Unified bounds for random subset generalization error and improved SGD Langevin dynamics.
problem Generalization error bounds for random subsets and stochastic gradient Langevin dynamics.
method Unified framework based on Hellström and Durisi's work, extending bounds for Langevin dynamics.
result Unified and refined bounds for generalization error in stochastic gradient Langevin dynamics.
Investigates multifractal scaling in critical dynamics of random surfaces.
problem Analyzing multifractal scaling in critical dynamics of random surfaces.
method Examined multifractal scaling in various conformal field theories on random surfaces.
result Higher moments of time variations of the order parameter exhibit multifractal scaling.
Machine learning identifies chimera states in complex dynamical systems.
problem Chimera states are hard to identify due to their varied appearance and peculiar nature.
method Machine learning techniques, specifically random forest and oblique random forest with null space regularization.
result High accuracy in identifying chimera states across different dynamical models.
Develops path integral for spiked tensor model dynamics.
problem Dynamics of spiked tensor model with random initial conditions.
method Path integral approach applied to partial differential equations.
result Large-N saddle point equations dominated by melonic diagrams. Paper introduces a novel method for dynamic covariance estimation with random forests.
problem Estimating high-dimensional dynamic covariance matrices with multiple covariates.
method Nonparametric approach using random forests.
result Uniform consistency theory and error rates established for high-dimensional scenarios.
dynnode2vec embeds dynamic networks efficiently.
problem Capturing evolving patterns in large dynamic networks.
method dynnode2vec: a random walk based method initialized with previous embedding vectors.
result Demonstrates advantages over static methods on large dynamic network datasets.
We investigate i.i.d. random complex dynamical systems generated by probability measures on finite unions of the loci of holomorphic families of rational maps on the Riemann sphere. We show that under certain conditions on the families, for a generic system, (especially, for a generic random polynomial dynamical system…
Deep neural nets approximate random dynamical system trajectories uniformly in time.
problem Approximating trajectories of random dynamical systems over infinite time horizons.
method Recurrent neural networks with simple feedback structures.
result Certain random trajectories can be approximated uniformly in time to any desired accuracy.
The paper studies random dynamical systems of polynomial automorphisms on C^2 and finds mean stability.
problem Random dynamical systems of polynomial automorphisms on C^2.
method Generic random dynamical systems of polynomial automorphisms are shown to have mean stability.
result A generic random dynamical system of polynomial automorphisms on C^2 has mean stability.
Improved sampling efficiency with Random Reshuffling for Langevin dynamics.
problem Sampling efficiency in stochastic gradient algorithms.
method Random Reshuffling for Stochastic Gradient Langevin Dynamics (SGLD).
result Random Reshuffling leads to improved performance in sampling.
We investigate the random dynamics of rational maps on the Riemann sphere and the dynamics of semigroups of rational maps on the Riemann sphere. We show that regarding random complex dynamics of polynomials, in most cases, the chaos of the averaged system disappears, due to the cooperation of the generators. We investi…
Dynamic programming helps manage fisheries affected by random disturbances.
problem Managing fisheries affected by random disturbances.
method Dynamic programming approach to analyze and optimize management strategies.
result Dynamic programming is crucial for fully characterizing optimal harvest strategies.
New model stabilizes asynchronous LTI systems, independent of synchronous stability.
problem Stability of asynchronous LTI systems under randomization and asynchrony.
method Introduced a new model for random asynchronous LTI systems and developed a method for system identification.
result Stability of random asynchronous LTI systems is independent of synchronous stability.
Random matrix theory analyzes learning dynamics in neural networks.
problem Understanding learning dynamics in neural networks.
method Random matrix approach to analyze a linear network.
result Insights into overfitting, early stopping, and initialization.
Random feature maps improve forecasting of chaotic dynamical systems.
problem Forecasting chaotic dynamical systems with high accuracy.
method Data-driven random feature maps with tanh activation, skip connections, and localization.
result Effective forecasting skill for dynamical systems with dimensions up to 512.
A new method de-randomizes MCMC dynamics using the Stein operator.
problem Estimating complex target distributions in Bayesian inference.
method De-randomized kernel-based particle samplers that discretize the fiber-gradient Hamiltonian flow.
result GSVGD de-randomizes complex MCMC dynamics, maintaining high sample quality.
Study shows how mini-batch GD with random reshuffling affects least squares regression dynamics.
problem Analyzing the error dynamics of mini-batch GD with random reshuffling for least squares regression.
method Represented training and generalization errors through a sample cross-covariance matrix Z, compared with sample covariance matrix of original features X, and used linear scaling rule for analysis.
result Mini-batch GD with random reshuffling exhibits subtle step-size dependence not detectable by gradient flow analysis, converging to a limit dependent on the step size.
