New data improves market impact estimation methods.
problem Improving efficiency of market impact estimation.
method Investigates the use of price trajectory data for market impact estimation.
result Estimation methods using early trade prices outperform established methods asymptotically.
The paper provides uniform length estimates for trajectories on flat cone surfaces.
problem Estimating the length of trajectories on flat cone surfaces.
method Using self-intersection numbers and constants depending only on the flat metric, the paper focuses on convex flat cone spheres with a positive curvature gap and a fixed number of singularities.
result Uniform two-sided estimates for trajectory lengths on convex flat cone spheres are obtained.
Algorithm learns mixtures of Markov chains and MDPs from short trajectories.
problem Learning mixtures of Markov chains and MDPs from short unlabeled trajectories.
method Subspace estimation, spectral clustering, EM algorithm, model estimation, classification.
result 96.6% average accuracy on a mixture of two MDPs in gridworld, outperforming EM algorithm with random initialization.
Bayesian method estimates dynamics from near-optimal trajectories.
problem Estimating dynamics from near-optimal expert trajectories in reinforcement learning.
method Constraint-based Bayesian approach integrating expert near-optimality.
result Significant improvements in decision-making and transfer success.
Proposes a method to estimate SDE noise from a single trajectory.
problem Estimating SDE noise from a single data trajectory without ergodicity or stationarity.
method Combining Taylor expansions, Girsanov transformations, and drift function's initial value for drift and noise estimation.
result First SSISDE algorithm capable of identifying SDE dynamics from a single trajectory.
This work tackles uncertainty in multi-agent multi-modal trajectory forecasting.
problem Measuring and ranking uncertainty in multi-agent multi-modal trajectory forecasting.
method Proposes collaborative uncertainty (CU) and a CU-aware regression framework.
result The CU-aware regression framework improves SOTA systems' performances.
We consider billiard trajectories in a smooth convex body in Rd and estimate the number of distinct periodic trajectories that make exactly p reflections per period at the boundary of the body. In the case of prime p we obtain the lower bound (d−2)(p−1)+2, which is much better than the previous estimat…
In this paper the problem of estimating the number of periodical billiard trajectories is considered. The main result is the theorem on Morse theory for periodical billiard trajectories.
Foot-mounted inertial positioning (FMIP) can face problems of inertial drifts and unknown initial states in real applications, which renders the estimated trajectories inaccurate and not obtained in a well defined coordinate system for matching trajectories of different users. In this paper, an approach adopting receiv…
A new method detects anomalies in trajectory data using normalizing flows.
problem Detecting anomalous patterns in high-dimensional, varying-length spatial data.
method Probability density estimation via normalizing flows for each trajectory segment, aggregating likelihoods.
result The proposed method, GRADINGS, effectively identifies anomalies in real-world trajectory data.
Method estimates forces from agent trajectories to infer static obstacles.
problem Estimating forces from agent trajectories to infer static obstacles.
method Artificial neural networks to estimate non-parametric velocity fields.
result Incrementally learns velocity fields due to static objects.
Paper characterizes optimal learning trajectories for high-dimensional nonlinear models.
problem Characterizing optimal learning trajectories in high-dimensional nonlinear models.
method Exploits maximum principle and dynamic programming for an optimal control problem of a gradient system.
result Constructs optimal learning trajectories leading to optimal model parameters.
Trajectory-wise CVs reduce variance in policy gradient methods.
problem High variance in estimating policy gradient estimates.
method Proposes trajectory-wise control variates to reduce variance without bias.
result Trajectory-wise CVs are optimal for variance reduction under reasonable assumptions.
The paper proposes a method to decompose value functions in RL for better understanding and prediction.
problem Understanding and predicting the dynamics and returns in reinforcement learning models.
method A two-step approach decomposing the value function into future dynamics and trajectory returns, with a practical deep RL algorithm.
result The proposed algorithm outperforms in MuJoCo tasks, especially under delayed reward settings.
Estimates MLDS using tensor decomposition, improving upon existing methods.
problem Learning mixtures of linear dynamical systems from input-output data.
method Proposes a moment-based estimator using tensor decomposition.
result Improves sample complexity bounds for estimating MLDS.
