New framework models complex spatial data with basis functions and graphical vectors.
problem Modeling highly-multivariate spatial processes with varying resolutions.
method Extends graphical lasso to multivariate Gaussian processes with independent graphical vectors at different resolutions, using an orthogonal basis and fusion penalty.
result Linear complexity and parsimonious conditional independence structure in multilevel graphical model.
Generative model for scalable vector graphics captures font design statistics.
problem Lack of higher-level understanding in vision and imagery modeling.
method Sequential generative models of vector graphics.
result Model captures statistical dependencies and richness of font datasets.
A new copula model for multi-attribute data using optimal transport.
problem Relaxing the Gaussian assumption for multi-attribute graphical models.
method Introducing a new copula (Cyclically Monotone Copula) and using optimal transport theory.
result The model allows arbitrary continuous distributions and is more flexible than classical methods.
Computes Lie algebra structure constants using a graphical calculus.
problem Computing Lie algebra structure constants efficiently.
method Graphical calculus for classical invariant theory.
result Generalizes known methods for sl2 to other Lie algebras. We present Vector-Space Markov Random Fields (VS-MRFs), a novel class of undirected graphical models where each variable can belong to an arbitrary vector space. VS-MRFs generalize a recent line of work on scalar-valued, uni-parameter exponential family and mixed graphical models, thereby greatly broadening the class o…
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 methods---have their own distinct strengths but also possess significant drawbacks. Conditio…
Proposes a method to estimate functional graphical models from multivariate random functions.
problem Estimating conditional independence structure of multivariate random functions.
method Neighborhood selection approach combining function-on-function regression and graph recovery.
result Statistical consistency of the method in high-dimensional settings.
We consider a graphical model where a multivariate normal vector is associated with each node of the underlying graph and estimate the graphical structure. We minimize a loss function obtained by regressing the vector at each node on those at the remaining ones under a group penalty. We show that the proposed estimator…
We describe various sets of conditional independence relationships, sufficient for qualitatively comparing non-vanishing squared partial correlations of a Gaussian random vector. These sufficient conditions are satisfied by several graphical Markov models. Rules for comparing degree of association among the vertices of…
Graphical normalizing flows use Bayesian networks to improve normalizing flows' interpretability and performance.
problem Improving the interpretability and performance of normalizing flows.
method Revisiting normalizing flows as probabilistic graphical models, proposing graphical normalizing flows with either prescribed or learnable graph structures.
result Graphical conditioners lead to competitive white box density estimators.
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 step for reducing the dimension of the feature space. We employ model assisted cl…
The paper extends Bernstein Theorem for minimal spacelike surfaces in 4D Minkowski space.
problem Analyzing Bernstein property for minimal spacelike surfaces in 4D Minkowski space.
method Study of an extension of the Bernstein Theorem for minimal spacelike surfaces in R^4_1.
result The Bernstein property does not hold in general for graphic spacelike surfaces in R^4_1.
This paper develops a nonparametric model for complex network data.
problem Capturing conditional independence structure in multivariate data with heterogeneous graph structures.
method Integrates network embedding with nonparametric graphical model estimation, solving a linear equation system.
result The proposed method effectively recovers heterogeneous graph structures without distributional assumptions.
We characterize the sample size required for accurate graphical model selection from non-stationary samples. The observed data is modeled as a vector-valued zero-mean Gaussian random process whose samples are uncorrelated but have different covariance matrices. This model contains as special cases the standard setting …
Develops a new method for network-linked data using Gaussian graphical models.
problem Graphical models for network-linked data violate independence and identically distributed assumptions.
method Proposes a Gaussian graphical model for network-linked data with varying mean vectors and smooth transitions over the network. Efficient estimation algorithm developed.
result Demonstrates effectiveness on simulated and real data, obtaining meaningful results on a statistics coauthorship network.
Profile graphical models represent multivariate dependence under varying risk factors.
problem Capturing varying conditional independence structures across different levels of a risk factor.
method Introducing a novel class of graphical models (profile graphical models) that represent multivariate dependence under varying risk factors, and developing a Bayesian approach for learning shared sparsity structures.
result Demonstrated enhanced ability to capture subject-specific differences in protein network data from acute myeloid leukemia.
