This work addresses dynamic KDE data structures with robustness to adversarial queries.
problem Efficient KDE data structures for dynamic changing data distributions.
method Developed a theoretical framework for KDE data structures that support subquadratic space, sublinear updates, and adaptive queries.
result Theoretical framework and practical implementation of KDE data structures robust to adversarial queries.
Anisotropic data structure affects learning dynamics and generalization error in linear networks.
problem Understanding the impact of data anisotropy on learning dynamics and generalization error in linear networks.
method Examined a spiked covariance structure as a model of anisotropy in a two-layer linear network in a linear regression setting.
result Learning dynamics proceed in two phases: initially driven by input-output correlation, then by other principal directions of the data structure. Derived an analytical expression for the generalization error.
Relational data-like graphs, networks, and matrices-is often dynamic, where the relational structure evolves over time. A fundamental problem in the analysis of time-varying network data is to extract a summary of the common structure and the dynamics of the underlying relations between the entities. Here we build on t…
New method detects long-term structures with internal dynamics in time series data.
problem Identifying patterns across time in data growth.
method Adaptive identification of majority overlaps between groups at different time points.
result Detection of persistent structural elements with internal dynamics.
Recurrent-DBN models dynamic relational data with interpretable latent structures.
problem Interpreting dynamic relational data with hidden structures.
method Recurrent Dirichlet Belief Network framework with hierarchical latent structures and efficient inference strategy.
result Recurrent-DBN discovers interpretable latent structures and improves link prediction.
Paper introduces a novel framework for recognizing dynamic ranking structures in preference-based data.
problem Complex and noisy preference-based data often hide underlying homogeneous structures.
method Developed an approach to identify dynamic ranking groups using temporal penalties and spectral estimation. Introduced an objective function for detecting structural changes.
result Consistent recognition of ranking groups and structural changes in preference-based data.
LOCAL learns dynamic causal structures from time series data efficiently.
problem Challenges in discovering DAG from time series data due to dynamic nature and nonlinear interactions.
method LOCAL proposes a quasi-maximum likelihood-based score function and adaptive modules ACML and DGPL.
result LOCAL significantly outperforms existing methods in dynamic causal discovery.
Proposes DCNAR for dynamic causal inference from neural time series.
problem Uncertainty and evolution of causal structure in real-world domains.
method Two-stage neural causal modeling integrating discovery and inference.
result Dynamic causal inferences are more stable and meaningful than alternatives.
A new method learns complex dynamical systems from data efficiently.
problem Learning complex dynamical systems from large-scale data efficiently.
method Low-rank structured variational autoencoding framework for nonlinear Gaussian state-space models.
result Consistently demonstrates better predictive capabilities compared to other models.
Model for dynamic relational data with regime changes.
problem Handling abrupt changes in dynamic relational data.
method Factorized fusion shrinkage model with global-local shrinkage priors.
result Posterior distribution attains minimax optimal rate up to logarithmic factors.
Topological data analysis quantifies structural dynamics using persistent homology.
problem Analyzing the shape and topology of structural dynamics data.
method Topological Data Analysis (TDA) with persistent homology to quantify shape over scales.
result Persistent homology reveals significant changes in manifold shape due to damage, not temperature.
URN neural network dynamically generates various neural structures during training.
problem Creating neural networks with flexible, dynamic structures during training.
method Introduced Unstructured Recursive Network (URN) and used gradient descent on a single loss function.
result Different neural structures can emerge from a single URN during training.
PMP extends GNNs to handle past states efficiently.
problem Efficient querying of data structures dependent on previous states.
method Persistent Message Passing (PMP) which persists past states through new nodes.
result Significantly outperforms GNNs in handling out-of-distribution data.
In evolving complex systems such as air traffic and social organizations, collective effects emerge from their many components' dynamic interactions. While the dynamic interactions can be represented by temporal networks with nodes and links that change over time, they remain highly complex. It is therefore often neces…
Quantum dynamics reveals hidden geometric structure in data.
problem Understanding complex, high-dimensional datasets through geometric structure.
method Introducing semiclassical and microlocal analysis to data analysis.
result First tractable algorithm for approximating wave dynamics and geodesics on data manifolds.
Improved generative models learn structured data better.
problem Training score-based generative models for structured data.
method Nonlinear denoising score matching with neural control variates.
result Enhanced learning of multimodal and symmetric data.
