When an online learning algorithm is used to estimate the unknown parameters of a model, the signals interacting with the parameter estimates should not decay too quickly for the optimal values to be discovered correctly. This requirement is referred to as persistency of excitation, and it arises in various contexts, s…
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48 results for “persistent excitation”
New method improves neural network robustness to adversarial attacks.
problem Improving adversarial robustness of neural networks.
method Inspired by adaptive control theory, the approach uses persistency of excitation to constrain gradient descent updates.
result Networks trained with the PoE-motivated learning rate schedule are significantly more robust to adversarial attacks.
Lower bounds and upper bounds on sample complexity for identifying linear dynamical systems.
problem Identifying an unknown linear dynamical system with limited data.
method Sample complexity lower and upper bounds, persistent excitation condition, active learning algorithm.
result Lower and upper bounds share the same dependency on key problem parameters.
Study models market volatility with persistent and temporary impacts.
problem Microstructure of rough volatility models driven by Poisson measures.
method Existence and uniqueness of solutions for stochastic path-dependent Volterra equations.
result Volatility process converges to fractional Heston model with spikes.
Paper revisits set membership estimation for linear systems with relaxed disturbance bounds.
problem Set membership estimation for linear systems with disturbances bounded by convex sets.
method Adopted block-martingale small-ball condition and random perturbed control policies to establish convergence rates.
result Established convergence rates for disturbances bounded by general convex sets.
Neural networks are based on a simplified model of the brain. In this project, we wanted to relax the simplifying assumptions of a traditional neural network by making a model that more closely emulates the low level interactions of neurons. Like in an RNN, our model has a state that persists between time steps, so tha…
We study the constrained linear quadratic regulator with unknown dynamics, addressing the tension between safety and exploration in data-driven control techniques. We present a framework which allows for system identification through persistent excitation, while maintaining safety by guaranteeing the satisfaction of st…
Machine learning speeds up quantum chemical calculations of excited states.
problem Accurate quantum chemical calculations of excited states are computationally expensive.
method Employing machine learning to speed up and advance excited-state simulations in various fields.
result Machine learning techniques can significantly reduce computational time for excited-state simulations.
New self-exciting random evolutions (SEREs) for modeling traffic and transport processes.
problem Modeling self-exciting and clustering effects in traffic and transport processes.
method Introducing a new process based on a superposition of a Markov chain and a Hawkes process, and constructing self-exciting random evolutions (SEREs).
result Developed new models and limit theorems for SEREs, including averaging and diffusion approximation.
Direct Mapping Hidden Excited State Interaction Patterns from ab initio Dynamics and Its Implications on Force Field Developmentphysics.chem-ph
The excited states of polyatomic systems are rather complex, and often exhibit meta-stable dynamical behaviors. Static analysis of reaction pathway often fails to sufficiently characterize excited state motions due to their highly non-equilibrium nature. Here, we proposed a time series guided clustering algorithm to ge…
Machine learning and excited-state molecular dynamicsphysics.chem-ph
Machine learning aids excited-state molecular dynamics studies.
problem Challenges in studying electronically excited states of molecules.
method Employing machine learning techniques for excited-state molecular dynamics.
result Highlight successes and challenges in machine learning for excited-state processes.
Algorithm estimates parameters over time-varying graphs without special assumptions.
problem Estimating parameters over time-varying graphs without assuming independence.
method Decentralized online regularized learning with innovation, consensus, and regularization terms.
result Estimations converge almost surely under certain conditions.
Optimal reinsurance strategy analyzed for dynamic risk model with self- and externally-excited jumps.
problem Optimal reinsurance in a dynamic contagion model with self-exciting and externally-exciting risks.
method Two methodologies: classical HJB approach and BSDE approach, focusing on Markovian setting.
result Comparison of self-exciting and externally-exciting risks highlights heightened risk from self-exciting component.
Paper presents a method for estimating Hawkes process parameters.
problem Estimating parameters of Hawkes processes with self-excitation or inhibition.
method Maximum likelihood estimation for Hawkes processes with self-excitation or inhibition.
result The proposed estimator provides more accurate estimations in the inhibition context.
In Levin-Wen (LW) models, a wide class of exactly solvable discrete models, for two dimensional topological phases, it is relatively easy to describe only single fluxon excitations, but not the charge and dyonic as well as many-fluxon excitations. To incorporate charged and dyonic excitations in (doubled) topological p…
3D ConvNets improved with Project & Excite for medical imaging segmentation.
problem Improving segmentation performance in 3D medical imaging.
method Proposed Project & Excite (PE) modules for 3D F-CNNs, extending 2D recalibration methods.
result Project & Excite modules boost segmentation performance up to 0.3 in Dice Score.
