Detecting dependencies among variables is a fundamental task across scientific disciplines. We propose a novel neural network model for graph structure inference, which aims to learn a mapping from observational data to the corresponding underlying dependence structures. The model is trained with variably shaped and coupled simulated input data and requires only a single forward pass through the trained network for inference. Central to our approach is a novel bilinear attention mechanism (BAM) operating on covariance matrices of transformed data while respecting the geometry of the manifold of symmetric positive definite (SPD) matrices. Inspired by graphical lasso methods, our model optimizes over continuous graph representations in the SPD space, where inverse covariance matrices encode conditional independence relations. Empirical evaluations demonstrate the robustness of our method in detecting diverse dependencies, excelling in undirected graph estimation and showing competitive performance in completed partially directed acyclic graph estimation via a novel two-step approach. The trained model effectively detects causal relationships and generalizes well across different functional forms of nonlinear dependencies.

Detecting dependencies among variables is a fundamental task across scientific disciplines. We propose a novel neural network model for graph structure inference, which aims to learn a mapping from observational data to the corresponding underlying dependence structures. The model is trained with variably shaped and coupled simulated input data and requires only a single forward pass through the trained network for inference. Central to our approach is a novel bilinear attention mechanism (BAM) operating on covariance matrices of transformed data while respecting the geometry of the manifold of symmetric positive definite (SPD) matrices. Inspired by graphical lasso methods, our model optimizes over continuous graph representations in the SPD space, where inverse covariance matrices encode conditional independence relations.

Graphical model selection refers to the problem of estimating the unknown graph structure given observations at the nodes in the model. We consider a challenging instance of this problem when some of the nodes are latent or hidden. We characterize conditions for tractable graph estimation and develop efficient methods with provable guarantees. We consider the class of Ising models Markov on locally tree-like graphs, which are in the regime of correlation decay. We propose an efficient method for graph estimation, and establish its structural consistency when the number of samples n scales as n \Omega(\theta_{\min} {-\delta \eta(\eta 1)-2}\log p), where \theta_{\min} is the minimum edge potential, \delta is the depth (i.e., distance from a hidden node to the nearest observed nodes), and \eta is a parameter which depends on the minimum and maximum node and edge potentials in the Ising model.

In statistics and machine learning, detecting dependencies in datasets is a central challenge. We propose a novel neural network model for supervised graph structure learning, i.e., the process of learning a mapping between observational data and their underlying dependence structure. The model is trained with variably shaped and coupled simulated input data and requires only a single forward pass through the trained network for inference. By leveraging structural equation models and employing randomly generated multivariate Chebyshev polynomials for the simulation of training data, our method demonstrates robust generalizability across both linear and various types of non-linear dependencies. We introduce a novel bilinear attention mechanism (BAM) for explicit processing of dependency information, which operates on the level of covariance matrices of transformed data and respects the geometry of the manifold of symmetric positive definite matrices. Empirical evaluation demonstrates the robustness of our method in detecting a wide range of dependencies, excelling in undirected graph estimation and proving competitive in completed partially directed acyclic graph estimation through a novel two-step approach.

Lane graph estimation is an essential and highly challenging task in automated driving and HD map learning. Existing methods using either onboard or aerial imagery struggle with complex lane topologies, out-of-distribution scenarios, or significant occlusions in the image space. Moreover, merging overlapping lane graphs to obtain consistent large-scale graphs remains difficult. To overcome these challenges, we propose a novel bottom-up approach to lane graph estimation from aerial imagery that aggregates multiple overlapping graphs into a single consistent graph. Due to its modular design, our method allows us to address two complementary tasks: predicting ego-respective successor lane graphs from arbitrary vehicle positions using a graph neural network and aggregating these predictions into a consistent global lane graph. Extensive experiments on a large-scale lane graph dataset demonstrate that our approach yields highly accurate lane graphs, even in regions with severe occlusions. The presented approach to graph aggregation proves to eliminate inconsistent predictions while increasing the overall graph quality. We make our large-scale urban lane graph dataset and code publicly available at http://urbanlanegraph.cs.uni-freiburg.de.

