Learning Mixtures of Linear Dynamical Systems (MoLDS) via Hybrid Tensor-EM Method

• URL: http://arxiv.org/abs/2510.06091v1
• Date: Tue, 07 Oct 2025 16:17:52 GMT
• Title: Learning Mixtures of Linear Dynamical Systems (MoLDS) via Hybrid Tensor-EM Method
• Authors: Lulu Gong, Shreya Saxena,
• Abstract summary: We propose a tensor-based method that provides identifiability guarantees for learning MoLDS.<n>We then analyze neural recordings from the primate somatosensory cortex while a non-human primate performs reaches in different directions.<n>Our method successfully models and clusters different conditions as separate subsystems, consistent with supervised single-LDS fits for each condition.
• Score: 3.1102602510192736
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Mixtures of linear dynamical systems (MoLDS) provide a path to model time-series data that exhibit diverse temporal dynamics across trajectories. However, its application remains challenging in complex and noisy settings, limiting its effectiveness for neural data analysis. Tensor-based moment methods can provide global identifiability guarantees for MoLDS, but their performance degrades under noise and complexity. Commonly used expectation-maximization (EM) methods offer flexibility in fitting latent models but are highly sensitive to initialization and prone to poor local minima. Here, we propose a tensor-based method that provides identifiability guarantees for learning MoLDS, which is followed by EM updates to combine the strengths of both approaches. The novelty in our approach lies in the construction of moment tensors using the input-output data to recover globally consistent estimates of mixture weights and system parameters. These estimates can then be refined through a Kalman EM algorithm, with closed-form updates for all LDS parameters. We validate our framework on synthetic benchmarks and real-world datasets. On synthetic data, the proposed Tensor-EM method achieves more reliable recovery and improved robustness compared to either pure tensor or randomly initialized EM methods. We then analyze neural recordings from the primate somatosensory cortex while a non-human primate performs reaches in different directions. Our method successfully models and clusters different conditions as separate subsystems, consistent with supervised single-LDS fits for each condition. Finally, we apply this approach to another neural dataset where monkeys perform a sequential reaching task. These results demonstrate that MoLDS provides an effective framework for modeling complex neural data, and that Tensor-EM is a reliable approach to MoLDS learning for these applications.

Related papers

• A new approach for combined model class selection and parameters learning for auto-regressive neural models [0.4779196219827507]
  This work focuses on a specific Recurrent Neural Networks (RNNs) family, i.e. Auto-Regressive with eXogenous inputs Echo State Networks (XENARSNs)<n>The method allows to simultaneously select the optimal model class and learn model parameters from data.<n>Results show the effectiveness of the approach in identifying parsimonious yet accurate models suitable for control applications.
  arXiv  Detail & Related papers  (2026-01-24T12:26:25Z)
• Disordered Dynamics in High Dimensions: Connections to Random Matrices and Machine Learning [52.26396748560348]
  We provide an overview of high dimensional dynamical systems driven by random matrices.<n>We focus on applications to simple models of learning and generalization in machine learning theory.
  arXiv  Detail & Related papers  (2026-01-03T00:12:32Z)
• Private Training & Data Generation by Clustering Embeddings [74.00687214400021]
  Differential privacy (DP) provides a robust framework for protecting individual data.<n>We introduce a novel principled method for DP synthetic image embedding generation.<n> Empirically, a simple two-layer neural network trained on synthetically generated embeddings achieves state-of-the-art (SOTA) classification accuracy.
  arXiv  Detail & Related papers  (2025-06-20T00:17:14Z)
• MIBP-Cert: Certified Training against Data Perturbations with Mixed-Integer Bilinear Programs [50.41998220099097]
  Data errors, corruptions, and poisoning attacks during training pose a major threat to the reliability of modern AI systems.<n>We introduce MIBP-Cert, a novel certification method based on mixed-integer bilinear programming (MIBP)<n>By computing the set of parameters reachable through perturbed or manipulated data, we can predict all possible outcomes and guarantee robustness.
  arXiv  Detail & Related papers  (2024-12-13T14:56:39Z)
• Combined Optimization of Dynamics and Assimilation with End-to-End Learning on Sparse Observations [1.492574139257933]
  CODA is an end-to-end optimization scheme for jointly learning dynamics and DA directly from sparse and noisy observations. We introduce a novel learning objective that combines unrolled auto-regressive dynamics with the data- and self-consistency terms of weak-constraint 4Dvar DA.
  arXiv  Detail & Related papers  (2024-09-11T09:36:15Z)
• Modeling Latent Neural Dynamics with Gaussian Process Switching Linear Dynamical Systems [2.170477444239546]
  We develop an approach that balances these two objectives: the Gaussian Process Switching Linear Dynamical System (gpSLDS)<n>Our method builds on previous work modeling the latent state evolution via a differential equation whose nonlinear dynamics are described by a Gaussian process (GP-SDEs)<n>Our approach resolves key limitations of the rSLDS such as artifactual oscillations in dynamics near discrete state boundaries, while also providing posterior uncertainty estimates of the dynamics.
  arXiv  Detail & Related papers  (2024-07-19T15:32:15Z)
• Online Variational Sequential Monte Carlo [49.97673761305336]
  We build upon the variational sequential Monte Carlo (VSMC) method, which provides computationally efficient and accurate model parameter estimation and Bayesian latent-state inference. Online VSMC is capable of performing efficiently, entirely on-the-fly, both parameter estimation and particle proposal adaptation.
  arXiv  Detail & Related papers  (2023-12-19T21:45:38Z)
• PINQI: An End-to-End Physics-Informed Approach to Learned Quantitative MRI Reconstruction [0.7199733380797579]
  Quantitative Magnetic Resonance Imaging (qMRI) enables the reproducible measurement of biophysical parameters in tissue. The challenge lies in solving a nonlinear, ill-posed inverse problem to obtain desired tissue parameter maps from acquired raw data. We propose PINQI, a novel qMRI reconstruction method that integrates the knowledge about the signal, acquisition model, and learned regularization into a single end-to-end trainable neural network.
  arXiv  Detail & Related papers  (2023-06-19T15:37:53Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• Parameter estimation for WMTI-Watson model of white matter using encoder-decoder recurrent neural network [0.0]
  In this study, we evaluate the performance of NLLS, the RNN-based method and a multilayer perceptron (MLP) on datasets rat and human brain. We showed that the proposed RNN-based fitting approach had the advantage of highly reduced computation time over NLLS.
  arXiv  Detail & Related papers  (2022-03-01T16:33:15Z)
• Using Data Assimilation to Train a Hybrid Forecast System that Combines Machine-Learning and Knowledge-Based Components [52.77024349608834]
  We consider the problem of data-assisted forecasting of chaotic dynamical systems when the available data is noisy partial measurements. We show that by using partial measurements of the state of the dynamical system, we can train a machine learning model to improve predictions made by an imperfect knowledge-based model.
  arXiv  Detail & Related papers  (2021-02-15T19:56:48Z)

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.