Gaussian process model learns Hamiltonian systems from noisy data.
problem Learning Hamiltonian systems from long, noisy trajectories.
method Efficient decoupled parameterisation, energy-conserving shooting method.
result Robust inference from short and long trajectories.
Enhances HNNs for conservative systems with noisy data.
problem Modeling conservative systems with neural networks.
method Proposes a deep hidden physics model for continuous-time trajectory estimation.
result Integration scheme works well for HNNs, especially with low sampling rates.
Algorithm generates private continuous-time data for sensitive domains.
problem Private generation of continuous-time data for sensitive domains.
method Mean-field Langevin dynamics and noisy particle gradient descent.
result Strong privacy guarantees for one-time data contributions.
Study supports recovery of PDEs from noisy data using a specific regularization method.
problem Support recovery of PDEs from a single noisy trajectory.
method Applying ℓ1-regularized Pseudo-Least Squares model to a given data set.
result Support of ℓ1-c coefficients asymptotically converges to the true signed-support of the PDE.
We apply variational inference to learn vehicle trajectory parameters from noisy data.
problem Learning parameters for vehicle trajectory estimation from noisy measurements.
method Gaussian variational inference with parameter learning in a motion and sensor model context.
result High-quality state estimates achieved even with outliers and false loop closures.
New metric compares noisy neural trajectories using optimal transport.
problem Existing metrics fail to capture differences in noisy, dynamic neural responses.
method Proposed an optimal transport distance metric for Gaussian processes.
result Metric effectively compares neural dynamics in different systems.
Proposes DGCN with trajectory sampling for data-efficient policy search in MBRL.
problem Improving data efficiency in model-based reinforcement learning.
method Combines trajectory sampling and DGCN for uncertainty propagation in probabilistic world models.
result Improves sample-efficiency over other uncertainty propagation methods and probabilistic models.
Map matching of GPS trajectories from a sequence of noisy observations serves the purpose of recovering the original routes in a road network. In this work in progress, we attempt to share our experience of feature construction in a spatial database by reporting our ongoing experiment of feature extrac-tion in Conditio…
We study the problem of discriminative sub-trajectory mining. Given two groups of trajectories, the goal of this problem is to extract moving patterns in the form of sub-trajectories which are more similar to sub-trajectories of one group and less similar to those of the other. We propose a new method called Statistica…
Map matching of the GPS trajectory serves the purpose of recovering the original route on a road network from a sequence of noisy GPS observations. It is a fundamental technique to many Location Based Services. However, map matching of a low sampling rate on urban road network is still a challenging task. In this paper…
A comprehensive methodology is provided for smoothing noisy, irregularly sampled data with non-Gaussian noise using smoothing splines. We demonstrate how the spline order and tension parameter can be chosen a priori from physical reasoning. We also show how to allow for non-Gaussian noise and outliers which are typical…
Novel methods improve Bayesian analysis of chaotic dynamical systems.
problem Bayesian parameter inference and trajectory reconstruction of chaotic systems with sparse and noisy data.
method Pilot MAGI (pMAGI) and Pilot MAGI Sequential Prediction (PMSP) methods.
result pMAGI and PMSP significantly outperform existing methods in accuracy and computational efficiency.
We consider the behavior of gradient flow and of discrete and noisy gradient descent. It is commonly noted that the addition of noise to the process of discrete gradient descent can affect the trajectory of gradient descent. In previous work, we observed such effects. There, we considered the case where the minima had …
New method learns vector fields from noisy time series data.
problem Learning vector fields from noisy time series data.
method Neural network architecture with tensor products of one-dimensional neural shape functions for vector field approximation, alternating minimization for noise handling.
result Neural shape function architecture robust to noise, learning accurate vector fields from data with up to 10% Gaussian noise.
New method learns chaotic dynamics from single noisy trajectory.
problem Chaos in complex systems is hard to model accurately with machine learning.
method Adversarial optimal transport objectives to learn summary statistics and emulator from single noisy data.
result Emulators trained with proposed objectives have significantly improved long-term statistical fidelity.
The paper improves model-based reinforcement learning by using multi-timestep objectives.
problem Compounding errors in one-step dynamics models as trajectory length increases.
method Developed a multi-timestep objective as a weighted sum of losses at various future horizons.
result Exponentially decaying weights significantly improve long-horizon performance.
New algorithm speeds up RNN time series prediction by filtering noise.
problem Predicting smooth trajectories from noisy time series data.
method Analyzed RNN dynamics to propose an efficient noise filtering algorithm.
result Significant speedup in predictive process without accuracy loss.
