The paper introduces surface signatures for irregular surfaces and rough surfaces.
problem Characterizing and integrating highly irregular paths and surfaces.
method Introducing surface signatures and proving extension theorems.
result Surface signatures are universal for surface holonomy and rough surfaces.
New BdryMatérn GP model for reliable boundary integration on irregular domains.
problem Incorporating boundary information in Gaussian process models for complex phenomena.
method Proposes a novel BdryMatérn GP framework with a new covariance kernel derived via path integral and stochastic PDE.
result Sample paths from the BdryMatérn GP satisfy desired boundaries with smoothness control on derivatives.
A new path development layer reduces dimensionality for irregular time series.
problem High-dimensional irregular paths in machine learning.
method Finite-dimensional Lie group representations for dimension reduction.
result The development layer outperforms signature features in accuracy and dimensionality.
PSLR classifies functional data with scalar covariates using path signatures.
problem Classical functional logistic regression models have limitations in capturing nonlinear and cross-channel dependencies.
method PSLR uses truncated path signatures to create a basis-free representation of functional data.
result PSLR outperforms traditional functional classifiers in accuracy and robustness, especially under non-uniform sampling.
New imputation strategies improve signature models for irregular time series.
problem Applying signature models to irregular time series requires continuous path construction.
method Characterized imputation as a problem, evaluated various strategies, proposed GP-PoM.
result Gaussian process adapters improve predictive performance and robustness.
Neural RDEs extend CDEs to irregular time series.
problem Modeling long irregular time series efficiently.
method Representing time series through log-signature and solving RDEs.
result Significant training speed-ups and improved model performance.
Neural Jump ODEs model Itô processes without adversarial training.
problem Generating samples from Itô processes with irregular data.
method Neural Jump ODEs framework for drift and diffusion approximation.
result NJODEs can recover true parameters of Itô processes in the limit.
Predicts next actions in soccer possessions using path signatures.
problem Predicting next actions in soccer possessions with high accuracy.
method Leveraging path signatures to encode spatio-temporal structure of recent possessions, avoiding manual feature engineering.
result Our approach outperforms transformer-based benchmarks across various loss metrics and reduces computational cost.
A model-free method analyzes trading strategies using excursion paths.
problem Analyzing risk and return for dynamic trading strategies without probabilistic assumptions.
method Pathwise analysis of trading signals using δ-excursions.
result Continuous paths can be uniquely decomposed into δ-excursions.
Scalable machine learning with path signatures for time series and graphs.
problem Challenges in real-world time series and graph data.
method Combines rough path theory with probabilistic, deep, and kernel methods.
result Scalable models for time series and graph data.
Paper improves neural ODEs for forecasting non-Markovian processes.
problem Forecasting irregularly observed time series with incomplete data.
method Path-dependent Neural Jump ODEs with signature transform.
result Path-dependent NJ-ODE outperforms original framework in non-Markovian data.
BWFlow improves graph generation by smoothly interpolating graph components.
problem Disjoint modeling of graph nodes and edges leads to irregular and non-smooth probability paths.
method Modeling graphs as MRFs and using optimal transport displacement for a smooth probability path.
result BWFlow achieves better training convergence and efficient sampling in graph generation.
Extends PD-NJ-ODE to noisy observations and dependent observation times.
problem Predicting continuous-time stochastic processes with irregular and noisy observations.
method Extends PD-NJ-ODE to handle conditional independence and noisy observations.
result Theoretical guarantees and empirical examples for handling noisy observations and dependent observation times.
Study on flat connections with controlled irregularity.
problem Boundedness of algebraic flat connections with limited irregularity.
method Analysis of families of algebraic flat connections and holonomic D-modules.
result Established boundedness of families of algebraic flat connections with controlled irregularity.
Neural SVEs model complex systems with memory, outperforming traditional methods.
problem Modeling systems with memory effects and irregular behavior.
method Introducing neural stochastic Volterra equations as a physics-inspired architecture.
result Neural SVEs outperform neural SDEs and DeepONets in various applications.
