This research calculates node similarity on graphs using path-based kernels.
problem Computing similarity between nodes on graphs.
method Derives closed-form expressions for co-presence and co-occurrence of nodes on paths.
result Introduced kernels provide competitive results in semi-supervised classification.
Tree++ graph kernel captures similarities at multiple granularities.
problem Lack of scale-adaptivity in existing graph kernels.
method Tree++ uses truncated BFS trees and super paths to represent graphs at different granularities.
result Tree++ achieves best classification accuracy on real-world graphs.
This research improves DNN defense by profiling and analyzing effective paths.
problem Defending against adversarial attacks on deep neural networks.
method Profiling DNN models into functional blocks and aggregating per-image effective paths to class-level effective paths.
result Adversarial images activate different effective paths from normal images.
A new graph kernel uses LCS and Wasserstein distance for better graph comparisons.
problem Graph learning methods can be limited by information from distant vertices and path length constraints.
method Proposes a Graph Kernel based on LCS similarity and Wasserstein distance in a novel metric space.
result The new kernel emphasizes comparisons between similar paths and reduces information loss.
New method detects and clusters market regimes in multidimensional data.
problem Detecting and clustering market regimes in complex data structures.
method Non-parametric online market regime detection and clustering using path-wise two-sample tests and maximum mean discrepancy.
result Successfully detected and clustered market regimes in various data structures.
New algebraic structures for topological pairs.
problem No specific problem stated; generalization of knot quandles.
method Introducing multi-quandles for topological pairs.
result New algebraic structures for topological pairs.
New algorithmic view of ℓ2 regularization using ODEs and path-following methods.
problem Optimizing convex loss functions with ℓ2 regularization.
method Established an equivalence between ℓ2-regularized solution paths and ODEs, proposing path-following algorithms based on homotopy methods and numerical ODE solvers.
result The solution path can be viewed as a hybrid of gradient descent and Newton method, providing novel schemes to choose grid points and reducing computational cost.
Meta-graph is currently the most powerful tool for similarity search on heterogeneous information networks,where a meta-graph is a composition of meta-paths that captures the complex structural information. However, current relevance computing based on meta-graph only considers the complex structural information, but i…
New estimator for digital options using path splitting and MLMC.
problem Estimating digital options with stochastic differential equations.
method Repeated path splitting, Multilevel Monte Carlo (MLMC).
result Estimator complexity similar to MLMC for Lipschitz payoffs.
Researchers compare different gradient methods for ridge regression, finding conjugate gradients have similar performance.
problem Comparing statistical properties of different gradient methods in ridge regression.
method Explicit non-standard error decomposition to bound prediction error of conjugate gradient iterates.
result Conjugate gradient iterates share optimality properties with gradient flow and ridge regression up to a constant factor.
Path integral method calculates barrier option prices.
problem Barrier option pricing in finance.
method Path integral method applied to trapezoid and square potential barriers.
result Analytical expressions for option pricing derived.
Clusters of crypto assets by path signature improve diversification and reduce fees.
problem Building diversified portfolios of volatile cryptocurrencies.
method Clustering digital assets using path signatures to identify similar behavior patterns.
result Optimal portfolios outperform unfiltered ones, reducing transaction fees.
Kernel for Lévy rough paths derived from PDE system.
problem Computing similarity measures for Lévy rough paths.
method Developed a PDE system for the expected signature of inhomogeneous Lévy processes.
result Gaussian martingales' expected signature kernel satisfies a Goursat PDE.
Quantum connections replace metrics with operator inner products.
problem Quantifying geometric properties in quantum systems.
method Defining quantum connections and duals using operator fields and inner products.
result Holonomy and dual connections are equivalent in quantum geometry.
A novel pedestrian path-planning model using reinforcement learning.
problem Challenges in replicating natural pedestrian navigation behavior.
method Reinforcement learning for collision avoidance and path planning.
result Path planning by the agent closely resembles human pedestrian behavior.
Let x denote a diffusion process defined on a closed compact manifold. In an earlier article, the author introduced a new approach to constructing admissible vector fields on the associated space of paths, under the assumption of ellipticity of x. In this article, this method is extended to yield similar results fo…
Improved sampling efficiency for molecular systems using path gradients after Flow Matching.
problem Improving sampling efficiency for complex molecular systems.
method Hybrid approach combining Flow Matching and path gradients.
result Up to a threefold increase in sampling efficiency for molecular systems.
