Under-Counted Tensor Completion with Neural Incorporation of Attributes

• URL: http://arxiv.org/abs/2306.03273v1
• Date: Mon, 5 Jun 2023 21:45:23 GMT
• Title: Under-Counted Tensor Completion with Neural Incorporation of Attributes
• Authors: Shahana Ibrahim, Xiao Fu, Rebecca Hutchinson, Eugene Seo
• Abstract summary: Under-counted tensor completion (UC-TC) is well-motivated for many data analytics tasks. A low-rank Poisson tensor model with an expressive unknown nonlinear side information extractor is proposed for under-counted multi-aspect data. A joint low-rank tensor completion and neural network learning algorithm is designed to recover the model. To our best knowledge, the result is the first to offer theoretical supports for under-counted multi-aspect data completion.
• Score: 18.21165063142917
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Systematic under-counting effects are observed in data collected across many disciplines, e.g., epidemiology and ecology. Under-counted tensor completion (UC-TC) is well-motivated for many data analytics tasks, e.g., inferring the case numbers of infectious diseases at unobserved locations from under-counted case numbers in neighboring regions. However, existing methods for similar problems often lack supports in theory, making it hard to understand the underlying principles and conditions beyond empirical successes. In this work, a low-rank Poisson tensor model with an expressive unknown nonlinear side information extractor is proposed for under-counted multi-aspect data. A joint low-rank tensor completion and neural network learning algorithm is designed to recover the model. Moreover, the UC-TC formulation is supported by theoretical analysis showing that the fully counted entries of the tensor and each entry's under-counting probability can be provably recovered from partial observations -- under reasonable conditions. To our best knowledge, the result is the first to offer theoretical supports for under-counted multi-aspect data completion. Simulations and real-data experiments corroborate the theoretical claims.

Related papers

• Understanding Forgetting in Continual Learning with Linear Regression [21.8755265936716]
  Continual learning, focused on sequentially learning multiple tasks, has gained significant attention recently. We provide a general theoretical analysis of forgetting in the linear regression model via Gradient Descent. We demonstrate that, given a sufficiently large data size, the arrangement of tasks in a sequence, where tasks with larger eigenvalues in their population data covariance matrices are trained later, tends to result in increased forgetting.
  arXiv  Detail & Related papers  (2024-05-27T18:33:37Z)
• Seeing Unseen: Discover Novel Biomedical Concepts via Geometry-Constrained Probabilistic Modeling [53.7117640028211]
  We present a geometry-constrained probabilistic modeling treatment to resolve the identified issues. We incorporate a suite of critical geometric properties to impose proper constraints on the layout of constructed embedding space. A spectral graph-theoretic method is devised to estimate the number of potential novel classes.
  arXiv  Detail & Related papers  (2024-03-02T00:56:05Z)
• Deep Learning With DAGs [5.199807441687141]
  We introduce causal-graphical normalizing flows (cGNFs) to empirically evaluate theories represented as directed acyclic graphs (DAGs) Unlike conventional approaches, cGNFs model the full joint distribution of the data according to a DAG supplied by the analyst.
  arXiv  Detail & Related papers  (2024-01-12T19:35:54Z)
• On the Dynamics Under the Unhinged Loss and Beyond [104.49565602940699]
  We introduce the unhinged loss, a concise loss function, that offers more mathematical opportunities to analyze closed-form dynamics. The unhinged loss allows for considering more practical techniques, such as time-vary learning rates and feature normalization.
  arXiv  Detail & Related papers  (2023-12-13T02:11:07Z)
• Joint Edge-Model Sparse Learning is Provably Efficient for Graph Neural Networks [89.28881869440433]
  This paper provides the first theoretical characterization of joint edge-model sparse learning for graph neural networks (GNNs) It proves analytically that both sampling important nodes and pruning neurons with the lowest-magnitude can reduce the sample complexity and improve convergence without compromising the test accuracy.
  arXiv  Detail & Related papers  (2023-02-06T16:54:20Z)
• Transfer learning for tensor Gaussian graphical models [0.6767885381740952]
  We propose a transfer learning framework for tensor GGMs, which takes full advantage of informative auxiliary domains. Our theoretical analysis shows substantial improvement of estimation errors and variable selection consistency.
  arXiv  Detail & Related papers  (2022-11-17T07:53:07Z)
• Generalization Guarantee of Training Graph Convolutional Networks with Graph Topology Sampling [83.77955213766896]
  Graph convolutional networks (GCNs) have recently achieved great empirical success in learning graphstructured data. To address its scalability issue, graph topology sampling has been proposed to reduce the memory and computational cost of training Gs. This paper provides first theoretical justification of graph topology sampling in training (up to) three-layer GCNs.
  arXiv  Detail & Related papers  (2022-07-07T21:25:55Z)
• Learnability of Competitive Threshold Models [11.005966612053262]
  We study the learnability of the competitive threshold model from a theoretical perspective. We demonstrate how competitive threshold models can be seamlessly simulated by artificial neural networks.
  arXiv  Detail & Related papers  (2022-05-08T01:11:51Z)
• Generalization of Neural Combinatorial Solvers Through the Lens of Adversarial Robustness [68.97830259849086]
  Most datasets only capture a simpler subproblem and likely suffer from spurious features. We study adversarial robustness - a local generalization property - to reveal hard, model-specific instances and spurious features. Unlike in other applications, where perturbation models are designed around subjective notions of imperceptibility, our perturbation models are efficient and sound. Surprisingly, with such perturbations, a sufficiently expressive neural solver does not suffer from the limitations of the accuracy-robustness trade-off common in supervised learning.
  arXiv  Detail & Related papers  (2021-10-21T07:28:11Z)
• The Interplay Between Implicit Bias and Benign Overfitting in Two-Layer Linear Networks [51.1848572349154]
  neural network models that perfectly fit noisy data can generalize well to unseen test data. We consider interpolating two-layer linear neural networks trained with gradient flow on the squared loss and derive bounds on the excess risk.
  arXiv  Detail & Related papers  (2021-08-25T22:01:01Z)
• Learning and Generalization in Overparameterized Normalizing Flows [13.074242275886977]
  Normalizing flows (NFs) constitute an important class of models in unsupervised learning. We provide theoretical and empirical evidence that for a class of NFs containing most of the existing NF models, overparametrization hurts training. We prove that unconstrained NFs can efficiently learn any reasonable data distribution under minimal assumptions when the underlying network is overparametrized.
  arXiv  Detail & Related papers  (2021-06-19T17:11:42Z)

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.