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.
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.
Analyzing the urban trajectory in cities has become an important topic in data mining. How can we model the human mobility consisting of stay and travel from the raw trajectory data? How can we infer such a mobility model from the single trajectory information? How can we further generalize the mobility inference to ac…
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.
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.
New algorithms learn stability certificates from data, avoiding complex dynamics.
problem Synthesizing stability certificates from complex dynamical systems.
method Developed algorithms to learn certificate functions from trajectory data, establishing generalization error bounds.
result Efficiently learned certificates can be used for adaptive control.
E-valuator converts verifier scores into reliable decision rules.
problem Ensuring the correctness of agent trajectories based on heuristic scores.
method Sequential hypothesis testing framework for online monitoring of agent trajectories.
result E-valuator provides better false alarm rate control and statistical power than other strategies.
The paper provides theoretical guarantees for behavior cloning using generative models.
problem Behavior cloning of complex expert demonstrations using generative models.
method The paper proposes a theoretical framework invoking low-level controllers to stabilize imitation around expert demonstrations. It shows that with suitable low-level stability guarantees and powerful generative models, pure supervised behavior cloning can match expert trajectories.
result The paper proves that with a suitable low-level stability guarantee and a powerful enough generative model, pure supervised behavior cloning can generate trajectories matching the per-time step distribution of essentially arbitrary expert trajectories in an optimal transport cost.
Gaussian Processes (GPs) are widely employed in control and learning because of their principled treatment of uncertainty. However, tracking uncertainty for iterative, multi-step predictions in general leads to an analytically intractable problem. While approximation methods exist, they do not come with guarantees, mak…
Study risk-controlling prediction sets for single trajectory data from dynamical systems.
problem Performance guarantees for risk-controlling prediction sets in single trajectory data from unknown stochastic dynamical systems.
method Used blocking and decoupling techniques to analyze performance guarantees under different data generating processes.
result Performance guarantees similar to iid setting when data is stationary and contractive, with graceful degradation otherwise.
Algorithm learns multiple LDS models from unlabeled short trajectories.
problem Learning from unlabeled short sample trajectories of multiple LDS models.
method Two-stage meta-algorithm with end-to-end performance guarantees.
result Efficiently recovers each ground-truth LDS model up to error i l d e O ( d / T ) ilde{O}(\sqrt{d/T}) i l d e O ( d / T ) . The paper extends conformal prediction to MDP trajectories for autonomous systems.
problem Ensuring reliability of autonomous systems by providing probabilistic guarantees.
method Applying conformal corrections to quantile regression prediction intervals.
result Conformal prediction intervals ensure the observed trajectory lies inside with high probability.
Guaranteed reachable set for unknown nonlinear systems on manifolds.
problem Determining reachable set for unknown nonlinear systems on manifolds.
method Underapproximations of reachable set using local dynamics and bounds on dynamics rate of change.
result Guaranteed set of reachable states for systems on complete Riemannian manifolds.
Method predicts biomarker trajectories with uncertainty bands for Alzheimer's disease.
problem Uncertainty in biomarker predictions poses risks in clinical deployment.
method Conformal prediction for randomly-timed biomarker trajectories.
result Conformal bands achieve desired coverage and are tighter than baseline.
Meta-algorithm for efficient reinforcement learning from human preferences.
problem Learning from human preference comparisons in Markov decision processes.
method Randomized exploration and experimental design for batch comparison queries.
result Meta-algorithm achieves both regret and last-iterate guarantees with minimal preference queries.
Stable GFlowNets prevent loss spikes and mode collapse in training.
problem Unstable training of GFlowNets leading to loss spikes and mode collapse.
method Assessed sensitivity of GFlowNet objectives, derived loss-to-TV bounds, and proposed Stable GFlowNets.
result Stable GFlowNets improve training behavior and distributional fidelity.
Paper proposes method for optimal control of unknown systems with latent states.
problem Jointly estimating dynamics and latent states in systems with unmeasurable states.
method Combination of particle Markov chain Monte Carlo methods and scenario theory.
result Probabilistic performance guarantees for optimal input trajectories.
