Expressivity of Hidden Markov Chains vs. Recurrent Neural Networks from a system theoretic viewpoint

• URL: http://arxiv.org/abs/2208.08175v1
• Date: Wed, 17 Aug 2022 09:23:41 GMT
• Title: Expressivity of Hidden Markov Chains vs. Recurrent Neural Networks from a system theoretic viewpoint
• Authors: Fran\c{c}ois Desbouvries (TSP), Yohan Petetin (TSP), Achille Sala\"un
• Abstract summary: We first consider Hidden Markov Chains (HMC) and Recurrent Neural Networks (RNN) as generative models. We embed both structures in a common generative unified model (GUM)
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Hidden Markov Chains (HMC) and Recurrent Neural Networks (RNN) are two well known tools for predicting time series. Even though these solutions were developed independently in distinct communities, they share some similarities when considered as probabilistic structures. So in this paper we first consider HMC and RNN as generative models, and we embed both structures in a common generative unified model (GUM). We next address a comparative study of the expressivity of these models. To that end we assume that the models are furthermore linear and Gaussian. The probability distributions produced by these models are characterized by structured covariance series, and as a consequence expressivity reduces to comparing sets of structured covariance series, which enables us to call for stochastic realization theory (SRT). We finally provide conditions under which a given covariance series can be realized by a GUM, an HMC or an RNN.

Related papers

• Generalization of Graph Neural Networks is Robust to Model Mismatch [84.01980526069075]
  Graph neural networks (GNNs) have demonstrated their effectiveness in various tasks supported by their generalization capabilities. In this paper, we examine GNNs that operate on geometric graphs generated from manifold models. Our analysis reveals the robustness of the GNN generalization in the presence of such model mismatch.
  arXiv  Detail & Related papers  (2024-08-25T16:00:44Z)
• Satellite Anomaly Detection Using Variance Based Genetic Ensemble of Neural Networks [7.848121055546167]
  We use an efficient ensemble of the predictions from multiple Recurrent Neural Networks (RNNs) For prediction, each RNN is guided by a Genetic Algorithm (GA) which constructs the optimal structure for each RNN model. This paper uses the Monte Carlo (MC) dropout as an approximation version of BNNs.
  arXiv  Detail & Related papers  (2023-02-10T22:09:00Z)
• Triadic Temporal Exponential Random Graph Models (TTERGM) [1.3806306909199906]
  TERGMs can be used to infer the temporal pattern of edge formation and elimination in complex networks. We show that our TTERGM model achieves improved fidelity and more accurate predictions compared to several benchmark methods on GitHub network data.
  arXiv  Detail & Related papers  (2022-11-29T14:07:29Z)
• 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)
• Continual Learning with Fully Probabilistic Models [70.3497683558609]
  We present an approach for continual learning based on fully probabilistic (or generative) models of machine learning. We propose a pseudo-rehearsal approach using a Gaussian Mixture Model (GMM) instance for both generator and classifier functionalities. We show that GMR achieves state-of-the-art performance on common class-incremental learning problems at very competitive time and memory complexity.
  arXiv  Detail & Related papers  (2021-04-19T12:26:26Z)
• Anomaly Detection of Time Series with Smoothness-Inducing Sequential Variational Auto-Encoder [59.69303945834122]
  We present a Smoothness-Inducing Sequential Variational Auto-Encoder (SISVAE) model for robust estimation and anomaly detection of time series. Our model parameterizes mean and variance for each time-stamp with flexible neural networks. We show the effectiveness of our model on both synthetic datasets and public real-world benchmarks.
  arXiv  Detail & Related papers  (2021-02-02T06:15:15Z)
• Improving the Reconstruction of Disentangled Representation Learners via Multi-Stage Modeling [54.94763543386523]
  Current autoencoder-based disentangled representation learning methods achieve disentanglement by penalizing the ( aggregate) posterior to encourage statistical independence of the latent factors. We present a novel multi-stage modeling approach where the disentangled factors are first learned using a penalty-based disentangled representation learning method. Then, the low-quality reconstruction is improved with another deep generative model that is trained to model the missing correlated latent variables.
  arXiv  Detail & Related papers  (2020-10-25T18:51:15Z)
• Variational Mixture of Normalizing Flows [0.0]
  Deep generative models, such as generative adversarial networks autociteGAN, variational autoencoders autocitevaepaper, and their variants, have seen wide adoption for the task of modelling complex data distributions. Normalizing flows have overcome this limitation by leveraging the change-of-suchs formula for probability density functions. The present work overcomes this by using normalizing flows as components in a mixture model and devising an end-to-end training procedure for such a model.
  arXiv  Detail & Related papers  (2020-09-01T17:20:08Z)
• Consistency of Spectral Clustering on Hierarchical Stochastic Block Models [5.983753938303726]
  We study the hierarchy of communities in real-world networks under a generic block model. We prove the strong consistency of this method under a wide range of model parameters. Unlike most of existing work, our theory covers multiscale networks where the connection probabilities may differ by orders of magnitude.
  arXiv  Detail & Related papers  (2020-04-30T01:08:59Z)
• GANs with Conditional Independence Graphs: On Subadditivity of Probability Divergences [70.30467057209405]
  Generative Adversarial Networks (GANs) are modern methods to learn the underlying distribution of a data set. GANs are designed in a model-free fashion where no additional information about the underlying distribution is available. We propose a principled design of a model-based GAN that uses a set of simple discriminators on the neighborhoods of the Bayes-net/MRF.
  arXiv  Detail & Related papers  (2020-03-02T04:31:22Z)
• Struct-MMSB: Mixed Membership Stochastic Blockmodels with Interpretable Structured Priors [13.712395104755783]
  Mixed membership blockmodel (MMSB) is a popular framework for community detection and network generation. We present a flexible MMSB model, textitStruct-MMSB, that uses a recently developed statistical relational learning model, hinge-loss Markov random fields (HL-MRFs) Our model is capable of learning latent characteristics in real-world networks via meaningful latent variables encoded as a complex combination of observed features and membership distributions.
  arXiv  Detail & Related papers  (2020-02-21T19:32:32Z)

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.