DeNOTS: Stable Deep Neural ODEs for Time Series

• URL: http://arxiv.org/abs/2408.08055v2
• Date: Tue, 15 Apr 2025 09:49:17 GMT
• Title: DeNOTS: Stable Deep Neural ODEs for Time Series
• Authors: Ilya Kuleshov, Evgenia Romanenkova, Galina Boeva, Vladislav Zhuzhel, Evgeni Vorsin, Alexey Zaytsev,
• Abstract summary: Neural ODEs are a prominent branch of methods designed to capture the temporal evolution of complex time-stamped data.<n>We provably stabilize these models by introducing an adaptive negative feedback mechanism.<n>For three open datasets, our method obtains up to 20% improvements in downstream quality.
• Score: 2.2544703147182172
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Neural ODEs are a prominent branch of methods designed to capture the temporal evolution of complex time-stamped data. Their idea is to solve an ODE with Neural Network-defined dynamics, which take the immediate parameters of the observed system into account. However, larger integration intervals cause instability, which forces most modern methods to normalize time to $[0, 1]$. We provably stabilize these models by introducing an adaptive negative feedback mechanism. This modification allows for longer integration, which in turn implies higher expressiveness, mirroring the behaviour of increasing depth in conventional Neural Networks.Additionally, it provides intriguing theoretical properties: forgetfulness and missing-value robustness. For three open datasets, our method obtains up to 20\% improvements in downstream quality if compared to existing baselines, including State Space Models and Neural~CDEs.