A new method for sparse regression models using graph structure.
problem Sparse regression models for high-dimensional data.
method Decomposes coefficient vector into latent variables, performs regularization on latent variables, uses proximal projection.
result Stable performance compared to other models, especially for high-dimensional data.
Gaussian graphical model is a graphical representation of the dependence structure for a Gaussian random vector. It is recognized as a powerful tool in different applied fields such as bioinformatics, error-control codes, speech language, information retrieval and others. Gaussian graphical model selection is a statist…
The purpose of this paper is twofold: firstly, to establish sufficient conditions under which the mean curvature flow supported on a hypersphere with exterior Dirichlet boundary exists globally in time and converges to a minimal surface, and secondly, to illustrate the application of Killing vector fields in the preser…
New method optimizes 3D training data generation for deep networks.
problem Challenges in generating realistic 3D training data for deep networks.
method Hybrid gradient optimization of design decisions in graphics-based generation pipelines.
result Our approach outperforms prior methods in computational efficiency and performance.
FuDGE estimates differences between functional graphs in high-dimensional settings.
problem Estimating differences between two undirected functional graphical models with shared structures.
method FuDGE: A method that directly estimates the functional differential graph without first estimating individual graphs.
result FuDGE consistently estimates the functional differential graph in high-dimensional settings.
BEGIN network models binary data without parametric assumptions.
problem Conditional independence in non-parametric families of binary data.
method BEGIN network models binary data using sparse linear representations and block factorizations.
result BEGIN network captures conditional independence for arbitrary binary and multinomial variables.
The sum-product or belief propagation (BP) algorithm is a widely-used message-passing algorithm for computing marginal distributions in graphical models with discrete variables. At the core of the BP message updates, when applied to a graphical model with pairwise interactions, lies a matrix-vector product with complex…
Rgtsvm provides a fast and flexible support vector machine (SVM) implementation for the R language. The distinguishing feature of Rgtsvm is that support vector classification and support vector regression tasks are implemented on a graphical processing unit (GPU), allowing the libraries to scale to millions of examples…
We characterize the effectiveness of a classical algorithm for recovering the Markov graph of a general discrete pairwise graphical model from i.i.d. samples. The algorithm is (appropriately regularized) maximum conditional log-likelihood, which involves solving a convex program for each node; for Ising models this is …
Paper analyzes multi-attribute data to estimate differences in Gaussian graphical models.
problem Estimating differences in two Gaussian graphical models with similar structure.
method Group lasso penalized D-trace loss function and ADMM algorithm for optimization.
result Consistency in support recovery and estimation in high-dimensional settings established.
LIBTwinSVM offers a free library for efficient Twin Support Vector Machines.
problem Large-scale classification problems.
method Efficient implementation of Twin Support Vector Machines.
result Effectiveness demonstrated through benchmarks.
This paper tackles structure learning in indirect observations of Gaussian and non-Gaussian random vectors.
problem Learning the graphical structure of random vectors indirectly observed through a sensing matrix and corrupted noise.
method Parametric and non-parametric approaches for Gaussian and non-Gaussian distributions, respectively.
result Correct graphical structure can be recovered under indefinite sensing systems with insufficient samples.
Neighborhood regression has been a successful approach in graphical and structural equation modeling, with applications to learning undirected and directed graphical models. We extend these ideas by defining and studying an algebraic structure called the neighborhood lattice based on a generalized notion of neighborhoo…
Method estimates differences between two functional graphs.
problem Estimating differences between two functional undirected graphical models.
method Direct estimation of graph difference, avoiding separate estimation.
result Method is consistent in high-dimensional settings.
Develops an efficient method for real-time data analysis and visualization.
problem Challenges of analyzing high-dimensional data.
method Incremental non-linear manifold approximation using GMRA framework.
result Accurately represents non-linear manifolds with small initial samples.
We learn sparse precision matrices from compressed data sketches.
problem Learning a graph from high-dimensional data with limited storage.
method Estimate a sparse precision matrix from a sketch of the data using non-linear random features.
result It is possible to estimate a sparse precision matrix from a sketch of size $m=Ω\left((d+2k)\log(d)
ight)$.
