New method aggregates nodes in sparse graphical models.
problem Estimating edge-sparse graphical models.
method Tree-aggregated graphical lasso (tag-lasso) method.
result Aggregates nodes in a data-driven fashion using a tree.
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48 results for “sparse graphical models”
We find a closed-form determinant for a specific sparse covariance matrix model.
problem Finding the determinant of a specific class of sparse positive definite matrices.
method Using Fourier transform of local factors, Normal Factor Graph Duality Theorem, and Matrix Determinant Lemma.
result We derive a closed-form expression for the determinant.
Simultaneous Identification of Sparse Structures and Communities in Heterogeneous Graphical Modelsstat.ML
Paper identifies sparse structures and communities in heterogeneous graphical models.
problem Detecting community structures in graphical models.
method Novel decomposition into sparse and low-rank parts, three-stage estimation procedure.
result Consistent model selection for adaptive penalized estimator.
Gaussian graphical models (GGM) have been widely used in many high-dimensional applications ranging from biological and financial data to recommender systems. Sparsity in GGM plays a central role both statistically and computationally. Unfortunately, real-world data often does not fit well to sparse graphical models. I…
The paper improves Bayesian precision matrix estimation for high-dimensional sparse data.
problem Estimating sparse precision matrices in high-dimensional settings.
method Tempered posterior with fully specified horseshoe prior.
result Concentration results and theoretical oracle inequality for posterior.
Proposes a method to estimate sparse Gaussian graphical models with hidden clustering structure.
problem Modeling statistical relationships between variables with sparsity and clustering.
method Two-phase algorithm using sGS-ADMM for initial point and pALM for solution.
result Demonstrates good performance and efficiency of the proposed model and algorithm on synthetic and real data.
Efficient algorithms solve joint graphical lasso problems.
problem Learning graphical models from sparse data.
method Proximal gradient procedures with ADMM backtracking option.
result Proposed algorithms achieve high accuracy and precision.
Estimates sparse Gaussian graphical models using discrete optimization.
problem Learning a sparse graph from Gaussian graphical models.
method Proposes GraphL0BnB, an -penalized MIP solved with a custom BnB framework.
result Significant runtime and statistical performance improvements over existing methods.
One of the fundamental tasks of science is to find explainable relationships between observed phenomena. One approach to this task that has received attention in recent years is based on probabilistic graphical modelling with sparsity constraints on model structures. In this paper, we describe two new approaches to Bay…
BPASGM uses sparse graphical models to optimize portfolio selection.
problem Portfolio optimization in high-dimensional settings with estimation error.
method BPASGM extends BPA to a sparse graphical model, screening assets for diversification.
result BPASGM portfolios outperform standard mean-variance portfolios in risk-adjusted performance.
This paper addresses the problem of scalable optimization for L1-regularized conditional Gaussian graphical models. Conditional Gaussian graphical models generalize the well-known Gaussian graphical models to conditional distributions to model the output network influenced by conditioning input variables. While highly …
New method learns graphical models with latent variables for extreme events.
problem Learning graphical models with latent variables for multivariate extremes.
method Tractable convex program exttt{eglatent} for Hüsler-Reiss models.
result Consistently recovers conditional graph and latent variables.
New method infers graph from dependent matrix data.
problem Inferring graph from dependent matrix data.
method Sparse-group lasso-based frequency-domain formulation with ADMM approach.
result Local convergence of inverse PSD estimators to true value.
Gaussian Graphical Models (GGMs) are popular tools for studying network structures. However, many modern applications such as gene network discovery and social interactions analysis often involve high-dimensional noisy data with outliers or heavier tails than the Gaussian distribution. In this paper, we propose the Tri…
NGRs merge sparse graph recovery with PGMs for efficient probabilistic inference.
problem Efficiently recover sparse graphs and learn distributions over variables.
method Integrates sparse graph recovery methods with PGMs using Graph-constrained path norm.
result NGRs can handle multimodal data and perform sparse graph recovery and probabilistic inference.
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.