Paper discovers structural dynamics equations from only acceleration data.
problem Discovering equations from only acceleration measurements in structural dynamics.
method Library-based approach with Approximate Bayesian Computation (ABC) prioritizing parsimonious models.
result Efficacy demonstrated in four structural dynamics examples, including linear and nonlinear systems.
Sequences of correlated binary patterns can represent many time-series data including text, movies, and biological signals. These patterns may be described by weighted combinations of a few dominant structures that underpin specific interactions among the binary elements. To extract the dominant correlation structures …
Bayesian framework detects symmetries in chaotic dynamical systems.
problem Detecting symmetries in chaotic attractors for insights into dynamical system structure.
method Bayesian framework using Gibbs posterior constructed from Wasserstein distances.
result Bayesian framework accurately recovers symmetries under high noise and small sample sizes.
Riemannian geometry improves protein dynamics analysis.
problem Efficient analysis of protein dynamics data in non-linear spaces.
method Developed a local approximation technique for geodesics and a smooth manifold of protein conformations.
result Geodesics approximate molecular dynamics trajectories and provide realistic summary statistics.
Proposes a new model to better handle overdispersed count time series.
problem Heterogeneous overdispersed count time series.
method Negative-Binomial Randomized Gamma Markov Process.
result Significantly improves predictive performance and fast convergence of inference algorithm.
The paper proposes a method to identify causal structure in complex dynamical systems.
problem Spurious correlations in data-driven models limit the performance of control systems.
method The method leverages controllability concepts to compute input trajectories and uses causal inference techniques.
result The method reliably identifies the true causal structure of control systems from real-world data.
DynDepNet learns dynamic brain graphs from fMRI data for better prediction performance.
problem Static brain graphs from fMRI data lead to poor GNN performance.
method Dynamic Graph Structure Learning for time-varying brain connectivity.
result DynDepNet achieves state-of-the-art sex classification accuracy on real-world fMRI data.
New model captures sparse, evolving multigraph structures.
problem Understanding sparse, evolving multigraph structures in dynamic interaction data.
method Dynamic nonparametric Bayesian model combining sparsity and clustering.
result Improved held-out likelihood and predictive performance.
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.
CoDA augments data with counterfactuals from local causal structures.
problem Improving sample efficiency in RL with complex dynamic processes.
method Local causal models (LCMs) and Counterfactual Data Augmentation (CoDA).
result CoDA significantly improves RL agent performance in locally factored tasks.
Tackles network structure inference from time series data using GNN.
problem Inferring network structure from incomplete or no information.
method Gumbel Graph Network (GGN) model for network reconstruction and completion.
result GGN can reconstruct up to 100% network structure and infer missing parts with up to 90% accuracy.
Stable topological summary captures evolving dependency structure in dynamic Bayesian networks.
problem Missing larger-scale patterns in evolving dependency structures in dynamic Bayesian networks.
method Topological approach using Dynamic Bayesian Graphs and persistent homology.
result Stable topological summary (barcodes) captures evolving dependency structure in DBNs.
PGNs dynamically infer and use graph structures to improve model generalization.
problem Static graph structures inferred by machine learning practitioners are often suboptimal for tasks.
method PGNs augment graphs with dynamically inferred pointers for improved model generalization.
result PGNs outperform unrestricted GNNs and Deep Sets on dynamic graph connectivity tasks.
Understanding nonlinear dynamical systems (NLDSs) is challenging in a variety of engineering and scientific fields. Dynamic mode decomposition (DMD), which is a numerical algorithm for the spectral analysis of Koopman operators, has been attracting attention as a way of obtaining global modal descriptions of NLDSs with…
New method learns latent group structures without clustering, using heat flow dynamics.
problem Learning with latent group sparsity in machine learning problems.
method Heat flow dynamics on network structure to incorporate group structure.
result Effective performance and provable bounds on sample complexity.
We demonstrate the application of an algorithmic trading strategy based upon the recently developed dynamic mode decomposition (DMD) on portfolios of financial data. The method is capable of characterizing complex dynamical systems, in this case financial market dynamics, in an equation-free manner by decomposing the s…
Bayesian method detects mesoscale structures in pathway data networks.
problem Mesoscale structures in pathway data networks are hard to detect due to dependencies between interactions.
method Bayesian approach modeling optimal partitioning and higher-order dynamics.
result Method can recover both proximity-based and role-based groupings of nodes.
