This work aims at recovering signals that are sparse on graphs. Compressed sensing offers techniques for signal recovery from a few linear measurements and graph Fourier analysis provides a signal representation on graph. In this paper, we leverage these two frameworks to introduce a new Lasso recovery algorithm on gra…
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48 results for “graph lasso”
Network Lasso improves semi-supervised regression on network data.
problem Improving regression accuracy on network data with limited labeled examples.
method Applying network Lasso to semi-supervised regression problems, leveraging message passing over an empirical graph.
result Network Lasso's accuracy is linked to the existence of large network flows over the empirical graph.
The "least absolute shrinkage and selection operator" (Lasso) method has been adapted recently for networkstructured datasets. In particular, this network Lasso method allows to learn graph signals from a small number of noisy signal samples by using the total variation of a graph signal for regularization. While effic…
Network Lasso clusters sparse graph clusters efficiently.
problem Local graph clustering of sparse and chain-like clusters.
method Network Lasso minimizes total variation of cluster indicator signals.
result Network Lasso handles sparse clusters difficult for spectral clustering.
The paper develops estimators for variance in graph structures using fused lasso.
problem Variance estimation in graph-structured problems.
method Developed linear time estimator for homoscedastic case and total variation regularization estimator for heteroscedastic case.
result Minimax rates and consistency for variance estimation in various graph structures.
We consider the sparse inverse covariance regularization problem or graphical lasso with regularization parameter . Suppose the co- variance graph formed by thresholding the entries of the sample covariance matrix at is decomposed into connected components. We show that the vertex-partition induced by the thresh…
Triangle lasso improves clustering and optimization in noisy graphs.
problem Noise and missing data in graph datasets lead to sub-optimal clustering results.
method Triangle lasso uses neighbors' similarity to find similar instances, avoiding direct feature comparison.
result Triangle lasso yields better results than state-of-the-art methods in practical scenarios.
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.
The paper tackles sparse graph learning under Laplacian-related constraints, improving upon existing methods.
problem Learning a sparse undirected graph from multivariate data under Laplacian-related constraints.
method Modifications to penalized log-likelihood approaches to enforce total positivity and lasso/adaptive lasso penalties using ADMM.
result The proposed constrained adaptive lasso approach significantly outperforms existing Laplacian-based approaches.
Paper links network Lasso to network flow optimization.
problem Joint clustering and optimization of networked data.
method Exploration of duality between network Lasso and network flow optimization.
result nLasso is equivalent to a minimum-cost flow problem on the data network structure.
Proposes a new method for hyperspectral image dimensionality reduction.
problem Highly correlated noisy hyperspectral images.
method Trace Lasso-L1 Graph Cut method using L1-norm for robustness and sparsity.
result Optimal projection matrix maximizing between-class dispersion to within-class dispersion.
Lasso proves consistent model selection for high-dimensional Ising models.
problem Model selection consistency of Lasso for high-dimensional Ising models.
method Theoretical analysis of Lasso with and without post-thresholding for Ising models.
result Lasso without post-thresholding is model selection consistent in the whole paramagnetic phase with .
New algorithm efficiently learns sparse causal graphs from time series data.
problem Learning sparse causal graphs from time series data efficiently and automatically selecting the number of edges.
method Cyclical coordinate descent algorithm with two non-parametric error metrics for LASSO coefficient selection.
result State-of-the-art performance on simulated and real datasets.
We propose a new algorithm for solving the graph-fused lasso (GFL), a method for parameter estimation that operates under the assumption that the signal tends to be locally constant over a predefined graph structure. Our key insight is to decompose the graph into a set of trails which can then each be solved efficientl…
New spectral clustering method using LASSO regularization for robust graph partitioning.
problem Lack of theoretical guarantees for spectral clustering on general graph models.
method 1-spectral clustering on a new random model with LASSO regularization.
result Effective and robust to small noise perturbations, validated by simulations and real data.
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.