Spectral sparsification improves Laplacian-constrained graph learning.
problem Improving accuracy of Laplacian-constrained graph learning.
method Spectral graph sparsification as a post-estimation operation.
result Improved accuracy of Laplacian-constrained graph learning.
In this paper we propose a unified framework for structured prediction with latent variables which includes hidden conditional random fields and latent structured support vector machines as special cases. We describe a local entropy approximation for this general formulation using duality, and derive an efficient messa…
We propose a method for inferring the conditional indepen- dence graph (CIG) of a high-dimensional discrete-time Gaus- sian vector random process from finite-length observations. Our approach does not rely on a parametric model (such as, e.g., an autoregressive model) for the vector random process; rather, it only assu…
Paper tackles structure learning of sparse GGMs over multiple access networks.
problem Estimating sparse Gaussian Graphical Model structure from multiple local machines with limited communication.
method Proposes Signs and Uncoded methods for reliable structure learning under power and bandwidth limitations.
result Both methods can recover the structure with high probability for large enough sample size.
A new algorithm improves GLasso for sparse precision matrix estimation.
problem Efficiently estimating sparse precision matrices in high-dimensional data.
method A new reparametrization and iterative block coordinate descent algorithm.
result Improved performance comparable to DP-GLasso with a simpler optimization target.
A new method identifies sub-populations in unlabelled heterogeneous data by accounting for co-features.
problem Estimating sub-populations in unlabelled heterogeneous data with co-features.
method Mixture of Conditional Gaussian Graphical Models (CGGM) with penalized EM algorithm.
result The method successfully identifies sub-populations disrupted by co-features.
Proposes a method to derive knowledge graphs from EHR data.
problem Challenges in deriving generalizable knowledge from EHR data.
method Infer conditional dependency structure via a latent graphical block model (LGBM).
result Perfect recovery of block structure demonstrated.
New proof of trapezoidal property for Alexander polynomials of special alternating links.
problem Proving trapezoidal property of Alexander polynomials for special alternating links.
method Analyzing vector configurations from matroids and totally positive matrices.
result Alexander polynomials of special alternating links exhibit log-concavity and trapezoidal properties.
Graphical lasso may fail to fit models when data points are insufficient.
problem When does graphical lasso fail to select and fit a graphical model?
method Computational experiments with graphical lasso.
result Graphical lasso may fail when the number of data points is less than the maximum likelihood threshold.
Study on rigidity of translating hypersurfaces not in graphical direction.
problem Rigidity of translating hypersurfaces not in graphical direction.
method Proved rigidity results for complete graphical translating hypersurfaces under specific conditions.
result Entire graphical translating surfaces are flat under certain conditions.
New method selects better graphs for GGM inference in small sample sizes.
problem Inference of conditional correlations in high-dimensional data with limited samples.
method Composite procedure combining nodewise edge selection and penalised likelihood maximisation.
result Our method produces graphs closer to the true distribution with better KL divergence.
Discrete vector bundles are important in Physics and recently found remarkable applications in Computer Graphics. This article approaches discrete bundles from the viewpoint of Discrete Differential Geometry, including a complete classification of discrete vector bundles over finite simplicial complexes. In particular,…
This is a short description of graphic lambda calculus, with special emphasis on a duality suggested by the two different appearances of knot diagrams, in lambda calculus and emergent algebra sectors of the graphic lambda calculus respectively. This duality leads to the introduction of the dual of the graphic beta move…
Bayesian Temporal Factorization predicts multidimensional time series with missing data.
problem Predicting large-scale, multidimensional spatiotemporal data with missing values.
method Integrates low-rank matrix/tensor factorization and VAR process into a probabilistic model.
result Superior performance on real-world spatiotemporal data sets compared to existing methods.
We consider the problem of learning high-dimensional Gaussian graphical models. The graphical lasso is one of the most popular methods for estimating Gaussian graphical models. However, it does not achieve the oracle rate of convergence. In this paper, we propose the graphical nonconvex optimization for optimal estimat…
New method for tuning Graphical Lasso hyperparameters.
problem Tuning hyperparameters of Graphical Lasso.
method Bilevel optimization with first-order method.
result Derivation of Graphical Lasso Jacobian.