Learning a Class of Mixed Linear Regressions: Global Convergence under General Data Conditionsstat.ML
Paper addresses global convergence of MLR estimation under weak data conditions.
problem Learning mixed linear regression models with general data conditions.
method Two-step recursive identification algorithm using least squares and EM principles.
result Global convergence and optimal clustering performance established under general data conditions.
Deep Learning for UV Absorption Spectra with SchNarc: First Steps Towards Transferability in Chemical Compound Spacephysics.chem-ph
Paper explores ML for UV spectra, showing transferability in chemical space.
problem Modeling excited states and predicting properties of unseen molecules.
method Adapting charge model for excited states, using SchNarc approach.
result ML models can predict properties of unseen molecules and different excited states.
Electronic excited states in deep variational Monte Carlophysics.chem-ph
Deep QMC method accurately computes electronic excited states.
problem Accurate calculation of electronic excited states in large systems.
method Extends variational QMC with deep neural networks for excited states.
result Consistently achieves high accuracy for low-lying excited states.
Linear Convergence of Entropy-Regularized Natural Policy Gradient with Linear Function Approximationcs.LG
Entropy-regularized NPG converges linearly with linear function approximation.
problem Analyzing convergence of entropy-regularized NPG with function approximation.
method Established finite-time convergence analyses with entropy regularization and linear function approximation.
result Entropy-regularized NPG achieves linear convergence up to a function approximation error.
A new model predicts discrete events with flexible, nonparametric baseline and excitation.
problem Limited flexibility in discrete Hawkes models for event prediction.
method Gaussian Process Discrete Hawkes Process (GP-DHP) with collapsed latent representation.
result Improves predictive log-likelihood for diverse event patterns.
Study learns linear system dynamics from noisy bilinear data.
problem Learning linear dynamics from bilinear observations with process and measurement noise.
method Regression with Kronecker product design, data-dependent and independent error bounds.
result Upper bounds on statistical error rates and sample complexity for learning dynamics matrices.
Price changes are induced by aggressive market orders in stock market. We introduce a bivariate marked Hawkes process to model aggressive market order arrivals at the microstructural level. The order arrival intensity is marked by an exogenous part and two endogenous processes reflecting the self-excitation and cross-e…
Coexisting Hidden and self-excited attractors in an economic system of integer or fractional orderq-fin.GN
Paper analyzes coexisting hidden and self-excited attractors in an economic system.
problem Existence of coexisting hidden and self-excited attractors in economic systems.
method Integer and fractional order analysis of an economic system.
result Integer-order system exhibits multiple combinations of coexisting hidden and self-excited attractors.
We provide a general probabilistic framework within which we establish scaling limits for a class of continuous-time stochastic volatility models with self-exciting jump dynamics. In the scaling limit, the joint dynamics of asset returns and volatility is driven by independent Gaussian white noises and two independent …
Optimal noise excitation for linear system identification reduces sample complexity.
problem Efficiently identifying linear systems with minimal data.
method Active learning algorithm using ordinary least squares and semidefinite programming.
result The proposed algorithm matches lower bounds on sample complexity for any active learning method.
Excited-state dynamics simulations are a powerful tool to investigate photo-induced reactions of molecules and materials and provide complementary information to experiments. Since the applicability of these simulation techniques is limited by the costs of the underlying electronic structure calculations, we develop an…
New algorithm learns LQR with regret using Langevin dynamics and excitation.
problem Learning LQR with a regret bound.
method Thompson sampling with Langevin dynamics and excitation mechanism.
result Achieved regret bound for LQR learning.
Paper forecasts financial trading durations using a new point process model.
problem Forecasting limit order book durations in high-frequency financial data.
method Self-exciting flexible residual point process incorporating empirical distributional features.
result The model achieves strong predictive performance compared to alternative approaches.
Motor control is a set of time-varying muscle excitations which generate desired motions for a biomechanical system. Muscle excitations cannot be directly measured from live subjects. An alternative approach is to estimate muscle activations using inverse motion-driven simulation. In this article, we propose a deep rei…
The Hawkes process is a simple point process, whose intensity function depends on the entire past history and is self-exciting and has the clustering property. The Hawkes process is in general non-Markovian. The linear Hawkes process has immigration-birth representation. Based on that, Fierro et al. recently introduced…
Technical Report: Adaptive Control for Linearizable Systems Using On-Policy Reinforcement Learningcs.LG
Paper proposes adaptive control for unknown systems using reinforcement learning.
problem Adaptive control for unknown, linearizable systems.
method On-policy reinforcement learning for discrete-time, stochastic systems.
result Stability and tracking errors concentrate near zero with high probability.