Manifold learning offers nonlinear dimensionality reduction of high-dimensional datasets. In this paper, we bring geometry processing to bear on manifold learning by introducing a new approach based on metric connection for generating a quasi-isometric, low-dimensional mapping from a sparse and irregular sampling of an…
To detect the irregular trade behaviors in the stock market is the important problem in machine learning field. These irregular trade behaviors are obviously illegal. To detect these irregular trade behaviors in the stock market, data scientists normally employ the supervised learning techniques. In this paper, we empl…
EDICT learns evidential distributions for irregular time series, improving predictions and uncertainty quantification.
problem Challenges in predicting and characterizing uncertainty for irregular time series data.
method EDICT (Evidential Distributions for Irregular Time Series) learns a continuous-time evidential distribution.
result EDICT achieves competitive performance on time series classification tasks and provides better uncertainty quantification.
With the developments of the last decade on complete constant mean curvature 1 (CMC 1) surfaces in the hyperbolic 3-space H3, many examples of such surfaces are now known. However, most of the known examples have regular ends. (An end is irregular, resp. regular, if the hyperbolic Gauss map of the surface has an ess…
We show that there are no irregular Sasaki-Einstein structures on rational homology 5-spheres. On the other hand, using K-stability we prove the existence of continuous families of non-toric irregular Sasaki-Einstein structures on odd connected sums of S2×S3.
The paper studies complex affine structures near irregular singularities.
problem Understanding complex affine structures near irregular singularities.
method Introducing local invariants and a Delaunay decomposition.
result Upper bounds on the complexity of the Delaunay decomposition.
Study deformation spaces of irregular isomonodromy systems on Riemann surfaces.
problem Understanding the topology of irregular isomonodromy systems.
method Define and study moduli spaces of deformations of irregular classes on Riemann surfaces.
result Generalize G-braid groups to study fundamental groups of deformation spaces.
We construct a new five parameter family of constant mean curvature trinoids with two asymptotically Delaunay ends and one irregular end.
LLapDiff models irregular multivariate time series without step-by-step integration.
problem Trade-off between discrete and continuous methods for long-horizon forecasting.
method Generative framework that models target as a low-dimensional latent trajectory, guided by modal parameterization and Laplace domain poles.
result Improves long-horizon forecasting over baselines and supports missing-value imputation.
CRUs model irregular time series with continuous hidden states.
problem Handling irregular time intervals in sequential data.
method Continuous Recurrent Units (CRUs) that integrate hidden states via a linear stochastic differential equation.
result CRUs outperform methods based on neural ordinary differential equations in irregular time series interpolation.
For a complex polynomial in two variables we study the morphism induced in homology by the embedding of an irregular fiber in a regular neighborhood of it. We give necessary and sufficient conditions for this morphism to be injective, surjective. Particularly this morphism is an isomorphism if and only if the correspon…
Framework learns continuous dynamics from sparse trajectories.
problem Learning dynamics from sparsely sampled and high-dimensional trajectories.
method Interpolative Multi-Marginal Flow Matching (IMMFM) framework.
result IMMFM outperforms existing methods in forecasting and downstream tasks.
EBM model for functional data using path measure tilting.
problem Modeling distributions of functions from irregularly sampled data.
method Spectral decomposition of an energy-based model with a Gaussian Process path measure to reweight the distribution.
result Effective approach to up-scaling functional data.
The book is devoted to study so-called irregular subsets of the Grassmannian manifold Gkn(V) (this class of sets was introduced by author). In the previous variant of the book we restrict ourself only to the case when V is an n-dimensional vector space under the field R. Now we consider irregular subsets …
ACSSM models irregular time series with continuous dynamics.
problem Modeling irregular time series data.
method ACSSM uses a multi-marginal Doob's h-transform and variational inference with stochastic optimal control.
result ACSSM outperforms in tasks like classification, regression, interpolation, and extrapolation.
Neural Laplace Control tackles offline RL for continuous-time delayed systems with irregular observations.
problem Offline reinforcement learning problems involving continuous-time environments with delays and irregular observations.
method Combines a Neural Laplace dynamics model with a model predictive control (MPC) planner.
result Achieves near expert policy performance on continuous-time delayed environments.
Machine learning methods such as convolutional neural networks (CNNs) are becoming an integral part of scientific research in many disciplines, spatial vector data often fail to be analyzed using these powerful learning methods because of its irregularities. With the aid of graph Fourier transform and convolution theor…
daep learns from irregular, multimodal astronomical data.
problem Learning from irregular, multimodal astronomical sequences.
method Diffusion Autoencoder with Perceivers (daep) tokenizes, compresses, and reconstructs data.
result daep outperforms VAE and maep baselines in reconstruction and fine-scale structure preservation.
