Framework infers Langevin dynamics from stochastic observations of latent systems.
problem Inferring non-stationary Langevin dynamics from indirect stochastic observations.
method Non-parametric framework explicitly modeling stochastic observation process and non-stationary latent dynamics.
result Correct inference of non-stationary dynamics requires accounting for non-equilibrium states and observation duration.
Novel approach detects early warning indicators in complex systems.
problem Detecting abrupt transitions in complex systems.
method Directed anisotropic diffusion map and latent stochastic dynamical systems.
result Early warning indicators can detect tipping points in state transitions.
We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear stochastic differential equation (SDE) driven by a Wiener process, with a drift evolu…
Method learns model for unknown stochastic system from data.
problem Modeling unknown stochastic dynamical systems.
method Autoencoder approach using deep neural networks (DNNs).
result Decoder serves as a predictive model for unknown stochastic systems.
New model captures state-dependent variability in partially observed systems.
problem Structured stochasticity not captured by constant-variance models.
method State-coupled stochastic volatility framework with particle expectation-maximization.
result Model consistently reduces recovery bias under partial observation.
Improved noise estimation in latent neural SDEs enhances model accuracy.
problem Latent neural SDEs underestimate noise, limiting their stochastic dynamics modeling.
method Explicit additional noise regularization in the loss function.
result Model accurately captures diffusion component of stochastic time series data.
Optimally explores dynamical systems with varying properties using context inference.
problem Learning dynamics models for systems with varying properties.
method Formulates dynamics models as stochastic processes conditioned on a latent context variable inferred from system transitions. Uses probabilistic formulation to compute optimal action sequences for exploration.
result Demonstrates effectiveness of the method on non-linear toy-problems and reinforcement learning environments.
Method learns latent dynamics of complex systems from noisy data.
problem Challenging to construct ROMs from noisy high-dimensional data.
method Recurrent stochastic variational deep kernel learning (SVDKL).
result Framework accurately predicts system evolution in low-dimensional latent spaces.
Model captures system input variations in latent space for actionable dynamics.
problem Learning dynamical systems from data without prescribing a mathematical model.
method Structured latent ODE model with stochastic factors of variation for each input.
result Improves generation of time-series data and inference of system inputs over baselines.
Model infers latent variables in sparse coding models using Langevin dynamics.
problem Sampling posterior distribution in sparse coding models.
method Langevin dynamics for inference and simultaneous learning of parameters.
result Langevin dynamics efficiently sample from 'L0 sparse' posterior distribution.
VSDN models sporadic time series with neural SDEs.
problem Modeling irregular and sparse time series data.
method Variational Bayesian method and neural SDEs.
result VSDNs outperform state-of-the-art models in prediction and interpolation.
Paper introduces OMD for ordered state transitions in SSMs.
problem Modeling ordered latent states in dynamic systems.
method Ordered Matrix Dirichlet (OMD) prior over ordered stochastic matrices.
result OMD models recover interpretable ordered latent structure without sacrificing predictive performance.
Studying a softmax-attention model, we show that the learned query converges to the latent signal subspace spanned by the informative direction.
problem Understanding the theoretical principles of attention mechanisms in large-scale token collections.
method Deriving a population objective and analyzing the limiting ordinary differential equation of the learning dynamics.
result The learned query asymptotically recovers the latent signal up to the intrinsic sign ambiguity.
We propose an efficient inference method for switching nonlinear dynamical systems. The key idea is to learn an inference network which can be used as a proposal distribution for the continuous latent variables, while performing exact marginalization of the discrete latent variables. This allows us to use the reparamet…
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.
Dynamic Structural Causal Models handle time-dependent systems with cycles and latent confounding.
problem Representing and analyzing systems of Stochastic Differential Equations (SDEs) with DSCMs.
method Define time-splitting and subsampling operations to analyze DSCMs of SDEs, and apply existing causal discovery algorithms to time-series data.
result DSCMs provide a graphical Markov property for SDEs and enable identification of time-dependent causal effects.