Approaches for approximating persistent homology for large datasets.
problem Inability to compute persistent homology for large datasets.
method Multiple subsampling framework for statistical approximation of persistent homology.
result Derivation of finite sample convergence rates for empirical means of persistent homology.
Persistence landscapes map persistence diagrams into a function space, which may often be taken to be a Banach space or even a Hilbert space. In the latter case, it is a feature map and there is an associated kernel. The main advantage of this summary is that it allows one to apply tools from statistics and machine lea…
Develops a goodness-of-fit test for self-exciting processes.
problem Quantifying how well generative models capture self-exciting point processes.
method Connects to Quasi-maximum-likelihood estimator (QMLE) theory and develops a non-parametric self-normalizing statistic, the Generalized Score (GS) statistics.
result Validates the proposed GS test's good performance through numerical simulation and real-data experiments.
Proposes deep graph persistence to address neural persistence issues in deep learning.
problem Variance of weights and lack of spatial structure in deep neural networks impact neural persistence.
method Extends neural persistence to the whole network, considering interactions between layers.
result Deep graph persistence alleviates variance-related issues and captures persistent paths through the network.
Paper proves -means clustering works on persistence diagrams.
problem Complex geometry of persistence diagram space.
method Proves convergence of -means on persistence diagram space.
result Performance of -means on persistence diagrams and measures is superior.
Formula for interleaving distance of rectangle persistence modules.
problem Calculating distances between rectangle persistence modules.
method Formulas based on rectangle geometry, extended to decomposable modules.
result Closed formulas for interleaving and bottleneck distances.
Multiplex Network Hawkes model for systemic risk measurement
problem Investigate how contagion in financial networks is affected by different transmission channels
method Multiplex Network Hawkes model
result Sparse contagion pathways, with systemic-risk transmission concentrated in outward flows from a small number of influential institutions
This paper demonstrates the flaws of co-persistence theory proposed by Bollerslev and Engle (1993) which cause the theory can hardly be applied. With the introduction of the half-life of decay coefficient as the measure of the persistence, and both the weak definition of persistence and co-persistence in variance, this…
Study optimal dividend and capital injection in insurance portfolios with self-exciting claim arrivals.
problem Optimal dividend and capital injection in insurance portfolios with Hawkes process claim arrivals.
method Analytical properties, explicit threshold, HJB variational inequality, finite-difference scheme, policy-gradient, actor-critic methods.
result Learned strategies closely match the PDE benchmark and remain stable across initial conditions.
Optimizes wavelets for graph classification using spectral wavelet signatures and persistence diagrams.
problem Graph classification with geometric properties encoded in persistence diagrams.
method Optimizes spectral wavelets for graph datasets to capture best-suited features for classification.
result Competitive performance in graph classification problems compared to other persistence-based architectures.
New method for analyzing multiparameter persistence modules from smooth functions.
problem Analyzing multiparameter persistence modules from smooth functions.
method Generalized Morse theory applied to cobordism and Cerf theory.
result Complete description of persistence modules as direct sums of indecomposables.
Develops robust persistence diagrams using kernel methods.
problem Persistence diagrams are sensitive to data perturbations.
method Constructs robust persistence diagrams from superlevel filtrations of robust density estimators using reproducing kernels.
result Robust persistence diagrams are consistent estimators in bottleneck distance.
Paper introduces MSPD for multivariate risk processes with dependencies.
problem Computing risk valuations with dynamic dependencies between frequency and severity.
method Combines Poisson imbedding, pseudo-chaotic expansion, and Malliavin calculus.
result Explicit general correlation formula for MSPDs.
In this paper we consider a mean-field model of interacting diffusions for the monetary reserves in which the reserves are subjected to a self- and cross-exciting shock. This is motivated by the financial acceleration and fire sales observed in the market. We derive a mean-field limit using a weak convergence analysis …
This paper interprets critical scales in persistent homology for compact metric spaces.
problem Understanding critical scales in persistent homology for general compact metric spaces.
method Analyzing local minima of the distance function and their impact on persistence.
result Each decrease in zero-dimensional persistence and increase in one-dimensional persistence is induced by local minima of the distance function.
The so(d+2,2) Minimal Representation and Ambient Tractors: the Conformal Geometry of Momentum Spacehep-th
Tractor Calculus is a powerful tool for analyzing Weyl invariance; although fundamentally linked to the Cartan connection, it may also be arrived at geometrically by viewing a conformal manifold as the space of null rays in a Lorentzian ambient space. For dimension d conformally flat manifolds we show that the (d+2)-di…