Paper models non-linear dynamics from time series data.
problem Modeling non-linear dynamical systems from time series data.
method Introduces latent state modeling and a novel alternating minimization algorithm.
result LaNoLem achieves competitive performance in dynamics estimation and prediction.
This paper introduces a linear state-space model with time-varying dynamics. The time dependency is obtained by forming the state dynamics matrix as a time-varying linear combination of a set of matrices. The time dependency of the weights in the linear combination is modelled by another linear Gaussian dynamical model…
Use simplified layerwise linear models to understand neural dynamics.
problem Complex neural network dynamics are hard to grasp.
method Apply simplified layerwise linear models to explain neural phenomena.
result Simplified models explain neural collapse, emergence, etc.
Efficiently extracts linear dynamics from complex observations.
problem Learning policies directly from rich, high-dimensional observations.
method Modeling linear dynamics in a hidden subspace and developing an efficient algorithm.
result Successfully extracts linear dynamics from rich observations.
New algorithm learns linear dynamical systems from measurements.
problem Learning system dynamics from linear measurements efficiently and accurately.
method Method of moments estimator to directly estimate Markov parameters.
result First polynomial time algorithm for learning linear dynamical systems.
Develops CLDS models to model neural activity with nonlinear dynamics.
problem Complex, nonlinear dynamics in neural population activity.
method Conditionally Linear Dynamical System (CLDS) models using Gaussian Process (GP) priors.
result CLDS models can perform well even in data-limited conditions.
dynoNet learns dynamical systems using linear operators.
problem Learning complex dynamical systems.
method dynoNet uses linear dynamical operators for sequence modeling and system identification.
result dynoNet effectively identifies systems on benchmarks.
This work identifies eigenvalues of unknown linear dynamics without full system identification.
problem Identifying parameters of a linear dynamical system is challenging.
method Developed a computationally efficient algorithm to estimate eigenvalues of the state-transition matrix.
result The algorithm can efficiently cluster multi-dimensional time series with temporal offsets and varying lengths.
Learn object dynamics from unlabeled images.
problem Unsupervised learning of multiple object dynamics from unlabeled video sequences.
method Probabilistic model generating noisy positions, followed by non-linear rendering. Efficient inference method for querying the model.
result Efficient inference of object dynamics from unlabeled images.
Develops a method to model neural dynamics with flexible yet interpretable latent states.
problem Capturing complex nonlinear dynamics in neural time series while maintaining interpretability.
method Gaussian Process Switching Linear Dynamical System (gpSLDS) that balances expressiveness and interpretability.
result Favorable performance in comparison to rSLDS on synthetic and real neuroscience data.
Paper proposes variational inference for piecewise-linear systems.
problem Intractability of switching dynamical systems.
method Variational approximation and expectation-maximization algorithms.
result Parameters can be estimated off-line, including the number of linear modes.
We learn linear models from nonlinear systems using multiple trajectories and regularization.
problem Identifying linear models from data when the underlying dynamics are nonlinear.
method Multiple trajectories data acquisition followed by regularized least squares.
result Learn linearized dynamics with arbitrarily small error given enough samples.
New approach learns mixtures of linear dynamical systems without separation conditions.
problem Learning mixtures of linear dynamical systems with better fit or understanding.
method Tensor decompositions to learn mixtures of linear dynamical systems.
result Algorithm succeeds without strong separation conditions and can compete with Bayes optimal clustering.
Switching linear dynamics improves model-based reinforcement learning and system identification.
problem Complex and nonlinear systems can be approximated by linear dynamical systems.
method Bayesian inference, Variational Autoencoders, Concrete relaxations.
result Improved accuracy in learning dynamics from partial and high-dimensional observations.
We identify linear models from nonlinear systems with initialization constraints.
problem Identifying linear models from nonlinear systems with initialization constraints.
method Multiple trajectories-based deterministic data acquisition algorithm followed by regularized least squares.
result We provide a finite sample error bound on the learned linearized dynamics.
This work studies learning dynamics in SSMs, linking them to deep linear networks.
problem Lack of theoretical understanding of SSMs, especially in deep state spaces.
method Analyzes learning dynamics of linear SSMs, focusing on frequency domain, and establishes links to deep linear networks.
result Analytical solutions for SSM learning dynamics under mild assumptions, linking to deep linear networks.
