Related papers: Learning Some Popular Gaussian Graphical Models wi…
We introduce the truncated Gaussian graphical model (TGGM) as a novel framework for designing statistical models for nonlinear learning. A TGGM is a Gaussian graphical model (GGM) with a subset of variables truncated to be nonnegative. The…
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…
In Gaussian graphical model selection, noise-corrupted samples present significant challenges. It is known that even minimal amounts of noise can obscure the underlying structure, leading to fundamental identifiability issues. A recent line…
Functional brain networks are well described and estimated from data with Gaussian Graphical Models (GGMs), e.g. using sparse inverse covariance estimators. Comparing functional connectivity of subjects in two populations calls for…
The time-evolving precision matrix of a piecewise-constant Gaussian graphical model encodes the dynamic conditional dependency structure of a multivariate time-series. Traditionally, graphical models are estimated under the assumption that…
The Collective Graphical Model (CGM) models a population of independent and identically distributed individuals when only collective statistics (i.e., counts of individuals) are observed. Exact inference in CGMs is intractable, and previous…
Time-series datasets are central in machine learning with applications in numerous fields of science and engineering, such as biomedicine, Earth observation, and network analysis. Extensive research exists on state-space models (SSMs),…
We propose estimating Gaussian graphical models (GGMs) that are fair with respect to sensitive nodal attributes. Many real-world models exhibit unfair discriminatory behavior due to biases in data. Such discrimination is known to be…
In this paper, we address the problem of learning the structure of a pairwise graphical model from samples in a high-dimensional setting. Our first main result studies the sparsistency, or consistency in sparsity pattern recovery,…
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…
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…
We propose a Bayesian approximate inference method for learning the dependence structure of a Gaussian graphical model. Using pseudo-likelihood, we derive an analytical expression to approximate the marginal likelihood for an arbitrary…
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 this paper, we introduce a new directed graphical model from Gaussian data: the Gaussian graphical interaction model (GGIM). The development of this model comes from considering stationary Gaussian processes on graphs, and leveraging the…
We study the problem of learning the topology of a directed Gaussian Graphical Model under the equal-variance assumption, where the graph has $n$ nodes and maximum in-degree $d$. Prior work has established that $O(d \log n)$ samples are…
Graphical models are widely used in scienti fic and engineering research to represent conditional independence structures between random variables. In many controlled experiments, environmental changes or external stimuli can often alter…
Gaussian Graphical Models (GGMs) or Gauss Markov random fields are widely used in many applications, and the trade-off between the modeling capacity and the efficiency of learning and inference has been an important research problem. In…
Studying conditional independence among many variables with few observations is a challenging task. Gaussian Graphical Models (GGMs) tackle this problem by encouraging sparsity in the precision matrix through $l_q$ regularization with…
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…
Standard Gaussian graphical models (GGMs) implicitly assume that the conditional independence among variables is common to all observations in the sample. However, in practice, observations are usually collected form heterogeneous…