In order to better model high-dimensional sequential data, we propose a collaborative multi-output Gaussian process dynamical system (CGPDS), which is a novel variant of GPDSs. The proposed model assumes that the output on each dimension is controlled by a shared global latent process and a private local latent process…
New technologies for recording the activity of large neural populations during complex behavior provide exciting opportunities for investigating the neural computations that underlie perception, cognition, and decision-making. Nonlinear state space models provide an interpretable signal processing framework by combinin…
We propose a method to infer stochastic low-rank RNNs from neural data.
problem Fitting low-rank RNNs to noisy, stochastic neural data.
method Variational sequential Monte Carlo methods for stochastic low-rank RNNs.
result Lower dimensional latent dynamics compared to state-of-the-art methods.
We develop deep Poisson-gamma dynamical systems (DPGDS) to model sequentially observed multivariate count data, improving previously proposed models by not only mining deep hierarchical latent structure from the data, but also capturing both first-order and long-range temporal dependencies. Using sophisticated but simp…
A new flow-based Bayesian filter tackles high-dimensional nonlinear stochastic systems.
problem Bayesian filtering for high-dimensional nonlinear systems is challenging due to non-Gaussian distributions and computational limitations.
method Integrates normalizing flows to construct a latent linear state-space model with efficient density estimation and sampling.
result Demonstrates superior accuracy and efficiency in numerical experiments.
New model predicts video sequences with latent dynamics.
problem Predicting video sequences with inherent uncertainty.
method Introduces a novel stochastic temporal model with latent dynamics.
result Latent model outperforms prior state-of-the-art methods.
SING improves state inference in latent SDE models for better drift function estimation.
problem Intractable posterior inference in latent SDE models.
method Natural gradient variational inference.
result SING provides faster and more reliable inference in latent SDE models.
Spectral method speeds fitting of binary time series models.
problem Modeling binary time series data with latent linear dynamical systems.
method Spectral learning of probit-Bernoulli latent linear dynamical systems.
result Spectral method provides robust, fixed-cost estimator.
Introduces R-SSM for modeling multi-object dynamics with GNNs and normalizing flows.
problem Complex interactions and evolutions in multi-object systems are hard to model.
method Relational state-space model (R-SSM) using graph neural networks (GNNs) and normalizing flows.
result Empirically validated on synthetic and real datasets.
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.
New method reconstructs hidden dynamics from low-dimensional time series.
problem Reconstructing hidden dynamics from limited experimental data.
method Autoencoder trained with a novel latent-space loss function.
result Reconstructs strange attractors better than existing techniques.
We solve continuous-time latent SDE identifiability using diffusion shifts.
problem Identifiability of latent SDEs in continuous-time time series.
method Environment-induced shifts in diffusion covariance for additive-noise latent SDEs.
result Two diagonal diffusion regimes with distinct variance ratios identify latent coordinates up to permutation and scaling.
Method learns dynamics from noisy partial observations.
problem Reconstructing stochastic dynamical systems from indirect noisy data.
method Amortized path generation method for nonlinear stochastic filtering.
result Learned conditional path generator quantifies uncertainty.
A new framework models uncertainty in structured temporal data using SDEs and neural networks.
problem Uncertainty quantification in machine learning applications involving structured and temporal data.
method Integrates stochastic differential equations (SDEs) with deep generative models in a variational autoencoder framework.
result Improves uncertainty quantification in machine learning applications involving structured and temporal data.
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.
Improves state space models' resistance to noise.
problem State space models' initialization assumes noise-free data, which is often violated.
method Uncertainty-aware initialization for state space models, reformulating HiPPO with measurement noise.
result Improves model resistance to noise at training and inference time.