TGD improves conditional sampling by concentrating computation on promising trajectories.
problem Efficiently training-free conditional sampling with diffusion priors.
method Tempered Guided Diffusion (TGD) using annealed sequential Monte Carlo.
result TGD yields a consistent particle approximation to the posterior as the number of particles grows.
In this note, we observe the behavior of gradient flow and discrete and noisy gradient descent in some simple settings. It is commonly noted that addition of noise to gradient descent can affect the trajectory of gradient descent. Here, we run some computer experiments for gradient descent on some simple functions, and…
New method for data assimilation using score-based models.
problem Bayesian inverse problem of identifying plausible state trajectories.
method Score-based data assimilation, learning a score-based generative model of state trajectories.
result Effective method for zero-shot observation scenarios.
TRS-ODENs learn dynamics with time-reversal symmetry for more efficient learning.
problem Learning dynamics with time-reversal symmetry for more efficient learning.
method Proposed a loss function and a new framework (TRS-ODENs) to learn dynamics efficiently.
result TRS-ODENs can learn dynamics from noisy and complex trajectories efficiently.
DHLNN improves deep hedging for financial derivatives with faster convergence and better stability.
problem Challenges in computational inefficiency, sensitivity to noisy data, and optimization complexity in deep hedging methods.
method Integrates periodic fixed-gradient optimization and linearized training dynamics to stabilize and accelerate deep learning model training.
result Demonstrates faster convergence, improved stability, and superior hedging performance across diverse market scenarios.
SDA method reduces memory and time for assimilating noisy geophysical data.
problem Challenges in identifying state trajectories of high-dimensional geophysical systems.
method Score-based data assimilation with modified score network architecture.
result Promising results for a two-layer quasi-geostrophic model.
New method infers population dynamics from snapshots using path space optimization.
problem Recover dynamics of a population from its temporal marginals.
method Grid-free algorithm using Schrödinger bridges coupled via noisy gradient descent in mean-field limit.
result Global convergence to min-entropy estimator with end-to-end theoretical guarantees.
The paper introduces a fast algorithm for learning and forecasting nonlinear dynamics from noisy time series data.
problem Challenges in capturing nonlinear dynamics from noisy time series data.
method A projected nonlinear state-space model with kernel functions applied to projected lines.
result The model effectively learns and forecasts complex nonlinear dynamics with computational efficiency.
A new framework for generating predictive features in noisy multivariate time series.
problem Predicting noisy multivariate time series with limited user effort.
method Develops a feature programming framework based on spin-gas dynamical Ising models.
result Validated the method on synthetic and real-world datasets.
New method detects metastable basins in high dimensions using trajectory sampling.
problem Identifying distinct basins in high-dimensional Markov processes.
method Discriminative approach based on marginal trajectory distribution comparison.
result Bayes-optimal classifier achieves high accuracy distinguishing between basins.
SIP framework discovers governing equations in uncertain systems.
problem Discovering governing equations in systems with input variability and noisy data.
method SIP framework treats unknown coefficients as random variables and infers their posterior distribution by minimizing Kullback-Leibler divergence.
result SIP consistently identifies correct equations and lowers coefficient error by 82% relative to SINDy.
Novel framework learns policies from noisy expert demonstrations.
problem Learning effective policies with noisy expert demonstrations.
method Adaptive learning framework that jointly interacts with the environment and expert demonstrations, assigning weights to filter out noisy demonstrations.
result The proposed approach learns robustly with noisy demonstrations and achieves higher performance in fewer iterations.
EFiGP uses Fourier and eigen-decomposition for efficient ODE parameter estimation.
problem Parameter estimation and trajectory reconstruction for noisy, sparse, nonlinear ODE systems.
method EFiGP integrates Fourier transformation and eigen-decomposition into a physics-informed Gaussian Process framework.
result EFiGP efficiently estimates ODE parameters and recovers trajectories from noisy data.
The extended Kalman filter is perhaps the most standard tool to estimate in real time the state of a dynamical system from noisy measurements of some function of the system, with extensive practical applications (such as position tracking via GPS). While the plain Kalman filter for linear systems is well-understood, th…
We propose Symplectic Recurrent Neural Networks (SRNNs) as learning algorithms that capture the dynamics of physical systems from observed trajectories. An SRNN models the Hamiltonian function of the system by a neural network and furthermore leverages symplectic integration, multiple-step training and initial state op…
A new particle filter uses diffusion models to improve state estimation from noisy data.
problem Sequentially estimating the state of a dynamical system from noisy and incomplete observations.
method Uses a diffusion model to simulate and predict system dynamics, incorporating noisy observations to refine predicted states.
result An unbiased particle filtering method that rigorously fuses observational data with diffusion model simulations.