Ensembles dynamic models using random feature approximations.
problem Online scalable Bayesian learning with dynamic models and ensembling.
method Random feature approximations and dynamic models using random walks.
result Better performance with alternative basis expansions like Hilbert space Gaussian processes.
A novel model uses ODE-based random features to model nonlinear dynamical systems.
problem Modeling highly nonlinear dynamical systems with uncertainty quantification.
method Compositions of physics-informed random features derived from ODEs, combined with deep Gaussian processes and approximate Bayesian inference.
result The model effectively captures nonlinear behavior in real-world multivariate time series data and achieves comparable performance to other models on benchmark tasks.
DDBF improves random forest for imbalanced data.
problem Learning from imbalanced data.
method Incorporates hard example mining into random forest, dynamically removing easy examples.
result DDBF outperforms random forest on multiple datasets.
HD algorithm simulates dynamics on random matrix ensembles without generating full matrices.
problem Simulating dynamics on dense random matrix ensembles with high space and time complexity.
method Householder reflectors for adaptive and recursive construction, deferring decisions.
result Significant reductions in runtime and memory footprint for practical T≪n. Paper develops metrics for random dynamical systems using vector-valued RKHSs.
problem Creating metrics for random nonlinear dynamical systems.
method Develops metrics on random dynamical systems using Perron-Frobenius operators in vector-valued reproducing kernel Hilbert spaces (vvRKHSs). Uses operator-valued kernels and time-wise independence criteria.
result Extends existing metrics for deterministic systems and introduces kernel maximal mean discrepancy for random processes.
The study analyzes deep linear networks from random initialization, capturing dynamics and hyperparameter effects.
problem Understanding training dynamics in deep linear networks from random initialization.
method Theoretical analysis of gradient descent dynamics in deep linear networks with random initialization and large data.
result Captures the 'wider is better' effect and hyperparameter transfer effects, contrasting with neural-tangent parameterization.
We show how random matrix theory can be applied to develop new algorithms to extract dynamic factors from macroeconomic time series. In particular, we consider a limit where the number of random variables N and the number of consecutive time measurements T are large but the ratio N / T is fixed. In this regime the unde…
Overview of high-dimensional dynamical systems and their applications to machine learning.
problem Characterizing behavior of high-dimensional dynamical systems driven by random matrices.
method Cavity method arguments, path integrals, dynamical mean field theory (DMFT), and random matrix resolvents.
result Connections between random matrix resolvents and DMFT response, and non-monotonic loss curves in training.
Randomized SINDy learns dynamic data structures using probabilistic methods.
problem Learning time-dependent data structures in dynamic systems.
method Sequential machine learning with a probabilistic approach, incorporating feature augmentation and Tikhonov regularization.
result Demonstrated effectiveness in regression and binary classification using real-world data.
New model predicts dynamic volatility in uncertain financial markets.
problem Predicting dynamic volatility in financial markets with uncertainty.
method Generalized Barndorff-Nielsen and Shephard (BN-S) model considering delay and fuzziness.
result Effective prediction of dynamic volatility with improved performance.
Learning the parameters of a (potentially partially observable) random field model is intractable in general. Instead of focussing on a single optimal parameter value we propose to treat parameters as dynamical quantities. We introduce an algorithm to generate complex dynamics for parameters and (both visible and hidde…
Study the dynamics and topology of random hyperbolic manifolds.
problem Understanding the dynamics and topology of random hyperbolic manifolds.
method Analyzing Delaunay graphs and capacity over point processes.
result Established conditions for recurrence and transience in random hyperbolic manifolds.
New algorithms update dynamic graph regression faster than existing methods.
problem Efficiently updating linear regression solutions for dynamic graphs.
method Subsampled randomized Hadamard transform and CountSketch.
result First sublinear update time randomized algorithms for dynamic graph regression.
We investigate the random dynamics of polynomial maps on the Riemann sphere and the dynamics of semigroups of polynomial maps on the Riemann sphere. In particular, the dynamics of a semigroup G of polynomials whose planar postcritical set is bounded and the associated random dynamics are studied. In general, the Juli…
Generative adversarial network for probabilistic forecasting of random systems.
problem Forecasting random dynamical systems without distributional assumptions.
method Recurrent neural network and generative adversarial network (GAN) with regularization based on maximum mean discrepancy (MMD).
result The proposed model successfully forecasts complex stochastic processes with multiple-step predictions.
