly defined using graphical structures. The most prevalent graphical prediction methods---probabilistic graphical models and large margin…

Node representation learning by using Graph Neural Networks (GNNs) has been widely explored. However, in recent years, compelling evidence has revealed that GNN-based node representation learning can be substantially deteriorated by…

Understanding the impact of data structure on the computational tractability of learning is a key challenge for the theory of neural networks. Many theoretical works do not explicitly model training data, or assume that inputs are drawn…

Machine learning frameworks such as graph neural networks typically rely on a given, fixed graph to exploit relational inductive biases and thus effectively learn from network data. However, when said graphs are (partially) unobserved,…

This paper presents an efficient variational inference framework for deriving a family of structured gaussian process regression network (SGPRN) models. The key idea is to incorporate auxiliary inducing variables in latent functions and…

We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational…

Probabilistic graphical models (PGMs) are widely used to discover latent structure in data, but their success hinges on selecting an appropriate model design. In practice, model specification is difficult and often requires iterative…

Hidden Markov models (HMMs) are powerful tools for analysing time series data that depend on discrete underlying but unobserved states. As such, they have gained prominence across numerous empirical disciplines, in particular ecology,…

In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…