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 equations between the resulting steady-state covariance matrix and the Laplacia…
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 $m=Ω\left((d+2k)\log(d)
ight)$.
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 data is drawn identically from a generating distribution. Introducing sparsity a…
The -norm fails to produce sparse solutions in Laplacian constrained graphical models, leading to a complete graph.
problem Learning a sparse graph under Laplacian constrained Gaussian graphical models.
method Introduced a nonconvex sparsity penalty and proposed a new estimator using a sequence of weighted -norm penalized sub-problems. Developed a projected gradient descent algorithm with linear convergence rate.
result The proposed estimator can recover the edges correctly with high probability and is effective on both synthetic and real-world data sets.
We present some nonparametric methods for graphical modeling. In the discrete case, where the data are binary or drawn from a finite alphabet, Markov random fields are already essentially nonparametric, since the cliques can take only a finite number of values. Continuous data are different. The Gaussian graphical mode…
The paper efficiently estimates parameters from truncated Gaussian and linear models.
problem Estimating parameters from truncated Gaussian and linear models.
method Minimizes finite population negative log-likelihood function with an l1-regularization term.
result Efficient estimation of parameters from truncated samples.
Delta-AI speeds up inference in sparse PGMs by local credit assignment.
problem Efficient inference in sparse probabilistic graphical models.
method Local credit assignment in agent's policy learning objective.
result Trained sampler recovers marginals and conditional distributions.
High dimensional piecewise stationary graphical models represent a versatile class for modelling time varying networks arising in diverse application areas, including biology, economics, and social sciences. There has been recent work in offline detection and estimation of regime changes in the topology of sparse graph…
New method for inferring time series graph from sparse-group log-sum penalty.
problem Inferring conditional independence graph from high-dimensional stationary multivariate Gaussian time series.
method Sparse-group log-sum penalty (LSP) and alternating direction method of multipliers (ADMM) for iterative optimization.
result Local convergence of inverse PSD estimators to the true value with rate of convergence.
Sparse graph learning for dependent time series using ADMM.
problem Inferring conditional independence graph of sparse, high-dimensional stationary multivariate Gaussian time series.
method Sparse-group lasso-based frequency-domain formulation and alternating direction method of multipliers (ADMM) optimization.
result Convergence of inverse PSD estimators to true value under certain conditions.
We show that the two-stage adaptive Lasso procedure (Zou, 2006) is consistent for high-dimensional model selection in linear and Gaussian graphical models. Our conditions for consistency cover more general situations than those accomplished in previous work: we prove that restricted eigenvalue conditions (Bickel et al.…
In this article, we propose a new class of priors for Bayesian inference with multiple Gaussian graphical models. We introduce fully Bayesian treatments of two popular procedures, the group graphical lasso and the fused graphical lasso, and extend them to a continuous spike-and-slab framework to allow self-adaptive shr…
Undirected graphical models are applied in genomics, protein structure prediction, and neuroscience to identify sparse interactions that underlie discrete data. Although Bayesian methods for inference would be favorable in these contexts, they are rarely used because they require doubly intractable Monte Carlo sampling…
Scalable Inference of Sparsely-changing Markov Random Fields with Strong Statistical Guaranteescs.LG
Efficiently infers time-varying sparse MRFs with strong statistical guarantees.
problem Inference of time-varying sparse MRFs with strong statistical guarantees.
method Constrained optimization with exact regularization, near-linear time and memory complexity.
result Sharp statistical guarantees for sparsely-changing Gaussian MRFs with as few as one sample per time.
We study the estimation of the latent variable Gaussian graphical model (LVGGM), where the precision matrix is the superposition of a sparse matrix and a low-rank matrix. In order to speed up the estimation of the sparse plus low-rank components, we propose a sparsity constrained maximum likelihood estimator based on m…
New method for disentangling latent factors with sparse dependencies.
problem Disentangling latent factors from observed variables and past factors.
method Mechanism sparsity regularization and sparse causal graphical model.
result Identifiability of latent factors up to a sparse causal graph.