The paper extends a neural model to estimate uncertainty in multi-interaction trajectory reconstruction.
problem Lack of uncertainty estimation in neural models for multi-interaction trajectory reconstruction.
method Extended Factorised Neural Relational Inference model to output mean and standard deviation for each component of the phase space vector, using various loss functions.
result Demonstrated the importance of physical meaning of variables and existence of local minima during training.
The study finds billiard trajectories with infinitely many reflections in certain cones.
problem Existence of billiard trajectories with infinitely many reflections.
method Analysis of C3 convex cones and elliptic cones in R3. result Existence of C2 convex cones with billiard trajectories having infinitely many reflections. 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.
Algorithm recovers graph from Glauber dynamics trajectory without mixing.
problem Learning Gaussian graphical models from a single Glauber dynamics trajectory.
method Three components: conditional variance estimation, pairwise influence test, robust median aggregation.
result Polynomial-time recovery of conditional independence graph from a single trajectory.
In this paper, we present a new location fingerprinting database comprised of Wi-Fi received signal strength (RSS) and geomagnetic field intensity measured with multiple devices at a multi-floor building in Xi'an Jiatong-Liverpool University, Suzhou, China. We also provide preliminary results of localization and trajec…
We use splines and the Sasaki metric to analyze and compare manifold-valued trajectories.
problem Analyzing and comparing trajectories on Riemannian manifolds.
method Riemannian hierarchical model, Bézier splines, Sasaki metric.
result Spline-based approaches outperform state-of-the-art methods in intensity classification of trajectories.
New method learns cell trajectories and network interactions from single-cell data.
problem Network inference in systems biology from steady-state data.
method Min-entropy estimation for stochastic dynamics, leveraging both temporal and perturbational data.
result Jointly learns cellular trajectories and network interactions.
Paper identifies sparse LTI systems from a single trajectory.
problem Identifying sparse linear time-invariant systems from a single sample trajectory.
method Lasso-like estimator for sparse parameters, considering stability or stabilizing controller.
result Sharp finite-time guarantees on accurate recovery of sparsity and parameter values.
Active learning method estimates nonlinear systems efficiently.
problem Identifying nonlinear dynamical systems with continuous states and actions.
method Repeating three steps: trajectory planning, tracking, and re-estimation.
result Estimates nonlinear dynamical systems at a parametric rate.
EPD method accurately captures parameter distributions from RCS data.
problem Limitations of traditional methods in estimating parameter distributions from RCS data.
method EPD method generates synthetic trajectories, estimates parameters, and selects parameters based on discrepancy.
result EPD provides accurate distribution of parameters without data loss.
LLMs learn probability density functions in-context, showing distinct learning trajectories.
problem Density estimation of time series data in LLMs.
method Intensive Principal Component Analysis (InPCA) to visualize and analyze LLMs' learning dynamics.
result LLMs follow similar learning trajectories in a low-dimensional InPCA space, distinct from traditional methods.
Improved neural network predicts tropical storm trajectories and Bayesian intervals.
problem Accurately predicting the trajectories of tropical storms to prevent damage.
method Developed an improved RNN model with dropout to predict Bayesian intervals.
result Neural network dropout values significantly affect prediction accuracy and intervals.
Novel framework predicts brain biomarker trajectories with superior performance.
problem Challenges in estimating longitudinal brain biomarker trajectories due to variability, inconsistencies, and irregular measurements.
method Personalized deep kernel regression with Adaptive Shrinkage Estimation.
result Superior predictive performance compared to state-of-the-art models.
Given a domain or, more generally, a Riemannian manifold with boundary, a billiard is the motion of a particle when the field of force is absent. Trajectories of such a motion are geodesics inside the domain; and the particle reflects from the boundary making the angle of incidence equal the angle of reflection. The bi…
Proposes a method to learn system dynamics and region of attraction from trajectories.
problem Learning accurate dynamics and region of attraction from system trajectories.
method Uses local stability information as a prior to learn vector field and region of attraction.
result Efficient sampling and accurate estimate of dynamics in inner approximation of region of attraction.
Paper proposes a method for optimizing local policies for trajectory-centric reinforcement learning.
problem Challenges in global policy optimization for non-linear systems and poor performance of open-loop trajectory optimization.
method Formulates trajectory optimization and local policy synthesis as a single optimization problem and solves it as a nonlinear programming instance.
result Demonstrates improved performance of the proposed technique under simplifying assumptions.