KalmanNet uses neural networks to improve state estimation in systems with unknown dynamics.
problem State estimation of systems with non-linear dynamics and partial information.
method KalmanNet integrates a recurrent neural network with the Kalman filter to handle non-linearities and model mismatches.
result KalmanNet outperforms classic filtering methods in systems with both mismatched and accurate domain knowledge.
New model explains market dynamics with phase transitions and non-linear interactions.
problem Understanding complex multi-asset market dynamics with phase transitions.
method Developed a Multi-Asset Non-Equilibrium Skew (MANES) model based on Langevin dynamics and McKean-Vlasov equation.
result The model accurately predicts market returns and phase transitions in both benign and distressed markets.
Many real-valued stochastic time-series are locally linear (Gassian), but globally non-linear. For example, the trajectory of a human hand gesture can be viewed as a linear dynamic system driven by a nonlinear dynamic system that represents muscle actions. We present a mixed-state dynamic graphical model in which a hid…
Estimates time-varying parameters from two OLS estimates.
problem Time-varying linear regression with hidden dynamics.
method Combines two OLS estimates for stable linear dynamics.
result Finite sample guarantee on estimation error.
SSL framework identifies non-linear systems without labeled data.
problem System identification in non-linear environments without labeled data.
method Dynamics contrastive learning framework.
result SSL can identify non-linear dynamics in latent space.
Paper uses black-box inference to estimate non-linear latent force models.
problem Estimating posterior state and forcing term in non-linear systems with unknown forcing terms.
method Black-box variational inference with local inverse autoregressive flows.
result Demonstrates effectiveness of approximation on known posterior systems and non-linear dynamics.
Dynamic linear models improve travel time prediction for congested freeways.
problem Accurate travel time prediction for congested freeways.
method Dynamic linear models (DLMs) with time-varying parameters.
result Significant improvements in travel time prediction accuracy, especially for short-term predictions.
Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments that are each explained by simpler dynamic units. Building on switching linear dy…
Modeling dynamical systems is important in many disciplines, e.g., control, robotics, or neurotechnology. Commonly the state of these systems is not directly observed, but only available through noisy and potentially high-dimensional observations. In these cases, system identification, i.e., finding the measurement map…
New framework for online control in evolving populations.
problem Control of evolving populations in real-world conditions.
method Online control framework for linear and non-linear dynamical systems.
result Near-optimal regret bounds for gradient-based controllers.
Study agnostic feature-based dynamic pricing models with linear policies and noisy valuations.
problem Tackles dynamic pricing with unknown noise and no assumptions on data.
method Studies two agnostic models: linear policy and linear noisy valuation, presenting algorithms and regret bounds.
result Demonstrates no-regret learning is possible under weak assumptions, but noisy feedback is not significantly more useful than bandit feedback.
Study forecasts stock returns on JSE using SGDLMs capturing cross-series dependencies.
problem Accurate forecasting of multivariate time series data.
method Simultaneous Graphical Dynamic Linear Models (SGDLMs) with customised DLMs and importance sampling/mean-field variational Bayes.
result SGDLMs accurately forecast stock data on JSE and respond to market changes.
AdaptOn achieves logarithmic regret in adaptive control of unknown partially observable linear systems.
problem Adaptive control in partially observable linear dynamical systems.
method AdaptOn algorithm that estimates system dynamics through online learning and gradient descent.
result AdaptOn achieves a logarithmic regret bound of polylog(T) after T steps.
This paper proposes a new method for inferring the latent dimension of linear dynamical systems.
problem Manual specification of latent dimension is impractical and leads to model limitations.
method The paper introduces a minimum description length criterion to infer latent dimension.
result The proposed method effectively infers latent dimension and improves model performance.
Many real-world systems studied are governed by complex, nonlinear dynamics. By modeling these dynamics, we can gain insight into how these systems work, make predictions about how they will behave, and develop strategies for controlling them. While there are many methods for modeling nonlinear dynamical systems, exist…
Proposes a new model for better speech segmentation.
problem Improving speech segmentation accuracy.
method Integrates recurrent explicit duration variables into rSLDS and uses Pólya-gamma augmentation for inference.
result Demonstrates improved segmentation on various datasets.
New algorithm improves dynamic mode decomposition for high-dimensional data.
problem Reduced modeling in high-dimensional spaces.
method Low rank constraint optimization and kernel-based computation.
result Gain in approximation accuracy and computational efficiency.
