A Bayesian Approach to Block-Term Tensor Decomposition Model Selection and Computation

• URL: http://arxiv.org/abs/2101.02931v1
• Date: Fri, 8 Jan 2021 09:37:21 GMT
• Title: A Bayesian Approach to Block-Term Tensor Decomposition Model Selection and Computation
• Authors: Paris V. Giampouras, Athanasios A. Rontogiannis, Eleftherios Kofidis
• Abstract summary: The so-called block-term decomposition (BTD) tensor model, especially in its rank-$(L_r,L_r,1)$ version, has been recently receiving increasing attention. The challenge of estimating the BTD model structure, namely the number of block terms and their individual ranks, has only recently started to attract significant attention. A Bayesian approach is taken to addressing the problem of rank-$(L_r,L_r,1)$ BTD model selection and computation, based on the idea of imposing column sparsity emphjointly on the
• Score: 10.91885508254207
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The so-called block-term decomposition (BTD) tensor model, especially in its rank-$(L_r,L_r,1)$ version, has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of \emph{blocks} of rank higher than one, a scenario encountered in numerous and diverse applications. Its uniqueness and approximation have thus been thoroughly studied. Nevertheless, the challenging problem of estimating the BTD model structure, namely the number of block terms and their individual ranks, has only recently started to attract significant attention. In this work, a Bayesian approach is taken to addressing the problem of rank-$(L_r,L_r,1)$ BTD model selection and computation, based on the idea of imposing column sparsity \emph{jointly} on the factors and in a \emph{hierarchical} manner and estimating the ranks as the numbers of factor columns of non-negligible energy. Using variational inference in the proposed probabilistic model results in an iterative algorithm that comprises closed-form updates. Its Bayesian nature completely avoids the ubiquitous in regularization-based methods task of hyper-parameter tuning. Simulation results with synthetic data are reported, which demonstrate the effectiveness of the proposed scheme in terms of both rank estimation and model fitting.

Related papers

• Unveiling the Statistical Foundations of Chain-of-Thought Prompting Methods [59.779795063072655]
  Chain-of-Thought (CoT) prompting and its variants have gained popularity as effective methods for solving multi-step reasoning problems. We analyze CoT prompting from a statistical estimation perspective, providing a comprehensive characterization of its sample complexity.
  arXiv  Detail & Related papers  (2024-08-25T04:07:18Z)
• An Optimization-based Deep Equilibrium Model for Hyperspectral Image Deconvolution with Convergence Guarantees [71.57324258813675]
  We propose a novel methodology for addressing the hyperspectral image deconvolution problem. A new optimization problem is formulated, leveraging a learnable regularizer in the form of a neural network. The derived iterative solver is then expressed as a fixed-point calculation problem within the Deep Equilibrium framework.
  arXiv  Detail & Related papers  (2023-06-10T08:25:16Z)
• Estimating Higher-Order Mixed Memberships via the $\ell_{2,\infty}$ Tensor Perturbation Bound [8.521132000449766]
  We propose the tensor mixed-membership blockmodel, a generalization of the tensor blockmodel. We establish the identifiability of our model and propose a computationally efficient estimation procedure. We apply our methodology to real and simulated data, demonstrating some effects not identifiable from the model with discrete community memberships.
  arXiv  Detail & Related papers  (2022-12-16T18:32:20Z)
• A Variational Inference Approach to Inverse Problems with Gamma Hyperpriors [60.489902135153415]
  This paper introduces a variational iterative alternating scheme for hierarchical inverse problems with gamma hyperpriors. The proposed variational inference approach yields accurate reconstruction, provides meaningful uncertainty quantification, and is easy to implement.
  arXiv  Detail & Related papers  (2021-11-26T06:33:29Z)
• Efficient semidefinite bounds for multi-label discrete graphical models [6.226454551201676]
  One of the main queries on such models is to identify the SDPWCSP Function on Cost of a Posteri (MAP) Networks. We consider a traditional dualized constraint approach and a dedicated dedicated SDP/Monteiro style method based on row-by-row updates.
  arXiv  Detail & Related papers  (2021-11-24T13:38:34Z)
• Exact Clustering in Tensor Block Model: Statistical Optimality and Computational Limit [10.8145995157397]
  High-order clustering aims to identify heterogeneous substructure in multiway dataset. Non- computation and nature of the problem poses significant challenges in both statistics and statistics.
  arXiv  Detail & Related papers  (2020-12-18T00:48:27Z)
• Goal-directed Generation of Discrete Structures with Conditional Generative Models [85.51463588099556]
  We introduce a novel approach to directly optimize a reinforcement learning objective, maximizing an expected reward. We test our methodology on two tasks: generating molecules with user-defined properties and identifying short python expressions which evaluate to a given target value.
  arXiv  Detail & Related papers  (2020-10-05T20:03:13Z)
• Slice Sampling for General Completely Random Measures [74.24975039689893]
  We present a novel Markov chain Monte Carlo algorithm for posterior inference that adaptively sets the truncation level using auxiliary slice variables. The efficacy of the proposed algorithm is evaluated on several popular nonparametric models.
  arXiv  Detail & Related papers  (2020-06-24T17:53:53Z)
• Consistent Second-Order Conic Integer Programming for Learning Bayesian Networks [2.7473982588529653]
  We study the problem of learning the sparse DAG structure of a BN from continuous observational data. The optimal solution to this mathematical program is known to have desirable statistical properties under certain conditions. We propose a concrete early stopping criterion to terminate the branch-and-bound process in order to obtain a near-optimal solution.
  arXiv  Detail & Related papers  (2020-05-29T00:13:15Z)
• Supervised Learning for Non-Sequential Data: A Canonical Polyadic Decomposition Approach [85.12934750565971]
  Efficient modelling of feature interactions underpins supervised learning for non-sequential tasks. To alleviate this issue, it has been proposed to implicitly represent the model parameters as a tensor. For enhanced expressiveness, we generalize the framework to allow feature mapping to arbitrarily high-dimensional feature vectors.
  arXiv  Detail & Related papers  (2020-01-27T22:38:40Z)

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.