Proposes neural networks that preserve physical system dynamics.
problem Learning accurate representations of dynamical systems.
method Variational integrator networks designed to preserve geometric structure.
result Accurately learns dynamical systems from noisy observations.
Dynamic tensor data are becoming prevalent in numerous applications. Existing tensor clustering methods either fail to account for the dynamic nature of the data, or are inapplicable to a general-order tensor. Also there is often a gap between statistical guarantee and computational efficiency for existing tensor clust…
New neural network designs learn contact dynamics efficiently.
problem Learning contact dynamics in robotics from noisy data.
method Physically structured neural networks.
result Data-efficient learning of discontinuous contact events.
We study the dynamical behavior of high-frequency data from the Korean Stock Price Index (KOSPI) using the movement of returns in Korean financial markets. The dynamical behavior for a binarized series of our models is not completely random. The conditional probability is numerically estimated from a return series of K…
Model learns latent dynamics of complex systems with closed transformation paths.
problem Euclidean latent space does not match data structure.
method Incorporates manifold model into autoencoder latent space.
result Generates transformation paths and classifies samples on same path.
The paper introduces a dynamic MVP model using high-frequency financial data.
problem Capturing the dynamics of minimum variance portfolio weights in financial markets.
method Imposes autoregressive structure on MVP processes and uses CLIME and LASSO for estimation.
result Proposes DR-MVP model with established asymptotic properties.
dCMF models evolving patterns in multiway data with temporal dynamics.
problem Capturing evolving patterns in multiway datasets with temporal dependencies.
method Time-aware coupled factorization model constrained by LDS structure.
result dCMF outperforms alternatives in capturing complex dynamics.
DOODL learns shared spectral dynamics across related dynamical systems.
problem Learning independent dynamical operators for each system limits discovery of shared structure.
method DOODL learns a dictionary of characteristic spectral dynamics on a manifold of related systems.
result DOODL achieves errors one to two orders of magnitude lower than independent operator estimation methods.
Develops a method for identifying structured dynamical systems from data.
problem Identifying structured dynamical systems from undersampled and noisy data.
method Sparse least-squares fitting via ℓ1−ℓ2 optimization with the alternating direction method of multipliers. result The method is stable and successful under certain conditions, as shown by theoretical guarantees and computational results.
This paper introduces Graph Convolutional Recurrent Network (GCRN), a deep learning model able to predict structured sequences of data. Precisely, GCRN is a generalization of classical recurrent neural networks (RNN) to data structured by an arbitrary graph. Such structured sequences can represent series of frames in v…
Manifold learning techniques for dynamical systems and time series have shown their utility for a broad spectrum of applications in recent years. While these methods are effective at learning a low-dimensional representation, they are often insufficient for visualizing the global and local structure of the data. In thi…
Study shows neural ODEs generalize well on synthetic graphs but struggle with degree heterogeneity and clustering.
problem Understanding neural ODEs on complex networks, especially with varying graph sizes and structures.
method Synthetic data from five dynamical systems on graphs, using Barabási-Barzel form vector fields.
result Degree heterogeneity and dynamical system type are primary factors affecting neural ODEs' generalization.
New analysis shows FM learns underlying dynamical structure, not just trajectory replay.
problem Understanding whether flow matching models learn transferable dynamical structure or merely replay trajectories.
method Derived velocity field implied by FM objective, characterized as a continuous-time dynamical system.
result FM models can be seen as parametric surrogates of nonparametric solutions, providing strong probabilistic forecasts.
Deep learning models converge to Gaussian dynamics with mixed structured inputs.
problem Understanding neural network dynamics with complex input distributions.
method Extended hidden manifold model to Gaussian mixtures, analyzed via SGD.
result Learning dynamics with mixed inputs converge to Gaussian behavior.
Proposes iVDFM for identifying latent factors in multivariate time series.
problem Identifying latent factors in multivariate time series with structural dynamics.
method Identifiable Variational Dynamic Factor Model (iVDFM) with iVAE-style conditioning.
result Identifiable latent factors up to permutation and component-wise affine transformations.