Related papers: Selective Inference for Sparse Graphs via Neighbor…
Bayesian estimation of Gaussian graphical models has proven to be challenging because the conjugate prior distribution on the Gaussian precision matrix, the G-Wishart distribution, has a doubly intractable partition function. Recent…
Inference and optimization of real-value edge variables in sparse graphs are studied using the Bethe approximation and replica method of statistical physics. Equilibrium states of general energy functions involving a large set of real…
Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear…
We present Selective Non-Gaussian Refinement (SNGR), a SLAM framework that augments iSAM2 with targeted nested sampling on windows where Gaussian approximations are likely to fail. We detect such regions using the condition number of joint…
Probabilistic graphical models (PGMs) are powerful tools for representing statistical dependencies through graphs in high-dimensional systems. However, they are limited to pairwise interactions. In this work, we propose the simplicial…
Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…
Bayesian graphical models are powerful tools to infer complex relationships in high dimension, yet are often fraught with computational and statistical challenges. If exploited in a principled way, the increasing information collected…
Gaussian processes are valuable tools for non-parametric modelling, where typically an assumption of stationarity is employed. While removing this assumption can improve prediction, fitting such models is challenging. In this work,…
Gaussian Processes (GPs) are Bayesian models that provide uncertainty estimates associated to the predictions made. They are also very flexible due to their non-parametric nature. Nevertheless, GPs suffer from poor scalability as the number…
We consider the problem of learning a graph modeling the statistical relations of the $d$ variables from a dataset with $n$ samples $X \in \mathbb{R}^{n \times d}$. Standard approaches amount to searching for a precision matrix $\Theta$…
Bayesian inference for graphical models has received much attention in the literature in recent years. It is well known that when the graph G is decomposable, Bayesian inference is significantly more tractable than in the general…
Selective inference (post-selection inference) is a methodology that has attracted much attention in recent years in the fields of statistics and machine learning. Naive inference based on data that are also used for model selection tends…
We contribute an approach to the problem of locally computing sparse connected subgraphs of dense graphs. In this setting, given an edge in a connected graph $G = (V, E)$, an algorithm locally decides its membership in a sparse connected…
A general approach to selective inference is considered for hypothesis testing of the null hypothesis represented as an arbitrary shaped region in the parameter space of multivariate normal model. This approach is useful for hierarchical…
Exploring and detecting community structures hold significant importance in genetics, social sciences, neuroscience, and finance. Especially in graphical models, community detection can encourage the exploration of sets of variables with…
A nonparametric Bayes approach is proposed for the problem of estimating a sparse sequence based on Gaussian random variables. We adopt the popular two-group prior with one component being a point mass at zero, and the other component being…
We are going to analyze local algorithms over sparse random graphs. These algorithms are based on local information where local regards to a decision made by the exploration of a small neighbourhood of a certain vertex plus a believe of the…
We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…
In the Network Inference problem, one seeks to recover the edges of an unknown graph from the observations of cascades propagating over this graph. In this paper, we approach this problem from the sparse recovery perspective. We introduce a…
We develop a class of rules spanning the range between quadratic discriminant analysis and naive Bayes, through a path of sparse graphical models. A group lasso penalty is used to introduce shrinkage and encourage a similar pattern of…