We consider unsupervised estimation of mixtures of discrete graphical models, where the class variable corresponding to the mixture components is hidden and each mixture component over the observed variables can have a potentially different Markov graph structure and parameters. We propose a novel approach for estimati…
SGM combines deep learning and planning for robust long-horizon tasks.
problem Combining deep learning and planning for robust long-horizon tasks.
method Sparse Graphical Memory (SGM) that stores states and feasible transitions in a sparse memory, aggregating states according to a two-way consistency objective.
result SGM significantly outperforms current state of the art methods on long horizon, sparse-reward visual navigation tasks.
In many applications, multivariate samples may harbor previously unrecognized heterogeneity at the level of conditional independence or network structure. For example, in cancer biology, disease subtypes may differ with respect to subtype-specific interplay between molecular components. Then, both subtype discovery and…
Deep networks can approximate score functions in high-dimensional graphical models efficiently.
problem Approximation efficiency of score functions by deep neural networks in high-dimensional graphical models like Markov random fields.
method Variational inference denoising algorithms and efficient neural network representation.
result Efficient sample complexity bound for diffusion-based generative modeling when score functions are learned by deep neural networks.
Identifying context-specific entity networks from aggregated data is an important task, arising often in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several co…
Paper introduces MGLasso for multiscale graph inference in clustering and network analysis.
problem Graphical models in high-dimensional data analysis need to handle clustering and sparsity simultaneously.
method MGLasso combines clustering and graph inference through a convex relaxation of k-means and hierarchical clustering. It uses CONESTA for regularization.
result MGLasso improves network interpretability by estimating graphs at multiple scales.
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.
Fair GLASSO estimates fair GGMs by balancing statistical dependencies across groups.
problem Fairness in graphical models with biased data.
method Regularized graphical lasso with bias metrics, proximal gradient algorithm.
result Preserves statistical accuracy while promoting fairness across groups.
The paper shows how instrumental variables can help identify sparse causal effects in linear models.
problem Identifying sparse causal effects in linear models with limited instruments.
method Conditions and graphical criteria for identifiability, spaceIV estimator.
result Causal effects can be identified from observed distributions with sparse effects and limited instruments.
The Gaussian graphical model, a popular paradigm for studying relationship among variables in a wide range of applications, has attracted great attention in recent years. This paper considers a fundamental question: When is it possible to estimate low-dimensional parameters at parametric square-root rate in a large Gau…
While graphical models for continuous data (Gaussian graphical models) and discrete data (Ising models) have been extensively studied, there is little work on graphical models linking both continuous and discrete variables (mixed data), which are common in many scientific applications. We propose a novel graphical mode…
A new framework uses matrix flows to unify frequentist and Bayesian approaches for sparse GGMs.
problem Challenges in studying conditional independence among many variables with few observations.
method General framework for variational inference with matrix-variate Normalizing Flow in Gaussian Graphical Models.
result Unified benefits of frequentist and Bayesian frameworks for sparse GGMs.
The paper shows cross-validation fails in learning Gaussian graphical model structures.
problem Cross-validation's failure in learning Gaussian graphical model structures.
method Finite-sample bounds on misidentification probability of Lasso estimator.
result Cross-validation is inconsistent for learning Gaussian graphical model structures.
Gaussian Graphical Models (GGMs) have wide-ranging applications in machine learning and the natural and social sciences. In most of the settings in which they are applied, the number of observed samples is much smaller than the dimension and they are assumed to be sparse. While there are a variety of algorithms (e.g. G…
Develops FGL for better portfolio allocation under common factor influence.
problem Sparsity assumption fails for stock returns driven by common factors.
method Integrates graphical models with factor structure to estimate portfolio weights and risk exposure robust to heavy-tailed distributions.
result FGL-based portfolios outperform equal-weighted and Index portfolios in empirical applications.
In this paper we study the problem of exact recovery of the pure-strategy Nash equilibria (PSNE) set of a graphical game from noisy observations of joint actions of the players alone. We consider sparse linear influence games --- a parametric class of graphical games with linear payoffs, and represented by directed gra…