On the Identifiability of Switching Dynamical Systems

• URL: http://arxiv.org/abs/2305.15925v4
• Date: Tue, 4 Jun 2024 14:28:29 GMT
• Title: On the Identifiability of Switching Dynamical Systems
• Abstract summary: identifiability of latent variable models has received increasing attention due to its relevance in interpretability and out-of-distribution generalisation. We study the identifiability of Switching Dynamical Systems, taking an initial step toward extending identifiability analysis to sequential latent variable models.
• Score: 34.514858559727266
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The identifiability of latent variable models has received increasing attention due to its relevance in interpretability and out-of-distribution generalisation. In this work, we study the identifiability of Switching Dynamical Systems, taking an initial step toward extending identifiability analysis to sequential latent variable models. We first prove the identifiability of Markov Switching Models, which commonly serve as the prior distribution for the continuous latent variables in Switching Dynamical Systems. We present identification conditions for first-order Markov dependency structures, whose transition distribution is parametrised via non-linear Gaussians. We then establish the identifiability of the latent variables and non-linear mappings in Switching Dynamical Systems up to affine transformations, by leveraging identifiability analysis techniques from identifiable deep latent variable models. We finally develop estimation algorithms for identifiable Switching Dynamical Systems. Throughout empirical studies, we demonstrate the practicality of identifiable Switching Dynamical Systems for segmenting high-dimensional time series such as videos, and showcase the use of identifiable Markov Switching Models for regime-dependent causal discovery in climate data.

Related papers

• Conditionally Identifiable Latent Representation for Multivariate Time Series with Structural Dynamics [9.736137697615003]
  We show that factors are identifiable up to permutation and component-wise affine (or monotone invertible) transformations.<n>We demonstrate improved factor recovery on synthetic data, stable intervention accuracy on synthetic SCMs, and competitive probabilistic forecasting on real-world benchmarks.
  arXiv  Detail & Related papers  (2026-03-24T07:35:27Z)
• Causal Representation Meets Stochastic Modeling under Generic Geometry [49.24293444627916]
  We develop causal representation learning for continuous-time latent point processes.<n>We develop MUTATE, an identifiable variational autoencoder framework with a time-adaptive transition module.<n>Across simulated and empirical studies, we find that MUTATE can effectively answer scientific questions.
  arXiv  Detail & Related papers  (2026-02-04T20:40:53Z)
• On the Identifiability of Regime-Switching Models with Multi-Lag Dependencies [42.274922469778545]
  We develop a general theoretical framework for multi-lag Regime-Switching Models (RSMs)<n>We prove identifiability of both the number of regimes and the multi-lag transitions in a nonlinear-Gaussian setting.<n>Our results hold in a fully unsupervised setting through architectural and noise assumptions.
  arXiv  Detail & Related papers  (2026-01-06T15:12:39Z)
• Identifiability Analysis of Linear ODE Systems with Hidden Confounders [45.14890063421295]
  This paper presents a systematic analysis of identifiability in linear ODE systems incorporating hidden confounders. In the first case, latent confounders exhibit no causal relationships, yet their evolution adheres to specific forms. Subsequently, we extend this analysis to encompass scenarios where hidden confounders exhibit causal dependencies.
  arXiv  Detail & Related papers  (2024-10-29T10:15:56Z)
• Identifiable Representation and Model Learning for Latent Dynamic Systems [0.0]
  We study the problem of identifiable representation and model learning for latent dynamic systems. We prove that, for linear or affine nonlinear latent dynamic systems, it is possible to identify the representations up to scaling and determine the models up to some simple transformations.
  arXiv  Detail & Related papers  (2024-10-23T13:55:42Z)
• A Poisson-Gamma Dynamic Factor Model with Time-Varying Transition Dynamics [51.147876395589925]
  A non-stationary PGDS is proposed to allow the underlying transition matrices to evolve over time. A fully-conjugate and efficient Gibbs sampler is developed to perform posterior simulation. Experiments show that, in comparison with related models, the proposed non-stationary PGDS achieves improved predictive performance.
  arXiv  Detail & Related papers  (2024-02-26T04:39:01Z)
• An Interventional Perspective on Identifiability in Gaussian LTI Systems with Independent Component Analysis [44.892642197610215]
  We show that in Gaussian Linear Time-Invariant (LTI) systems, the system parameters can be identified by introducing diverse intervention signals. We show that Hidden Markov Models, in general, and (Gaussian) LTI systems, fulfil a generalization of the Causal de Finetti theorem with continuous parameters.
  arXiv  Detail & Related papers  (2023-11-29T19:51:35Z)
• Machine Learning for the identification of phase-transitions in interacting agent-based systems: a Desai-Zwanzig example [0.0]
  We propose a data-driven framework that pinpoints phase transitions for an agent-based model in its mean-field limit. To this end, we use the manifold learning algorithm Maps to identify a parsimonious set of data-driven latent variables. We then utilize a deep learning framework to obtain a conformal reparametrization of the data-driven coordinates.
  arXiv  Detail & Related papers  (2023-10-29T15:07:08Z)
• Hybrid hidden Markov LSTM for short-term traffic flow prediction [0.0]
  We propose a hybrid hidden Markov-LSTM model that is capable of learning complementary features in traffic data. Results indicate significant performance gains in using hybrid architecture compared to conventional methods.
  arXiv  Detail & Related papers  (2023-07-11T00:56:44Z)
• Score-based Causal Representation Learning with Interventions [54.735484409244386]
  This paper studies the causal representation learning problem when latent causal variables are observed indirectly. The objectives are: (i) recovering the unknown linear transformation (up to scaling) and (ii) determining the directed acyclic graph (DAG) underlying the latent variables.
  arXiv  Detail & Related papers  (2023-01-19T18:39:48Z)
• Topographic VAEs learn Equivariant Capsules [84.33745072274942]
  We introduce the Topographic VAE: a novel method for efficiently training deep generative models with topographically organized latent variables. We show that such a model indeed learns to organize its activations according to salient characteristics such as digit class, width, and style on MNIST. We demonstrate approximate equivariance to complex transformations, expanding upon the capabilities of existing group equivariant neural networks.
  arXiv  Detail & Related papers  (2021-09-03T09:25:57Z)
• Estimation of Switched Markov Polynomial NARX models [75.91002178647165]
  We identify a class of models for hybrid dynamical systems characterized by nonlinear autoregressive (NARX) components. The proposed approach is demonstrated on a SMNARX problem composed by three nonlinear sub-models with specific regressors.
  arXiv  Detail & Related papers  (2020-09-29T15:00:47Z)
• Euclideanizing Flows: Diffeomorphic Reduction for Learning Stable Dynamical Systems [74.80320120264459]
  We present an approach to learn such motions from a limited number of human demonstrations. The complex motions are encoded as rollouts of a stable dynamical system. The efficacy of this approach is demonstrated through validation on an established benchmark as well demonstrations collected on a real-world robotic system.
  arXiv  Detail & Related papers  (2020-05-27T03:51:57Z)

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.