Nonparametric approaches for graphical We consider the problem of inferring the conditional independence modeling of real time series in high-dimensional settings (p is graph (CIG) of a high-dimensional stationary multivariate Gaussian large and/or sample size n is of the order of p) have been formulated time series. In a time series graph, each component of the vector series in the form of group-lasso penalized log-likelihood in frequencydomain is represented by distinct node, and associations between components in [10]. Sparse-group lasso penalized log-likelihood approach are represented by edges between the corresponding nodes. in frequency-domain has been considered in [11-13]. We formulate the problem as one of multi-attribute graph estimation In this paper we investigate graph structure estimation for for random vectors where a vector is associated with each node of the stationary Gaussian multivariate time series using a time-domain graph. At each node, the associated random vector consists of a time approach, unlike [10-12] who, as noted earlier, use a frequencydomain series component and its delayed copies.

The exogeneity bias and instrument validation have always been critical topics in statistics, machine learning and biostatistics. In the era of big data, such issues typically come with dimensionality issue and, hence, require even more attention than ever. In this paper we ensemble two well-known tools from machine learning and biostatistics -- stable variable selection and random graph -- and apply them to estimating the house pricing mechanics and the follow-up socio-economic effect on the 2010 Sydney house data. The estimation is conducted on an over-200-gigabyte ultrahigh dimensional database consisting of local education data, GIS information, census data, house transaction and other socio-economic records. The technique ensemble carefully improves the variable selection sparisty, stability and robustness to high dimensionality, complicated causal structures and the consequent multicollinearity, which is ultimately helpful on the data-driven recovery of a sparse and intuitive causal structure. The new ensemble also reveals its efficiency and effectiveness on endogeneity detection, instrument validation, weak instruments pruning and selection of proper instruments. From the perspective of machine learning, the estimation result both aligns with and confirms the facts of Sydney house market, the classical economic theories and the previous findings of simultaneous equations modeling. Moreover, the estimation result is totally consistent with and supported by the classical econometric tool like two-stage least square regression and different instrument tests (the code can be found at https://github.com/isaac2math/solar_graph_learning).

We describe an R package named huge which provides easy-to-use functions for estimating high dimensional undirected graphs from data. This package implements recent results in the literature, including Friedman et al. (2007), Liu et al. (2009, 2012) and Liu et al. (2010). Compared with the existing graph estimation package glasso, the huge package provides extra features: (1) instead of using Fortan, it is written in C, which makes the code more portable and easier to modify; (2) besides fitting Gaussian graphical models, it also provides functions for fitting high dimensional semiparametric Gaussian copula models; (3) more functions like data-dependent model selection, data generation and graph visualization; (4) a minor convergence problem of the graphical lasso algorithm is corrected; (5) the package allows the user to apply both lossless and lossy screening rules to scale up large-scale problems, making a tradeoff between computational and statistical efficiency.

Graphical model selection refers to the problem of estimating the unknown graph structure given observations at the nodes in the model. We consider a challenging instance of this problem when some of the nodes are latent or hidden. We characterize conditions for tractable graph estimation and develop efficient methods with provable guarantees. We consider the class of Ising models Markov on locally tree-like graphs, which are in the regime of correlation decay. We propose an efficient method for graph estimation, and establish its structural consistency when the number of samples $n$ scales as $n \Omega(\theta_{\min} {-\delta \eta(\eta 1)-2}\log p)$, where $\theta_{\min}$ is the minimum edge potential, $\delta$ is the depth (i.e., distance from a hidden node to the nearest observed nodes), and $\eta$ is a parameter which depends on the minimum and maximum node and edge potentials in the Ising model.

In applications of graphical models, we typically have more information than just the samples themselves. A prime example is the estimation of brain connectivity networks based on fMRI data, where in addition to the samples themselves, the spatial positions of the measurements are readily available. With particular regard for this application, we are thus interested in ways to incorporate additional knowledge most effectively into graph estimation. Our approach to this is to make neighborhood selection receptive to additional knowledge by strengthening the role of the tuning parameters. We demonstrate that this concept (i) can improve reproducibility, (ii) is computationally convenient and efficient, and (iii) carries a lucid Bayesian interpretation. We specifically show that the approach provides effective estimations of brain connectivity graphs from fMRI data. However, providing a general scheme for the inclusion of additional knowledge, our concept is expected to have applications in a wide range of domains.