Penalized Likelihood Methods for Estimation of Sparse High Dimensional Directed Acyclic Graphsstat.ML
Directed acyclic graphs (DAGs) are commonly used to represent causal relationships among random variables in graphical models. Applications of these models arise in the study of physical, as well as biological systems, where directed edges between nodes represent the influence of components of the system on each other.…
Improves graph recovery in Gaussian graphical modeling.
problem Calibrating regularization parameters for graph recovery.
method Thresholded adaptive validation applied to graphical lasso.
result Thresholding pipeline improves graph recovery.
A simple thresholding technique improves graph selection in neural connectivity studies.
problem Graphical model selection for functional neural connectivity in the presence of latent variables.
method Apply a hard thresholding operator to graphical Lasso, neighborhood selection, or CLIME estimators.
result Thresholded estimators outperform existing methods in graph selection consistency and empirical results.
Genome-wide association studies (GWA studies or GWAS) investigate the relationships between genetic variants such as single-nucleotide polymorphisms (SNPs) and individual traits. Recently, incorporating biological priors together with machine learning methods in GWA studies has attracted increasing attention. However, …
Efficient algorithms for clustered Lasso and OSCAR reduce computational costs.
problem High dimensional regression with feature clustering.
method Efficient path algorithms for clustered Lasso and OSCAR, reducing computational costs.
result Proposed algorithms are more efficient than existing methods in numerical experiments.
A method for inferring graph from multivariate time series using ADMM.
problem Inferring conditional independence graph from multivariate Gaussian time series.
method Formulated as multi-attribute graph estimation, used ADMM to minimize penalized negative log-likelihood.
result Proposed method outperforms existing frequency-domain approaches in graph edge detection.
PANDA augments data to regularize graph models, improving parameter estimation and graph construction.
problem Regularizing estimation and construction of undirected graphical models.
method AdaPtive Noise Augmentation (PANDA) iteratively optimizes augmented data loss function.
result Noise-augmented loss function converges to expected penalized loss function, enabling efficient parameter inference.
The network Lasso is a recently proposed convex optimization method for machine learning from massive network structured datasets, i.e., big data over networks. It is a variant of the well-known least absolute shrinkage and selection operator (Lasso), which is underlying many methods in learning and signal processing i…
Paper estimates differences in conditional independence graphs from time-dependent data.
problem Estimating changes in conditional dependencies between two time series with known similar structure.
method Penalized D-trace loss function approach in the frequency domain, using Wirtinger calculus, with convex and non-convex penalties.
result Established sufficient conditions for consistency and graph recovery in high-dimensional settings.
HSIC-based method explains GNN structures.
problem Interpreting GNNs' complex dynamics.
method Flexible model-agnostic explanation using HSIC.
result Identifies crucial structures in GNNs.
Graph-Structured Multi-task Regression and an Efficient Optimization Method for General Fused Lassostat.ML
We consider the problem of learning a structured multi-task regression, where the output consists of multiple responses that are related by a graph and the correlated response variables are dependent on the common inputs in a sparse but synergistic manner. Previous methods such as l1/l2-regularized multi-task regressio…
A new feature selection method using structural correlation between samples.
problem Feature selection in high-dimensional data overlooks structural correlation information.
method Converts features into graph representations, uses fused lasso for feature selection.
result Demonstrates effectiveness of the proposed approach through experiments.
Efficiently infers sparse networks from count data with reduced memory usage.
problem Sparse network inference for count data with high dimensions and dependencies.
method Improved Bigraphical Lasso using eigenvalue decomposition of Cartesian product graph.
result Reduced computational complexity from to .
New method recovers relative rates in spatial compositional data from IMS.
problem Challenges in analyzing spatial data from IMS due to competitive sampling.
method Hierarchical Variational Graph Fused Lasso using heavy-tailed graphical lasso prior and automatic differentiation variational inference.
result Our method outperforms state-of-the-practice point estimate methodologies in IMS and has superior posterior coverage.
