An Advance on Variable Elimination with Applications to Tensor-Based Computation

• URL: http://arxiv.org/abs/2002.09320v1
• Date: Fri, 21 Feb 2020 14:17:44 GMT
• Title: An Advance on Variable Elimination with Applications to Tensor-Based Computation
• Authors: Adnan Darwiche
• Abstract summary: We present new results on the classical algorithm of variable elimination, which underlies many algorithms including for probabilistic inference. The results relate to exploiting functional dependencies, allowing one to perform inference and learning efficiently on models that have very large treewidth.
• Score: 11.358487655918676
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present new results on the classical algorithm of variable elimination, which underlies many algorithms including for probabilistic inference. The results relate to exploiting functional dependencies, allowing one to perform inference and learning efficiently on models that have very large treewidth. The highlight of the advance is that it works with standard (dense) factors, without the need for sparse factors or techniques based on knowledge compilation that are commonly utilized. This is significant as it permits a direct implementation of the improved variable elimination algorithm using tensors and their operations, leading to extremely efficient implementations especially when learning model parameters. Moreover, the proposed technique does not require knowledge of the specific functional dependencies, only that they exist, so can be used when learning these dependencies. We illustrate the efficacy of our proposed algorithm by compiling Bayesian network queries into tensor graphs and then learning their parameters from labeled data using a standard tool for tensor computation.

Related papers

• Knowledge Composition using Task Vectors with Learned Anisotropic Scaling [51.4661186662329]
  We introduce aTLAS, an algorithm that linearly combines parameter blocks with different learned coefficients, resulting in anisotropic scaling at the task vector level. We show that such linear combinations explicitly exploit the low intrinsicity of pre-trained models, with only a few coefficients being the learnable parameters. We demonstrate the effectiveness of our method in task arithmetic, few-shot recognition and test-time adaptation, with supervised or unsupervised objectives.
  arXiv  Detail & Related papers  (2024-07-03T07:54:08Z)
• Efficient and Generalizable Certified Unlearning: A Hessian-free Recollection Approach [8.875278412741695]
  Machine unlearning strives to uphold the data owners' right to be forgotten by enabling models to selectively forget specific data. We develop an algorithm that achieves near-instantaneous unlearning as it only requires a vector addition operation.
  arXiv  Detail & Related papers  (2024-04-02T07:54:18Z)
• Surprisal Driven $k$-NN for Robust and Interpretable Nonparametric Learning [1.4293924404819704]
  We shed new light on the traditional nearest neighbors algorithm from the perspective of information theory. We propose a robust and interpretable framework for tasks such as classification, regression, density estimation, and anomaly detection using a single model. Our work showcases the architecture's versatility by achieving state-of-the-art results in classification and anomaly detection.
  arXiv  Detail & Related papers  (2023-11-17T00:35:38Z)
• Equation Discovery with Bayesian Spike-and-Slab Priors and Efficient Kernels [57.46832672991433]
  We propose a novel equation discovery method based on Kernel learning and BAyesian Spike-and-Slab priors (KBASS) We use kernel regression to estimate the target function, which is flexible, expressive, and more robust to data sparsity and noises. We develop an expectation-propagation expectation-maximization algorithm for efficient posterior inference and function estimation.
  arXiv  Detail & Related papers  (2023-10-09T03:55:09Z)
• A Generic Performance Model for Deep Learning in a Distributed Environment [0.7829352305480285]
  We propose a generic performance model of an application in a distributed environment with a generic expression of the application execution time. We have evaluated the proposed model on three deep learning frameworks (i.e., MXnet, and Pytorch)
  arXiv  Detail & Related papers  (2023-05-19T13:30:34Z)
• Equivariance with Learned Canonicalization Functions [77.32483958400282]
  We show that learning a small neural network to perform canonicalization is better than using predefineds. Our experiments show that learning the canonicalization function is competitive with existing techniques for learning equivariant functions across many tasks.
  arXiv  Detail & Related papers  (2022-11-11T21:58:15Z)
• HyperImpute: Generalized Iterative Imputation with Automatic Model Selection [77.86861638371926]
  We propose a generalized iterative imputation framework for adaptively and automatically configuring column-wise models. We provide a concrete implementation with out-of-the-box learners, simulators, and interfaces.
  arXiv  Detail & Related papers  (2022-06-15T19:10:35Z)
• Simple Stochastic and Online Gradient DescentAlgorithms for Pairwise Learning [65.54757265434465]
  Pairwise learning refers to learning tasks where the loss function depends on a pair instances. Online descent (OGD) is a popular approach to handle streaming data in pairwise learning. In this paper, we propose simple and online descent to methods for pairwise learning.
  arXiv  Detail & Related papers  (2021-11-23T18:10:48Z)
• Neural Active Learning with Performance Guarantees [37.16062387461106]
  We investigate the problem of active learning in the streaming setting in non-parametric regimes, where the labels are generated from a class of functions on which we make no assumptions whatsoever. We rely on recently proposed Neural Tangent Kernel (NTK) approximation tools to construct a suitable neural embedding that determines the feature space the algorithm operates on and the learned model computed atop.
  arXiv  Detail & Related papers  (2021-06-06T20:44:23Z)
• Learning Generalized Relational Heuristic Networks for Model-Agnostic Planning [29.714818991696088]
  This paper develops a new approach for learning generalizeds in the absence of symbolic action models. It uses an abstract state representation to facilitate data efficient, generalizable learning.
  arXiv  Detail & Related papers  (2020-07-10T06:08:28Z)
• AdaS: Adaptive Scheduling of Stochastic Gradients [50.80697760166045]
  We introduce the notions of textit"knowledge gain" and textit"mapping condition" and propose a new algorithm called Adaptive Scheduling (AdaS) Experimentation reveals that, using the derived metrics, AdaS exhibits: (a) faster convergence and superior generalization over existing adaptive learning methods; and (b) lack of dependence on a validation set to determine when to stop training.
  arXiv  Detail & Related papers  (2020-06-11T16:36:31Z)

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.