Distribution Learning Meets Graph Structure Sampling

• URL: http://arxiv.org/abs/2405.07914v1
• Date: Mon, 13 May 2024 16:47:05 GMT
• Title: Distribution Learning Meets Graph Structure Sampling
• Authors: Arnab Bhattacharyya, Sutanu Gayen, Philips George John, Sayantan Sen, N. V. Vinodchandran,
• Abstract summary: This work establishes a novel link between PAC-learning high-dimensional models and the task of (optimal) counting and sampling of graph structures. We show that the average regret incurred by the forecaster's predictions can be used to bound the expected KL divergence between P and the predictions. Known regret bounds for EWA and RWM then yield new sample complexity for learning Bayes nets.
• Score: 10.095280456019367
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This work establishes a novel link between the problem of PAC-learning high-dimensional graphical models and the task of (efficient) counting and sampling of graph structures, using an online learning framework. We observe that if we apply the exponentially weighted average (EWA) or randomized weighted majority (RWM) forecasters on a sequence of samples from a distribution P using the log loss function, the average regret incurred by the forecaster's predictions can be used to bound the expected KL divergence between P and the predictions. Known regret bounds for EWA and RWM then yield new sample complexity bounds for learning Bayes nets. Moreover, these algorithms can be made computationally efficient for several interesting classes of Bayes nets. Specifically, we give a new sample-optimal and polynomial time learning algorithm with respect to trees of unknown structure and the first polynomial sample and time algorithm for learning with respect to Bayes nets over a given chordal skeleton.

Related papers

• Supervised Score-Based Modeling by Gradient Boosting [49.556736252628745]
  We propose a Supervised Score-based Model (SSM) which can be viewed as a gradient boosting algorithm combining score matching. We provide a theoretical analysis of learning and sampling for SSM to balance inference time and prediction accuracy. Our model outperforms existing models in both accuracy and inference time.
  arXiv  Detail & Related papers  (2024-11-02T07:06:53Z)
• Collapsed Inference for Bayesian Deep Learning [36.1725075097107]
  We introduce a novel collapsed inference scheme that performs Bayesian model averaging using collapsed samples. A collapsed sample represents uncountably many models drawn from the approximate posterior. Our proposed use of collapsed samples achieves a balance between scalability and accuracy.
  arXiv  Detail & Related papers  (2023-06-16T08:34:42Z)
• Less is More: Rethinking Few-Shot Learning and Recurrent Neural Nets [2.824895388993495]
  We provide theoretical guarantees for reliable learning under the information-theoretic AEP. We then focus on a highly efficient recurrent neural net (RNN) framework and propose a reduced-entropy algorithm for few-shot learning. Our experimental results demonstrate significant potential for improving learning models' sample efficiency, generalization, and time complexity.
  arXiv  Detail & Related papers  (2022-09-28T17:33:11Z)
• Scalable computation of prediction intervals for neural networks via matrix sketching [79.44177623781043]
  Existing algorithms for uncertainty estimation require modifying the model architecture and training procedure. This work proposes a new algorithm that can be applied to a given trained neural network and produces approximate prediction intervals.
  arXiv  Detail & Related papers  (2022-05-06T13:18:31Z)
• Bayesian Structure Learning with Generative Flow Networks [85.84396514570373]
  In Bayesian structure learning, we are interested in inferring a distribution over the directed acyclic graph (DAG) from data. Recently, a class of probabilistic models, called Generative Flow Networks (GFlowNets), have been introduced as a general framework for generative modeling. We show that our approach, called DAG-GFlowNet, provides an accurate approximation of the posterior over DAGs.
  arXiv  Detail & Related papers  (2022-02-28T15:53:10Z)
• Multi-Sample Online Learning for Spiking Neural Networks based on Generalized Expectation Maximization [42.125394498649015]
  Spiking Neural Networks (SNNs) capture some of the efficiency of biological brains by processing through binary neural dynamic activations. This paper proposes to leverage multiple compartments that sample independent spiking signals while sharing synaptic weights. The key idea is to use these signals to obtain more accurate statistical estimates of the log-likelihood training criterion, as well as of its gradient.
  arXiv  Detail & Related papers  (2021-02-05T16:39:42Z)
• Expectation propagation on the diluted Bayesian classifier [0.0]
  We introduce a statistical mechanics inspired strategy that addresses the problem of sparse feature selection in the context of binary classification. A computational scheme known as expectation propagation (EP) is used to train a continuous-weights perceptron learning a classification rule. EP is a robust and competitive algorithm in terms of variable selection properties, estimation accuracy and computational complexity.
  arXiv  Detail & Related papers  (2020-09-20T23:59:44Z)
• Bandit Samplers for Training Graph Neural Networks [63.17765191700203]
  Several sampling algorithms with variance reduction have been proposed for accelerating the training of Graph Convolution Networks (GCNs) These sampling algorithms are not applicable to more general graph neural networks (GNNs) where the message aggregator contains learned weights rather than fixed weights, such as Graph Attention Networks (GAT)
  arXiv  Detail & Related papers  (2020-06-10T12:48:37Z)
• Learned Factor Graphs for Inference from Stationary Time Sequences [107.63351413549992]
  We propose a framework that combines model-based algorithms and data-driven ML tools for stationary time sequences. neural networks are developed to separately learn specific components of a factor graph describing the distribution of the time sequence. We present an inference algorithm based on learned stationary factor graphs, which learns to implement the sum-product scheme from labeled data.
  arXiv  Detail & Related papers  (2020-06-05T07:06:19Z)
• Belief Propagation Reloaded: Learning BP-Layers for Labeling Problems [83.98774574197613]
  We take one of the simplest inference methods, a truncated max-product Belief propagation, and add what is necessary to make it a proper component of a deep learning model. This BP-Layer can be used as the final or an intermediate block in convolutional neural networks (CNNs) The model is applicable to a range of dense prediction problems, is well-trainable and provides parameter-efficient and robust solutions in stereo, optical flow and semantic segmentation.
  arXiv  Detail & Related papers  (2020-03-13T13:11:35Z)

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.