Graphical Transformation Models

• URL: http://arxiv.org/abs/2503.17845v2
• Date: Thu, 10 Apr 2025 12:45:22 GMT
• Title: Graphical Transformation Models
• Authors: Matthias Herp, Johannes Brachem, Michael Altenbuchinger, Thomas Kneib,
• Abstract summary: We introduce a novel approach to effectively model multivariate data with intricate marginals and complex dependency structures non-parametrically.<n>We show how to approximately regularize GTMs using a lasso penalty towards pairwise conditional independencies.<n>The model's robustness and effectiveness are validated through simulations, showcasing its ability to accurately learn parametric vine copulas.
• Score: 0.9999629695552195
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Graphical Transformation Models (GTMs) are introduced as a novel approach to effectively model multivariate data with intricate marginals and complex dependency structures non-parametrically, while maintaining interpretability through the identification of varying conditional independencies. GTMs extend multivariate transformation models by replacing the Gaussian copula with a custom-designed multivariate transformation, offering two major advantages. Firstly, GTMs can capture more complex interdependencies using penalized splines, which also provide an efficient regularization scheme. Secondly, we demonstrate how to approximately regularize GTMs using a lasso penalty towards pairwise conditional independencies, akin to Gaussian graphical models. The model's robustness and effectiveness are validated through simulations, showcasing its ability to accurately learn parametric vine copulas and identify conditional independencies. Additionally, the model is applied to a benchmark astrophysics dataset, where the GTM demonstrates favorable performance compared to non-parametric vine copulas in learning complex multivariate distributions.

Related papers

• H-AddiVortes: Heteroscedastic (Bayesian) Additive Voronoi Tessellations [0.0]
  The Heteroscedastic AddiVortes model simultaneously models the conditional mean and variance of a response variable.<n>By employing a sum-of-tessellations approach for the mean and a product-of-tessellations approach for the variance, the model provides a flexible and interpretable means to capture complex, predictor-dependent relationships.
  arXiv  Detail & Related papers  (2025-03-17T10:41:31Z)
• Multi-View Oriented GPLVM: Expressiveness and Efficiency [8.459922325396155]
  We introduce a new duality between the spectral density and the kernel function.<n>We derive a generic and expressive kernel termed Next-Gen Spectral Mixture (NG-SM) for MV-GPLVMs.<n>Our proposed method consistently outperforms state-of-the-art models in learning meaningful latent representations.
  arXiv  Detail & Related papers  (2025-02-12T09:49:25Z)
• Clusterpath Gaussian Graphical Modeling [0.0]
  We introduce the Clusterpath estimator of the Gaussian Graphical Model (CGGM) that encourages variable clustering in a data-driven way. We present a computationally efficient implementation of the CGGM estimator by using a cyclic block coordinate descent algorithm. In simulations, we show that CGGM not only matches, but oftentimes outperforms other state-of-the-art methods for variable clustering in graphical models.
  arXiv  Detail & Related papers  (2024-06-30T10:11:18Z)
• UniTST: Effectively Modeling Inter-Series and Intra-Series Dependencies for Multivariate Time Series Forecasting [98.12558945781693]
  We propose a transformer-based model UniTST containing a unified attention mechanism on the flattened patch tokens. Although our proposed model employs a simple architecture, it offers compelling performance as shown in our experiments on several datasets for time series forecasting.
  arXiv  Detail & Related papers  (2024-06-07T14:39:28Z)
• Sample Complexity Characterization for Linear Contextual MDPs [67.79455646673762]
  Contextual decision processes (CMDPs) describe a class of reinforcement learning problems in which the transition kernels and reward functions can change over time with different MDPs indexed by a context variable. CMDPs serve as an important framework to model many real-world applications with time-varying environments. We study CMDPs under two linear function approximation models: Model I with context-varying representations and common linear weights for all contexts; and Model II with common representations for all contexts and context-varying linear weights.
  arXiv  Detail & Related papers  (2024-02-05T03:25:04Z)
• Online Variational Sequential Monte Carlo [49.97673761305336]
  We build upon the variational sequential Monte Carlo (VSMC) method, which provides computationally efficient and accurate model parameter estimation and Bayesian latent-state inference. Online VSMC is capable of performing efficiently, entirely on-the-fly, both parameter estimation and particle proposal adaptation.
  arXiv  Detail & Related papers  (2023-12-19T21:45:38Z)
• Heterogeneous Multi-Task Gaussian Cox Processes [61.67344039414193]
  We present a novel extension of multi-task Gaussian Cox processes for modeling heterogeneous correlated tasks jointly. A MOGP prior over the parameters of the dedicated likelihoods for classification, regression and point process tasks can facilitate sharing of information between heterogeneous tasks. We derive a mean-field approximation to realize closed-form iterative updates for estimating model parameters.
  arXiv  Detail & Related papers  (2023-08-29T15:01:01Z)
• T-LoHo: A Bayesian Regularization Model for Structured Sparsity and Smoothness on Graphs [0.0]
  In graph-structured data, structured sparsity and smoothness tend to cluster together. We propose a new prior for high dimensional parameters with graphical relations. We use it to detect structured sparsity and smoothness simultaneously.
  arXiv  Detail & Related papers  (2021-07-06T10:10:03Z)
• Joint Network Topology Inference via Structured Fusion Regularization [70.30364652829164]
  Joint network topology inference represents a canonical problem of learning multiple graph Laplacian matrices from heterogeneous graph signals. We propose a general graph estimator based on a novel structured fusion regularization. We show that the proposed graph estimator enjoys both high computational efficiency and rigorous theoretical guarantee.
  arXiv  Detail & Related papers  (2021-03-05T04:42:32Z)
• Probabilistic Circuits for Variational Inference in Discrete Graphical Models [101.28528515775842]
  Inference in discrete graphical models with variational methods is difficult. Many sampling-based methods have been proposed for estimating Evidence Lower Bound (ELBO) We propose a new approach that leverages the tractability of probabilistic circuit models, such as Sum Product Networks (SPN) We show that selective-SPNs are suitable as an expressive variational distribution, and prove that when the log-density of the target model is aweighted the corresponding ELBO can be computed analytically.
  arXiv  Detail & Related papers  (2020-10-22T05:04:38Z)

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.