Simultaneous Identification of Sparse Structures and Communities in Heterogeneous Graphical Models
- URL: http://arxiv.org/abs/2405.09841v1
- Date: Thu, 16 May 2024 06:38:28 GMT
- Title: Simultaneous Identification of Sparse Structures and Communities in Heterogeneous Graphical Models
- Authors: Dapeng Shi, Tiandong Wang, Zhiliang Ying,
- Abstract summary: We introduce a novel decomposition of the underlying graphical structure into a sparse part and low-rank diagonal blocks.
We propose a three-stage estimation procedure with a fast and efficient algorithm for the identification of the sparse structure and communities.
- Score: 8.54401530955314
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: 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 group-like properties. In this paper, within the framework of Gaussian graphical models, we introduce a novel decomposition of the underlying graphical structure into a sparse part and low-rank diagonal blocks (non-overlapped communities). We illustrate the significance of this decomposition through two modeling perspectives and propose a three-stage estimation procedure with a fast and efficient algorithm for the identification of the sparse structure and communities. Also on the theoretical front, we establish conditions for local identifiability and extend the traditional irrepresentability condition to an adaptive form by constructing an effective norm, which ensures the consistency of model selection for the adaptive $\ell_1$ penalized estimator in the second stage. Moreover, we also provide the clustering error bound for the K-means procedure in the third stage. Extensive numerical experiments are conducted to demonstrate the superiority of the proposed method over existing approaches in estimating graph structures. Furthermore, we apply our method to the stock return data, revealing its capability to accurately identify non-overlapped community structures.
Related papers
- Bayesian Intrinsic Groupwise Image Registration: Unsupervised
Disentanglement of Anatomy and Geometry [53.645443644821306]
This article presents a general Bayesian learning framework for groupwise registration on medical images.
We propose a novel hierarchical variational auto-encoding architecture to realize the inference procedure of the latent variables.
Experiments were conducted to validate the proposed framework, including four datasets from cardiac, brain and abdominal medical images.
arXiv Detail & Related papers (2024-01-04T08:46:39Z) - Inconsistency of cross-validation for structure learning in Gaussian
graphical models [20.332261273013913]
Cross-validation to discern the structure of a Gaussian graphical model is a challenging endeavor.
We provide finite-sample bounds on the probability that the Lasso estimator for the neighborhood of a node misidentifies the neighborhood.
We conduct an empirical investigation of this inconsistency by contrasting our outcomes with other commonly used information criteria.
arXiv Detail & Related papers (2023-12-28T14:47:28Z) - Understanding and Constructing Latent Modality Structures in Multi-modal
Representation Learning [53.68371566336254]
We argue that the key to better performance lies in meaningful latent modality structures instead of perfect modality alignment.
Specifically, we design 1) a deep feature separation loss for intra-modality regularization; 2) a Brownian-bridge loss for inter-modality regularization; and 3) a geometric consistency loss for both intra- and inter-modality regularization.
arXiv Detail & Related papers (2023-03-10T14:38:49Z) - Unified Multi-View Orthonormal Non-Negative Graph Based Clustering
Framework [74.25493157757943]
We formulate a novel clustering model, which exploits the non-negative feature property and incorporates the multi-view information into a unified joint learning framework.
We also explore, for the first time, the multi-model non-negative graph-based approach to clustering data based on deep features.
arXiv Detail & Related papers (2022-11-03T08:18:27Z) - Towards Robust and Adaptive Motion Forecasting: A Causal Representation
Perspective [72.55093886515824]
We introduce a causal formalism of motion forecasting, which casts the problem as a dynamic process with three groups of latent variables.
We devise a modular architecture that factorizes the representations of invariant mechanisms and style confounders to approximate a causal graph.
Experiment results on synthetic and real datasets show that our three proposed components significantly improve the robustness and reusability of the learned motion representations.
arXiv Detail & Related papers (2021-11-29T18:59:09Z) - Amortized Probabilistic Detection of Communities in Graphs [49.46170819501234]
We propose a simple framework for amortized community detection.
We combine the expressive power of GNNs with recent methods for amortized clustering.
We evaluate several models from our framework on synthetic and real datasets.
arXiv Detail & Related papers (2020-10-29T16:18:48Z) - Parsimonious Feature Extraction Methods: Extending Robust Probabilistic
Projections with Generalized Skew-t [0.8336315962271392]
We propose a novel generalisation to the Student-t Probabilistic Principal Component methodology.
The new framework provides a more flexible approach to modelling groups of marginal tail dependence in the observation data.
The applicability of the new framework is illustrated on a data set that consists of crypto currencies with the highest market capitalisation.
arXiv Detail & Related papers (2020-09-24T05:53:41Z) - Community detection in sparse time-evolving graphs with a dynamical
Bethe-Hessian [47.82639003096941]
This article considers the problem of community detection in sparse dynamical graphs in which the community structure evolves over time.
A fast spectral algorithm based on an extension of the Bethe-Hessian matrix is proposed, which benefits from the positive correlation in the class labels and in their temporal evolution.
arXiv Detail & Related papers (2020-06-03T11:44:19Z) - Semi-Structured Distributional Regression -- Extending Structured
Additive Models by Arbitrary Deep Neural Networks and Data Modalities [0.0]
We propose a general framework to combine structured regression models and deep neural networks into a unifying network architecture.
We demonstrate the framework's efficacy in numerical experiments and illustrate its special merits in benchmarks and real-world applications.
arXiv Detail & Related papers (2020-02-13T21:01:26Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.