The vision of automated driving is to increase both road safety and efficiency, while offering passengers a convenient travel experience. This requires that autonomous systems correctly estimate the current traffic scene and its likely evolution. In highway scenarios early recognition of cut-in maneuvers is essential f…
Study learns dynamics of linear systems from multiple short trajectories.
problem Learning dynamics of autonomous linear systems from multiple short trajectories.
method Finite sample analysis for stable and unstable systems, adjusting trajectory length for marginally stable systems.
result Learning rate of O ( 1 N ) \mathcal{O}(\frac{1}{\sqrt{N}}) O ( N 1 ) for both stable and unstable systems. New algorithm infers trajectories from partial observations using optimal transport.
problem Inferring trajectories from partial observations of coupled systems.
method Extends MFL algorithm to latent SDEs using observable state space models and partial observations.
result Experiments show significant outperformance over latent-free baseline.
Estimates network structure and interaction rules from multiple agent trajectories.
problem Modeling multi-agent systems on networks from data.
method Jointly infers network topology and interaction kernels using non-convex optimization.
result ORALS estimator is consistent and asymptotically normal under coercivity conditions.
Proposes a recursive MPC scheme with probabilistic safety guarantees for uncertain dynamic systems.
problem Probabilistic safety guarantees for MPC in dynamic environments with unknown stochastic agents.
method Uses conformal prediction to derive high-confidence prediction regions and gradually relax safety constraints online.
result Ensures recursive feasibility of MPC schemes by relaxing safety constraints over time.
Study of supervised learning from multiple non-independent sequences.
problem Efficient learning from many non-independent sequences.
method Generalizes conditions for efficient learning from independent examples and single auto-correlated sequences.
result Error rate changes from Θ ( n / m T ) Θ(n / m T) Θ ( n / m T ) to Ω ( n 2 / m 2 T ) Ω(n^2 / m^2 T) Ω ( n 2 / m 2 T ) as the number of trajectories increases. Probabilistic vehicle trajectory prediction is essential for robust safety of autonomous driving. Current methods for long-term trajectory prediction cannot guarantee the physical feasibility of predicted distribution. Moreover, their models cannot adapt to the driving policy of the predicted target human driver. In th…
Trajectory-level supervision allows efficient offline reinforcement learning.
problem Offline reinforcement learning
method Developing a statistical theory for offline policy optimization from trajectory-level labels
result Proving a high-probability guarantee of order O ~ ( H 2 C s a ( π ⋆ ) / n ) \widetilde O(H^2\sqrt{C_{sa}(\pi^\star)/n}) O ( H 2 C s a ( π ⋆ ) / n ) New method predicts Alzheimer's risk with individual uncertainty estimates.
problem Predicting conversion from mild cognitive impairment to Alzheimer's disease.
method Persistent homology of clinical trajectories combined with stacking ensemble.
result Pipeline achieves high accuracy and individual-level uncertainty quantification.
The paper provides a non-asymptotic error bound for linear system identification under nonlinear policies.
problem System identification for linear systems with nonlinear and/or time-varying policies under i.i.d. random excitation noises.
method Least square estimation with non-asymptotic error bound for bounded state and action trajectories.
result The error bound is consistent with linear policies and generalizes existing guarantees.
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.
Adaptive stopping in MCMC using classifier-based dynamics
problem Sampling from complex, unnormalized probability densities
method Training state-dependent neural classifiers
result Significant reduction in average trajectory lengths
New algorithm improves RL performance across different environments.
problem Improving reinforcement learning performance across various environments.
method Designing a fully model-free DRRL algorithm that learns from a single trajectory.
result Demonstrates superior robustness and sample efficiency compared to existing methods.
Paper tackles offline preference-based RL with human feedback.
problem Offline Preference-based Reinforcement Learning with preference feedback.
method Two-step approach: MLE for reward estimation and distributionally robust planning.
result First guarantee for learning any target policy with polynomial samples.