Discrete gradient dynamics in linear networks implicitly regularize model solutions.
problem Optimizing over-parameterized models leads to multiple solutions; the choice of algorithm introduces biases.
method Analyzed discrete gradient dynamics in a two-layer linear network with least-squares loss.
result The dynamics sequentially learns solutions of a reduced-rank regression with increasing rank.
Improved robust latent variable estimation for neural dynamics.
problem Inconsistent results due to noise and nonlinearity in existing models.
method Probabilistic approach to latent variable estimation in decomposed models.
result More accurate latent variable inference in nonlinear systems with diverse noise conditions.
This paper studies the dynamic generator model for spatial-temporal processes such as dynamic textures and action sequences in video data. In this model, each time frame of the video sequence is generated by a generator model, which is a non-linear transformation of a latent state vector, where the non-linear transform…
We introduce Embed to Control (E2C), a method for model learning and control of non-linear dynamical systems from raw pixel images. E2C consists of a deep generative model, belonging to the family of variational autoencoders, that learns to generate image trajectories from a latent space in which the dynamics is constr…
Study confirms complex crypto market dynamics via non-linear potentials.
problem Linear models fail to capture complex financial market dynamics.
method Analyzed high-frequency crypto currency data to confirm non-linear drift and potential functions.
result Markets exhibit either single-well or double-well potentials, indicating varying levels of uncertainty or stress.
Many complex dynamical phenomena can be effectively modeled by a system that switches among a set of conditionally linear dynamical modes. We consider two such models: the switching linear dynamical system (SLDS) and the switching vector autoregressive (VAR) process. Our Bayesian nonparametric approach utilizes a hiera…
Optimized DMD for fast atmospheric chemistry forecasting.
problem Forecasting global atmospheric chemistry dynamics efficiently.
method Optimized Dynamic Mode Decomposition (DMD) for reduced order modeling.
result Significant improvement in computational speed and interpretability.
This work extends identifiability analysis to sequential latent variable models, focusing on Switching Dynamical Systems.
problem Identifying latent variables in sequential data models.
method Proved identifiability of Markov Switching Models and established conditions for Switching Dynamical Systems.
result Identifiability of latent variables and non-linear mappings in Switching Dynamical Systems up to affine transformations.
This work optimizes reservoir computing models by linking recurrence and non-linear dynamics.
problem Understanding how recurrence and non-linear dynamics in cortical networks contribute to their function.
method Transformed time-continuous, recurrent dynamics into an effective feed-forward structure of linear and non-linear temporal kernels.
result Optimal time-series classifiers can be built from random reservoir networks, demonstrating significant performance gains.
Optimal linear contracts are possible even with memory in Gaussian settings.
problem Can optimal dynamic contracts be linear when agents control memory processes?
method Developed a methodology for non-Markovian and non-semimartingale settings, showed linear contracts are optimal for one-dimensional models.
result Linear contracts are optimal for one-dimensional models with memory, and for radial effort cost functions in higher dimensions.
Breaks down complex nonlinear dynamics into simpler components.
problem Control of nonlinear dynamical systems remains challenging.
method Inspired by hybrid switching systems, decomposes dynamics into simpler stochastic switching linear dynamical systems.
result Extracts hierarchies of Markovian and auto-regressive locally linear controllers from nonlinear experts.
Weak correlations explain linear dynamics in deep learning models.
problem Understanding the linear structure in gradient-based learning algorithms.
method Characterization of weak correlations between derivatives and parameters.
result Weak correlations are the underlying principle for linearization in deep learning models.
Endogenous business cycles explain higher comovement across countries.
problem Standard models struggle to explain high comovement in business cycles across countries.
method Developed a demand-driven reduced-form model with strategic complementarities and international trade linkages.
result Combining endogenous business cycles with exogenous shocks matches empirical comovement levels.
Linear attention in Transformers can be interpreted as dynamic VAR models.
problem Misalignment between Transformers and autoregressive forecasting objectives.
method Interpreting linear attention as VAR, rearranging MLP, attention, and flow.
result SAMoVAR improves performance, interpretability, and efficiency.
We present a detailed study of the statistical properties of an Agent Based Model and of its generalization to the multiplicative dynamics. The aim of the model is to consider the minimal elements for the understanding of the origin of the Stylized Facts and their Self-Organization. The key elements are fundamentalist …