We generalize to tree graphs obtained by connecting path graphs an oracle result obtained for the Fused Lasso over the path graph. Moreover we show that it is possible to substitute in the oracle inequality the minimum of the distances between jumps by their harmonic mean. In doing so we prove a lower bound on the comp…
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.
New research shows how preconditioning can solve sparse linear regression problems efficiently.
problem Efficiently solving sparse linear regression problems without restrictive conditions.
method Preconditioned Lasso approach to solve sparse linear regression problems.
result Preconditioning can solve a large class of sparse linear regression problems nearly optimally.
We investigate the high-dimensional regression problem using adjacency matrices of unbalanced expander graphs. In this frame, we prove that the -prediction error and the -risk of the lasso and the Dantzig selector are optimal up to an explicit multiplicative constant. Thus we can estimate a high-dim…
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.
GraphLIME explains GNN models by selecting key features locally.
problem Explaining the effectiveness of GNN models is challenging due to complex nonlinear transformations.
method GraphLIME uses HSIC Lasso for nonlinear feature selection in GNN models.
result GraphLIME provides more descriptive explanations than existing methods.
A new GCN model learns higher-order neighbors without explicit adjacency matrix computation.
problem GCN's performance drops for deeper structures due to limited neighborhood information.
method Assumes higher-order neighbors are similar to first-order neighbors, learns weights through Lasso to minimize feature loss.
result HWGCN achieves state-of-the-art results on various datasets.
Unified framework infers time-varying graphs from incomplete signals.
problem Jointly inferring time-varying network topologies and imputing missing data from partial observations.
method Unified non-convex optimization framework with Proximal Alternating Direction Method of Multipliers (PADMM) algorithm.
result Superior robustness in high missing-data regimes, demonstrated through extensive numerical experiments.
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.
Unified analysis of multi-attribute graph learning with non-convex penalties.
problem Graph inference from multi-attribute data.
method Penalized log-likelihood objective function with ADMM and local linear approximation.
result Local consistency in support recovery and precision matrix estimation for non-convex penalties.
GNL addresses dynamic network regression by learning dynamic graph structures and capturing sequence information.
problem Dynamic network regression of multiple inter-connected data entities.
method Graph Neural Lasso (GNL) using gated diffusive units and attention mechanism.
result GNL outperforms existing methods in dynamic network regression tasks.
We study the problem of estimating high-dimensional regression models regularized by a structured sparsity-inducing penalty that encodes prior structural information on either the input or output variables. We consider two widely adopted types of penalties of this kind as motivating examples: (1) the general overlappin…
A new method learns DAG structures from data without false edges.
problem Learning DAG structures from observational data is hard due to combinatorial search space and non-sparse solutions.
method Developed NOTEARS-AL using adaptive Lasso to ensure sparsity and rule out false edges.
result NOTEARS-AL outperforms NOTEARS in synthetic and real-world datasets.
In variable or graph selection problems, finding a right-sized model or controlling the number of false positives is notoriously difficult. Recently, a meta-algorithm called Stability Selection was proposed that can provide reliable finite-sample control of the number of false positives. Its benefits were demonstrated …
Online graph learning from matrix-valued time series data.
problem Identifying dependency structure among sensors in a network.
method Extends VAR models to matrix-variate models, proposes online procedures for graph learning, and introduces Lasso-type approaches.
result Demonstrates effectiveness of online graph learning methods in both synthetic and real data.
In this paper, we consider the problem of estimating multiple graphical models simultaneously using the fused lasso penalty, which encourages adjacent graphs to share similar structures. A motivating example is the analysis of brain networks of Alzheimer's disease using neuroimaging data. Specifically, we may wish to e…
SyGlasso models tensor data dependencies using Sylvester equations.
problem Capturing multiway dependencies in tensor-valued data.
method Based on Sylvester equation, uses nodewise regression for estimation.
result Demonstrates simultaneous estimation of brain connectivity and temporal dependencies.
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.