This work presents a methodology to design trajectory tracking feedback control laws, which embed non-parametric statistical models, such as Gaussian Processes (GPs). The aim is to minimize unmodeled dynamics such as undesired slippages. The proposed approach has the benefit of avoiding complex terramechanics analysis …
A method for inferring motility models and heterogeneity from particle trajectories.
problem Understanding motility patterns from discrete trajectory data of biological agents.
method Maximum likelihood approach for second-order Langevin models with population heterogeneity.
result The proposed method outperforms alternative approaches for short trajectories.
Physics-informed diffusion model detects anomalous trajectories in GPS data.
problem Detecting fake GPS trajectories in international waters.
method Physics-informed diffusion model integrating kinematic constraints.
result Higher prediction accuracy and lower error rate for anomaly detection.
Estimates interaction laws from agent trajectories without assuming their form.
problem Inferring interaction laws from observational data in complex systems.
method Non-parametric statistical learning approach from trajectory data.
result Effectiveness demonstrated in various disciplines, including physics, opinion dynamics, and biology.
New method improves learning from multiple correlated data trajectories.
problem Learning from multiple correlated data trajectories without mixing assumptions.
method Hellinger localization framework for maximum likelihood estimation.
result Instance-optimal bounds that scale with full data budget under broad conditions.
New method for predicting paths of unpredictable objects with high confidence.
problem Need for dependable uncertainty estimates in motion planning with diverse unpredictable objects.
method Blend online conformal prediction, multiple time series techniques, and heteroscedasticity addressing.
result Simultaneous forecasting bands that cover entire paths with high probability.
Paper learns interaction laws from multiple trajectories of heterogeneous systems.
problem Estimating unknown interaction laws from multiple trajectories of heterogeneous systems.
method Nonparametric learning of interaction kernels based on pairwise distances, with convergence guarantees in L2 space. result Estimators converge at optimal min-max rate for 1-dimensional nonparametric regression.
Improves model-based control and exploration by estimating model uncertainty.
problem Inaccuracies in model predictions lead to frequent re-planning, inefficiency, and unreliability.
method Estimates model uncertainty using reconstruction error and uses it for better control and active exploration.
result Improves control performance and exploration efficiency by choosing confident model predictions and planning for high uncertainty.
Estimates causal effects from patient trajectories using DeepACE model.
problem Estimating causal effects from observational data in medical practice.
method DeepACE model using iterative G-computation formula and sequential targeting procedure.
result DeepACE achieves state-of-the-art performance in estimating time-varying ACEs.
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.
NDDV estimates data point value from a single stochastic trajectory.
problem Estimating marginal contributions of data points over stochastic training paths.
method Introduces Neural Dynamic Data Valuation (NDDV) using stochastic state and adjoint equations.
result NDDV provides a one-run, trajectory-conditioned estimator of data point value.
We propose a method to learn a distribution of shape trajectories from longitudinal data, i.e. the collection of individual objects repeatedly observed at multiple time-points. The method allows to compute an average spatiotemporal trajectory of shape changes at the group level, and the individual variations of this tr…
New method learns particle system potentials from unlabeled data.
problem Learning potentials of interacting particle systems from unlabeled data with trajectory information missing.
method Introduces a self-test loss function based on stochastic evolution equation.
result Method outperforms baseline methods in robust estimation of large, high-dimensional systems.
WMPG reduces policy gradient variance using world models.
problem Reducing variance in policy gradient estimates.
method Trains a world model online to estimate policy gradients and uses imagined trajectories as a baseline.
result WMPG achieves better sample efficiency compared to AC and MAC.
The study analyzes the performance of a nonparametric estimator for dynamical systems.
problem Analyzing the performance of a nonparametric estimator for dynamical systems.
method Nonparametric least squares estimator (LSE) and information-theoretic methods.
result Rate-optimal error bounds for nonparametric hypotheses classes.
Reinforcement learning with trajectory feedback instead of state-action rewards.
problem Frequent feedback not available in practice.
method Extended reinforcement learning algorithms using trajectory feedback for known and unknown transition models.
result Hybrid optimistic-Thompson Sampling algorithm for unknown transition models.
TD learning reduces prediction error in Markov chain problems.
problem Estimating value functions in Markov chains with temporal inconsistency.
method Temporal difference learning minimizes temporal inconsistency between successive estimates.
result TD learning can significantly reduce mean-squared error in value estimates.