Study on estimating unstable open-loop matrices from state trajectories.
problem System identification for stochastic continuous-time dynamics.
method Employing randomized control inputs to estimate unstable open-loop matrix.
result Estimation error decays with trajectory length, signal-to-noise ratio, and excitability.
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.
In the generalized Legendre approach, the equation describing an asymptotically locally Euclidean space of type D n D_n D n is found to admit an algebraic formulation in terms of the group law on a Weierstrass cubic. This curve has the structure of a Cayley cubic for a pencil generated by two transversal plane conics, that i…
Modeling driver trajectories using inverse reinforcement learning and random utility.
problem Modeling rational driver behavior in road networks from sparse sensor data.
method Apply random utility theory to model unknown reward function, introduce extended state, and use Markov decision process.
result Maximum entropy inverse reinforcement learning is a special case of the proposed approach.
We consider a vector field X X X on a closed manifold which admits a Lyapunov one form. We assume X X X has Morse type zeros, satisfies the Morse--Smale transversality condition and has non-degenerate closed trajectories only. For a closed one form η η η , considered as flat connection on the trivial line bundle, the differen…
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.
A new metric compares dynamical systems using operator eigenvalues.
problem Comparing and interpolating nonlinear dynamical systems from trajectory data.
method Representing systems as distributions of operator eigenvalues and projectors, defining a spectral-Grassmann Wasserstein metric.
result The proposed metric outperforms standard operator-based distances in machine learning applications.
Ability to quantify and predict progression of a disease is fundamental for selecting an appropriate treatment. Many clinical metrics cannot be acquired frequently either because of their cost (e.g. MRI, gait analysis) or because they are inconvenient or harmful to a patient (e.g. biopsy, x-ray). In such scenarios, in …
Hamiltonian dynamics-based algorithms achieve deterministic and accelerated convergence for convex optimization.
problem Accelerating convex optimization
method Hamiltonian dynamics
result Hamiltonian dynamics-based algorithms achieve deterministic and accelerated convergence for convex optimization.
Develops anytime-valid stopping rules for SGD based on observed trajectory.
problem Stopping stochastic gradient descent (SGD) based on observed trajectory.
method Develops anytime-valid confidence sequences for stochastic gradient methods.
result Statistically valid, time-uniform stopping rules for SGD across convex and nonconvex settings.
Algorithm learns weight matrix from single trajectory of nonlinear dynamical system.
problem Learning weight matrix from a single trajectory of nonlinear dynamical system.
method Algorithm uses global stability and well-conditioned covariance to recover weight matrix.
result Algorithm recovers weight matrix with optimal sample complexity and linear running time.
MA-COPP predicts multi-agent system outcomes using data from a different policy, with probabilistic guarantees.
problem Predicting outcomes in multi-agent systems using data from a different policy.
method Conformal prediction framework applied to multi-agent systems, avoiding exhaustive search.
result Achieves probabilistic guarantees for multi-agent system predictions.
Paper tackles hard shape constraints in kernel machines.
problem Enforcing shape requirements in a hard fashion is challenging.
method Tightened second-order cone constrained reformulation for kernel machines.
result Performance guarantees and efficiency demonstrated in various applications.
Improves BC policies by generating new plausible trajectories.
problem Sub-optimal data quality in BC leads to poor policy performance.
method Trajectory Stitching (TS) generates new plausible transitions.
result TS significantly improves behavioural policies over original data.
Paper proves higher-order flow matching preserves optimality in generative modeling.
problem Theoretical guarantees for higher-order flow matching in generative modeling.
method Neural network approximations with controlled depth, width, and sparsity.
result Proves worst case optimality for second-order flow matching.
Inferring the laws of interaction between particles and agents in complex dynamical systems from observational data is a fundamental challenge in a wide variety of disciplines. We propose a non-parametric statistical learning approach to estimate the governing laws of distance-based interactions, with no reference or a…
New method learns nonlinear systems from single finite trajectory samples.
problem Learning stabilizable nonlinear systems from single finite trajectory samples.
method Gradient-based algorithms with noise-sensitive uniform convergence guarantees.
result Efficient learning of general nonlinear systems with high accuracy and small sample complexity.