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.
Hybrid approach combines transformer and Bayesian filtering for robust multiple particle tracking.
problem Challenges in tracking multiple particles in noisy scenes due to combinatorial explosion of hypotheses.
method Attention-Bayesian hybrid framework using transformer for association and Bayesian filtering for pruning hypotheses.
result Improved tracking accuracy and robustness against spurious detections.
We learn higher-order Markov random fields from evolving data, bypassing computational barriers.
problem Learning graphical models from temporally correlated samples, especially with noisy data.
method Using the trajectory data from Glauber dynamics, we develop an algorithm to recover the graph and parameters efficiently.
result We demonstrate efficient learning of higher-order Markov random fields from trajectory data, overcoming computational hardness.
Improved averaging method for noisy observations converges strongly.
problem Noisy observations from random dynamical systems require stable estimates.
method Introduced p-EMA, a modified exponential moving average with subharmonic weight decay. result Stochastic convergence guarantees for p-EMA under mild assumptions. CDLF predicts product life-cycles in cold-start phases with high accuracy.
problem Forecasting new products in early phases when data is scarce.
method Conditional Diffusion Life-cycle Forecaster (CDLF) combining static descriptors, reference trajectories, and new observations.
result CDLF outperforms classical models in accuracy and probabilistic forecasting.
New findings explain why online methods outperform offline methods in noisy expert feedback settings.
problem The challenge of learning from imperfect expert feedback in sequential decision-making systems.
method Introduced a noisy expert model and a novel variant of on-policy distillation (OPD) to address the gap between offline and online imitation learning.
result Online interaction with a noisy expert via OPD enables polynomial dependence on the horizon, unlike offline methods which require exponential growth in sample complexity.
New bounds on trajectory safety in training models with Langevin Dynamics.
problem Bounding the probability of a model's trajectory staying away from a designated failure region.
method Analyzes Langevin dynamics on smooth, strongly convex loss landscapes, introducing shape-free and local relaxation bounds.
result The in-set probability relaxes to the static value after a burn-in time of order d, using only the global spectral gap of the loss.
Deep reinforcement learning methods traditionally struggle with tasks where environment rewards are particularly sparse. One successful method of guiding exploration in these domains is to imitate trajectories provided by a human demonstrator. However, these demonstrations are typically collected under artificial condi…
NESS improves neighbor embedding for smooth cell-state transitions in single-cell data.
problem Challenges in extracting smooth, low-dimensional representations from noisy single-cell data.
method Builds on PCS framework to develop NESS, a stable machine learning approach.
result NESS consistently yields useful biological insights across diverse single-cell datasets.
We present a numerical approach for approximating unknown Hamiltonian systems using observation data. A distinct feature of the proposed method is that it is structure-preserving, in the sense that it enforces conservation of the reconstructed Hamiltonian. This is achieved by directly approximating the underlying unkno…
In a world of global trading, maritime safety, security and efficiency are crucial issues. We propose a multi-task deep learning framework for vessel monitoring using Automatic Identification System (AIS) data streams. We combine recurrent neural networks with latent variable modeling and an embedding of AIS messages t…
The paper introduces a multi-step loss function to improve model-based reinforcement learning.
problem Compounding of one-step prediction errors in long trajectories.
method A multi-step objective function combining MSE losses at various future horizons.
result Models trained with the multi-step loss achieve significant improvement in future prediction.
Algorithm identifies bilinear dynamical systems from noisy data.
problem Learning a realization of a partially observed bilinear dynamical system.
method Regression of outputs to highly correlated covariates for Markov-like parameters.
result High probability error bounds on identification algorithm under uniform stability assumption.
CT-OT Flow estimates continuous-time dynamics from discrete snapshots.
problem Estimating continuous-time dynamics from temporally aggregated snapshots with noisy or uncertain timestamps.
method Two-stage framework: aligning neighboring intervals via partial optimal transport (POT) and reconstructing a continuous-time distribution through temporal kernel smoothing.
result Reduces distributional and trajectory errors compared with existing methods across synthetic and real datasets.
Neural surrogate predicts SPN rates from token trajectories.
problem Challenging parameter estimation in SPNs with covariates.
method 1D Convolutional Residual Network trained on Gillespie-simulated SPN realizations.
result Surrogate predicts rate-function coefficients with RMSE = 0.043.