New approach models sustained growth leading to stationary distributions.
problem Understanding stationary distributions in fast-growing systems.
method Applied discrete and continuous master equations, derived rates from stationary distributions.
result Reconstructed distributions for various growing systems.
The supplement proves the existence and properties of a dynamical system related to asset price bubbles.
problem Modeling asset price bubbles using liquidity and random matching.
method Proves the existence and properties of a dynamical system D.
result Existence and properties of the dynamical system D are proven.
Study reveals trade dynamics in dry bulk shipping networks, highlighting their randomness and periodic changes.
problem Understanding the randomness and periodic changes in dry bulk shipping networks.
method Analysis of micro-level trade flow data from 2015 to 2023, focusing on grain, coal, and iron ore networks.
result Dry bulk shipping networks exhibit small-world phenomena and periodic life cycles, influenced by importing ports and global events.
This paper studies the critical dynamics of random surfaces, focusing on area and genus evolution.
problem Understanding the time evolution of random surfaces and their genus.
method Analyzes the dynamics of area and genus using Cox-Ingersoll-Ross process and critical phenomena.
result The genus of surfaces evolves into two phases: planar surfaces and foamy surfaces.
Two randomized algorithms improve performance in non-stationary linear bandits.
problem Conservatism in optimistic algorithms for non-stationary linear bandits.
method Two perturbation approaches: randomization and random perturbations.
result D-RandLinUCB and D-LinTS achieve optimal dynamic regret and are oracle-efficient.
We investigate random complex dynamics of rational or polynomial maps on the Riemann sphere. We show that regarding random complex dynamics of polynomials, generically, the chaos of the averaged system disappears at any point in the Riemann sphere due to the automatic coopeartion of many kinds of maps in the system, ev…
Novel adaptive multi-kernel learning scheme for dynamic environments.
problem Learning nonlinear functions in environments with unknown dynamics.
method Random feature approximation and adaptive multi-kernel learning.
result Unique capability to track nonlinear functions in dynamic environments with performance guarantees.
Experimental fractal landscape dynamics observed in emulsions.
problem Understanding anomalous motions in soft glassy materials.
method Quantitative analysis of oil droplet trajectories in dense emulsions.
result Experimental fractal geometry matches computational model of soft glassy dynamics.
Analyze message passing algorithms using free probability theory.
problem Dynamics of message passing algorithms for probabilistic models.
method Use freeness assumptions of random matrix theory.
result Recover and analyze properties of message passing algorithms.
HF-opt uses Hamiltonian dynamics to optimize functions, achieving accelerated rates with randomized integration time.
problem Optimizing functions efficiently and accelerating convergence rates.
method Randomized Hamiltonian flow (RHF) with accelerated convergence rates.
result RHGD achieves accelerated convergence rates similar to Nesterov's AGD.
Randomized feature models learn interaction kernels from agent paths.
problem Learning interaction kernels from noisy agent paths.
method Randomized feature algorithm and sparse regression.
result Pruned features reduce overfitting and lower simulation cost.
This study analyzes cryptocurrency price dynamics using complexity-entropy causality.
problem Understanding the price dynamics of cryptocurrencies during market booms and busts.
method Used permutation-information-theory quantifiers and complexity-entropy causality plane.
result Discerned three distinct dynamics in cryptocurrency price data.
New framework analyzes SGD dynamics in large samples and dimensions.
problem Analyzing stochastic gradient descent in large-scale settings.
method Inspired by random matrix theory, new framework for fixed stepsize and finite sum settings.
result SGD dynamics become deterministic in the large sample and dimensional limit, governed by a Volterra integral equation.
A new method for decision tree selection in recommendation systems.
problem Feature-based selection of a single tree from an ensemble for dynamic interpretation.
method A multi-armed contextual bandit recommendation framework that trains a system on top of Random Forests to identify the most relevant tree.
result The dynamic method outperforms an independent CART tree and is comparable to Random Forest in predictive performance.
Classical algorithms approximate quantum dynamics using subsampling.
problem Simulating quantum mechanical systems efficiently on classical computers.
method Randomized numerical linear algebra and the Nyström method for approximating matrix exponentials.
result Classical algorithms can efficiently simulate quantum computations under specific conditions.
Improved Hawkes model captures price dynamics and volatility.
problem Modeling price tick structures and estimating volatility.
method Extended Hawkes model with random marks, incorporating market noise and clustering.
result Volatility formula derived and compared with realized volatility.