Related papers

• Balanced Neural ODEs: nonlinear model order reduction and Koopman operator approximations [0.0]
  Variational Autoencoders (VAEs) are a powerful framework for learning latent representations of reduced dimensionality. Neural ODEs excel in learning transient system dynamics. We show that standard Latent ODEs struggle with dimensionality reduction in systems with time-varying inputs.
  arXiv  Detail & Related papers  (2024-10-14T05:45:52Z)
• von Mises Quasi-Processes for Bayesian Circular Regression [57.88921637944379]
  We explore a family of expressive and interpretable distributions over circle-valued random functions. The resulting probability model has connections with continuous spin models in statistical physics. For posterior inference, we introduce a new Stratonovich-like augmentation that lends itself to fast Markov Chain Monte Carlo sampling.
  arXiv  Detail & Related papers  (2024-06-19T01:57:21Z)
• Data-Driven Model Selections of Second-Order Particle Dynamics via Integrating Gaussian Processes with Low-Dimensional Interacting Structures [0.9821874476902972]
  We focus on the data-driven discovery of a general second-order particle-based model. We present applications to modeling two real-world fish motion datasets.
  arXiv  Detail & Related papers  (2023-11-01T23:45:15Z)
• Multi-Response Heteroscedastic Gaussian Process Models and Their Inference [1.52292571922932]
  We propose a novel framework for the modeling of heteroscedastic covariance functions. We employ variational inference to approximate the posterior and facilitate posterior predictive modeling. We show that our proposed framework offers a robust and versatile tool for a wide array of applications.
  arXiv  Detail & Related papers  (2023-08-29T15:06:47Z)
• Learning minimal representations of stochastic processes with variational autoencoders [52.99137594502433]
  We introduce an unsupervised machine learning approach to determine the minimal set of parameters required to describe a process. Our approach enables for the autonomous discovery of unknown parameters describing processes.
  arXiv  Detail & Related papers  (2023-07-21T14:25:06Z)
• Score-based Data Assimilation [7.215767098253208]
  We introduce score-based data assimilation for trajectory inference. We learn a score-based generative model of state trajectories based on the key insight that the score of an arbitrarily long trajectory can be decomposed into a series of scores over short segments.
  arXiv  Detail & Related papers  (2023-06-18T14:22:03Z)
• Continuous time recurrent neural networks: overview and application to forecasting blood glucose in the intensive care unit [56.801856519460465]
  Continuous time autoregressive recurrent neural networks (CTRNNs) are a deep learning model that account for irregular observations. We demonstrate the application of these models to probabilistic forecasting of blood glucose in a critical care setting.
  arXiv  Detail & Related papers  (2023-04-14T09:39:06Z)
• The Past Does Matter: Correlation of Subsequent States in Trajectory Predictions of Gaussian Process Models [0.7734726150561089]
  We consider approximations of the model's output and trajectory distribution. We show that previous work on uncertainty propagation incorrectly included an independence assumption between subsequent states of the predicted trajectories.
  arXiv  Detail & Related papers  (2022-11-20T22:19:39Z)
• Likelihood-Free Inference in State-Space Models with Unknown Dynamics [71.94716503075645]
  We introduce a method for inferring and predicting latent states in state-space models where observations can only be simulated, and transition dynamics are unknown. We propose a way of doing likelihood-free inference (LFI) of states and state prediction with a limited number of simulations.
  arXiv  Detail & Related papers  (2021-11-02T12:33:42Z)
• Variational Inference for Continuous-Time Switching Dynamical Systems [29.984955043675157]
  We present a model based on an Markov jump process modulating a subordinated diffusion process. We develop a new continuous-time variational inference algorithm. We extensively evaluate our algorithm under the model assumption and for real-world examples.
  arXiv  Detail & Related papers  (2021-09-29T15:19:51Z)
• Closed-form Continuous-Depth Models [99.40335716948101]
  Continuous-depth neural models rely on advanced numerical differential equation solvers. We present a new family of models, termed Closed-form Continuous-depth (CfC) networks, that are simple to describe and at least one order of magnitude faster.
  arXiv  Detail & Related papers  (2021-06-25T22:08:51Z)
• On Contrastive Representations of Stochastic Processes [53.21653429290478]
  Learning representations of processes is an emerging problem in machine learning. We show that our methods are effective for learning representations of periodic functions, 3D objects and dynamical processes.
  arXiv  Detail & Related papers  (2021-06-18T11:00:24Z)
• Piecewise-constant Neural ODEs [41.116259317376475]
  We make a piecewise-constant approximation to Neural ODEs to mitigate these issues. Our model can be integrated exactly via Euler integration and can generate autoregressive samples in 3-20 times fewer steps than comparable RNN and ODE-RNN models.
  arXiv  Detail & Related papers  (2021-06-11T21:46:55Z)
• Stochastic Recurrent Neural Network for Multistep Time Series Forecasting [0.0]
  We leverage advances in deep generative models and the concept of state space models to propose an adaptation of the recurrent neural network for time series forecasting. Our model preserves the architectural workings of a recurrent neural network for which all relevant information is encapsulated in its hidden states, and this flexibility allows our model to be easily integrated into any deep architecture for sequential modelling.
  arXiv  Detail & Related papers  (2021-04-26T01:43:43Z)
• Neural ODE Processes [64.10282200111983]
  We introduce Neural ODE Processes (NDPs), a new class of processes determined by a distribution over Neural ODEs. We show that our model can successfully capture the dynamics of low-dimensional systems from just a few data-points.
  arXiv  Detail & Related papers  (2021-03-23T09:32:06Z)
• Social NCE: Contrastive Learning of Socially-aware Motion Representations [87.82126838588279]
  Experimental results show that the proposed method dramatically reduces the collision rates of recent trajectory forecasting, behavioral cloning and reinforcement learning algorithms. Our method makes few assumptions about neural architecture designs, and hence can be used as a generic way to promote the robustness of neural motion models.
  arXiv  Detail & Related papers  (2020-12-21T22:25:06Z)
• An Ode to an ODE [78.97367880223254]
  We present a new paradigm for Neural ODE algorithms, called ODEtoODE, where time-dependent parameters of the main flow evolve according to a matrix flow on the group O(d) This nested system of two flows provides stability and effectiveness of training and provably solves the gradient vanishing-explosion problem.
  arXiv  Detail & Related papers  (2020-06-19T22:05:19Z)
• Multiplicative noise and heavy tails in stochastic optimization [62.993432503309485]
  empirical optimization is central to modern machine learning, but its role in its success is still unclear. We show that it commonly arises in parameters of discrete multiplicative noise due to variance. A detailed analysis is conducted in which we describe on key factors, including recent step size, and data, all exhibit similar results on state-of-the-art neural network models.
  arXiv  Detail & Related papers  (2020-06-11T09:58:01Z)
• Liquid Time-constant Networks [117.57116214802504]
  We introduce a new class of time-continuous recurrent neural network models. Instead of declaring a learning system's dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems. These neural networks exhibit stable and bounded behavior, yield superior expressivity within the family of neural ordinary differential equations.
  arXiv  Detail & Related papers  (2020-06-08T09:53:35Z)
• Time Dependence in Non-Autonomous Neural ODEs [74.78386661760662]
  We propose a novel family of Neural ODEs with time-varying weights. We outperform previous Neural ODE variants in both speed and representational capacity.
  arXiv  Detail & Related papers  (2020-05-05T01:41:46Z)

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.