Many dynamical systems exhibit similar structure, as often captured by hand-designed simplified models that can be used for analysis and control. We develop a method for learning to correspond pairs of dynamical systems via a learned latent dynamical system. Given trajectory data from two dynamical systems, we learn a …
We present the particle stochastic approximation EM (PSAEM) algorithm for learning of dynamical systems. The method builds on the EM algorithm, an iterative procedure for maximum likelihood inference in latent variable models. By combining stochastic approximation EM and particle Gibbs with ancestor sampling (PGAS), PS…
This paper reviews deep learning methods for state space models.
problem Analyzing temporal dynamics in dynamical systems.
method Selective review of deep neural network approaches for state space models.
result Unified perspective on discrete and continuous time SSMs.
This research improves dynamical systems understanding by identifying latent states and their nonlinear transitions.
problem Previous work on dynamical systems could not identify nonlinear transition dynamics, leading to unreliable predictions.
method Proposes a state-space modeling framework using variational auto-encoders to identify latent states and their nonlinear transition functions.
result Demonstrates high accuracy in recovering latent state dynamics and future prediction accuracy.
ACSSM models irregular time series with continuous dynamics.
problem Modeling irregular time series data.
method ACSSM uses a multi-marginal Doob's h-transform and variational inference with stochastic optimal control.
result ACSSM outperforms in tasks like classification, regression, interpolation, and extrapolation.
Latent MoS learns multiple symmetries for efficient dynamic learning.
problem Efficiently learning dynamics from limited system measurements.
method Latent Mixture of Symmetries (Latent MoS) with hierarchical architecture.
result Latent MoS outperforms baselines in interpolation and extrapolation tasks.
This paper studies when particle filtering is efficient for planning in partially observed systems.
problem The efficiency of particle filtering for planning in partially observed linear dynamical systems.
method Coupling of ideal and approximate sequences to bound particle complexity.
result Polynomially many particles suffice for stable systems to approximate optimal planning.
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.
Method learns low-dim. state vars from noisy high-dim. data.
problem Discovering dynamical models from noisy high-dimensional data.
method Stochastic Variational Deep Kernel Learning with encoder and latent model.
result Effective denoising, compact state representation, and uncertainty quantification.
A framework learns multiscale dynamics from single trajectories using normalizing flows.
problem Learning effective stochastic dynamics from single observed paths of slow variables.
method Data-driven approach based on coupled multiscale SDEs, stochastic averaging, and normalizing flows for density modeling.
result Scalable approach to capturing epistemic uncertainty in multiscale systems.
Bayesian inference for stochastic differential equations using Wishart diffusions.
problem Inferring stochastic differential equations for regression and dynamical modeling.
method Bayesian non-parametric approach with semi-parametric Wishart processes.
result Modeling diffusion in stochastic differential equations improves performance and avoids overfitting.
Study identifies latent variables and models from spacecraft data.
problem Learning reliable models from spacecraft data with complex relationships.
method Inductive bias inspired by controllable canonical forms for sparse, input-dependent latent variables.
result Identifies latent variables up to scaling and determines dynamic models up to transformations for linear and affine systems.
Dynamic transportation networks have been analyzed for years by means of static graph-based indicators in order to study the temporal evolution of relevant network components, and to reveal complex dependencies that would not be easily detected by a direct inspection of the data. This paper presents a state-of-the-art …
New BED method handles online inference for partially observed dynamical systems.
problem Optimizing data collection for partially observable, partially online dynamical systems.
method Derived estimators of expected information gain and its gradient for SSMs, using nested particle filters.
result Successfully handles both partial observability and online inference in realistic models.
SDE Matching eliminates simulation for training Latent SDEs, achieving similar performance.
problem Training Latent SDEs with adjoint sensitivity methods is computationally expensive and limited.
method SDE Matching, inspired by Score- and Flow Matching, eliminates simulation for training Latent SDEs.
result SDE Matching achieves performance comparable to adjoint sensitivity methods while reducing computational complexity.
Neuroscience is experiencing a data revolution in which many hundreds or thousands of neurons are recorded simultaneously. Currently, there is little consensus on how such data should be analyzed. Here we introduce LFADS (Latent Factor Analysis via Dynamical Systems), a method to infer latent dynamics from simultaneous…