Study local wild mapping class groups for irregular connections on complex curves.
problem Understanding the moduli spaces of irregular connections on complex curves.
method Using isomonodromic deformations, focusing on reflections cosets, and introducing fission trees.
result Complete classification of local wild mapping class groups for various structure groups.
Improved MCMC sampling for expensive, irregular likelihoods.
problem Bayesian inference challenges with irregular, expensive likelihoods.
method Adapt subset samplers, introduce data-driven proxies, adaptive controller.
result Improved HINTS algorithm achieves best sampling error in fixed budget.
We study topological recursion on the irregular spectral curve xy2−xy+1=0, which produces a weighted count of dessins d'enfant. This analysis is then applied to topological recursion on the spectral curve xy2=1, which takes the place of the Airy curve x=y2 to describe asymptotic behaviour of enumerative proble…
Paper develops a method for causal representation learning from irregular tensors.
problem Complex patterns in high-dimensional, irregular tensor data.
method Novel causal formulation and CaRTeD framework integrating temporal causal representation learning with irregular tensor decomposition.
result Framework provides theoretical guarantees and outperforms state-of-the-art techniques.
The paper extends metrics and solitons on toric Fano manifolds with irregular Sasaki-Einstein metrics.
problem Extension of metrics and solitons on toric Fano manifolds with irregular Sasaki-Einstein metrics.
method Verification of the extension of momentum construction of Kaehler-Einstein metrics and Kaehler-Ricci solitons on the total space of positive rational powers of the canonical line bundle.
result The extended metric along the zero section has an expression that can be extended to the total space, and restricts to a transversely Kaehler-Einstein (Sasakian eta-Einstein) metric.
Paper introduces non-adversarial training for Neural SDEs using signature kernel scores.
problem Stability and mode collapse issues in adversarial training of Neural SDEs.
method Uses signature kernel scores as objective function for non-adversarial training.
result Non-adversarial training leads to better performance and more stable models.
We study triangulations T defined on a closed disc X satisfying the following condition: In the interior of X, the valence of all vertices of T except one of them (the irregular vertex) is 6. By using a flat singular Riemannian metric adapted to T, we prove a uniqueness theorem when the valen…
The paper discusses new Lagrangian constructions and examples.
problem Exploring new Lagrangian constructions in complex projective spaces.
method Generalized Delaunay construction among minimal Lagrangians.
result Uncountably many new special Lagrangian cones found.
Paper connects Painlevé VI equation to irregular systems, solving monodromy data.
problem Solving monodromy data for irregular systems related to Painlevé VI.
method Expressed Frobenius integrability in terms of PVI, computed monodromy data for coalescing eigenvalues.
result Computed monodromy data for transcendentals holomorphic at critical points of PVI.
We describe the moduli spaces of meromorphic connections on trivial holomorphic vector bundles over the Riemann sphere with at most one (unramified) irregular singularity and arbitrary number of simple poles as Nakajima's quiver varieties. This result enables us to solve partially the additive irregular Deligne-Simpson…
Given a closed oriented PL four-manifold X and a closed surface B embedded in X with isolated cone singularities, we give a formula for the signature of an irregular dihedral cover of X branched along B. For X simply-connected, we deduce a necessary condition on the intersection form of a simply-connected i…
New method forecasts values and timing in irregular time series.
problem Forecasting values and timing in sparse, irregularly sampled multivariate time series.
method Proposes a novel approach for forecasting values and timing in irregular time series.
result Successfully forecasts values and timing in irregular time series.
Short survey based on talk given at the Institut Henri Poincare January 17th 2012, during program on surface groups. The aim was to describe some background results before describing in detail (in subsequent talks) the results of [Boa11c] related to wild character varieties and irregular mapping class groups.
A new method uses sinusoidal functions to represent timestamps as dense vectors for improving irregularly sampled time series learning.
problem Challenges in supervised learning with irregularly sampled time series due to irregular time intervals.
method Proposes a novel method to represent timestamps as dense vectors using sinusoidal functions, called Time Embeddings.
result Improves LSTM-based and classical machine learning models, especially with very irregular data.
We consider the optimal stopping problem with non-linear f-expectation (induced by a BSDE) without making any regularity assumptions on the reward process ξ. and with general filtration. We show that the value family can be aggregated by an optional process Y. We characterize the process Y as the $\mathcal{E}^f…