The dual representation of the martingale optimal transport problem in the Skorokhod space of multi dimensional cadlag processes is proved. The dual is a minimization problem with constraints involving stochastic integrals and is similar to the Kantorovich dual of the standard optimal transport problem. The constraints…
Geometrically represents path integral reduction Jacobian for interacting systems.
problem Quantizing a model mechanical system with dependent coordinates.
method Geometric representation using scalar curvature and Christoffel symbols in a nonholonomic basis.
result Found a geometric representation for the path integral reduction Jacobian.
PathRank ranks paths in spatial networks using multi-task learning.
problem Ranking paths in spatial networks for better navigation services.
method Data-driven framework using multi-task learning, spatial network embedding, and recurrent neural networks.
result PathRank effectively ranks paths based on historical trajectories.
Improved path-length regret bounds for adaptive and oblivious adversaries.
problem Adaptive and oblivious adversaries in multi-armed bandit and linear bandit problems.
method Developed two new algorithms based on optimistic mirror descent framework with novel techniques.
result Strictly improved path-length bounds for adaptive adversary and better results for oblivious adversary.
The paper analyzes how grid cells perform path integration and learns hexagon grid patterns.
problem Understanding how grid cells perform path integration calculations.
method Theoretical analysis of a general representation model of path integration by grid cells, identifying group representation and isotropic scaling conditions.
result The learned model of hexagon grid patterns is capable of accurate long distance path integration.
A new method interprets astrophysical spectra using geometric paths to distinguish line profiles.
problem Tackling the indistinguishability of spectral line profiles under scalar summaries.
method Introduces a geometric representation of line profiles using rough path theory, mapping profiles to a common velocity grid and defining descriptors from path properties.
result Compact descriptors separate morphologies with similar scalar summaries, revealing ordered line structures.
PAN uses path integrals for graph convolution and pooling, improving GNN performance.
problem Designing efficient graph convolution and pooling for graph neural networks.
method Path integral based graph convolution and pooling using learnable weights for path lengths.
result PAN achieves state-of-the-art performance on various graph classification/regression tasks.
Optimal transport semi-supervised learning improves GNSS multi-path detection.
problem GNSS multi-path interference detection.
method Wasserstein distance based semi-supervised manifold learning.
result Significant improvement in classification accuracy over fully supervised training.
Single-Path NAS designs efficient ConvNets in under 4 hours.
problem Designing efficient ConvNets for mobile devices under time constraints.
method Differentiable NAS method using one single-path ConvNet.
result Achieves 74.96% top-1 accuracy on ImageNet with 79ms latency.
The present work extends the randomized shortest-paths framework (RSP), interpolating between shortest-path and random-walk routing in a network, in three directions. First, it shows how to deal with equality constraints on a subset of transition probabilities and develops a generic algorithm for solving this constrain…
Single-Path NAS designs efficient ConvNets for mobile devices in hours.
problem Designing efficient ConvNets for mobile devices under latency constraints.
method Single-Path NAS, a differentiable method that reduces search cost and inference time.
result Achieves state-of-the-art accuracy on ImageNet with 79ms inference latency.
Extends convex clustering to graph-structured data.
problem Handling graph-structured data with convex clustering.
method Formulates a convex objective and uses a proximal dual algorithm for efficient recovery.
result Demonstrates the effectiveness of the method on real-life datasets.
NEXT learns efficient paths in high dimensions using neural exploration-exploitation trees.
problem Learning efficient path planning in high-dimensional spaces.
method Neural Exploration-Exploitation Trees (NEXT) integrating neural architecture and UCB algorithm.
result NEXT achieves better sample efficiency and outperforms state-of-the-art methods.
Landmark-based node embeddings approximate shortest path distances in random graphs.
problem Capturing global graph distances in node representations.
method Landmark-based node embeddings using shortest path distances from a subset of reference nodes (landmarks).
result Random graphs require lower dimensions in landmark-based embeddings compared to worst-case graphs.
Cubature on Wiener space [Lyons, T.; Victoir, N.; Proc. R. Soc. Lond. A 8 January 2004 vol. 460 no. 2041 169-198] provides a powerful alternative to Monte Carlo simulation for the integration of certain functionals on Wiener space. More specifically, and in the language of mathematical finance, cubature allows for fast…
We study a simplification of GAN training: the problem of transporting particles from a source to a target distribution. Starting from the Sobolev GAN critic, part of the gradient regularized GAN family, we show a strong relation with Optimal Transport (OT). Specifically with the less popular dynamic formulation of OT …
Overlay framework simplifies exotic derivative pricing.
problem Inconsistent pricing models for exotics.
method Combines path reweighting and conic optimisation.
result Practically model-independent price bands for exotics.
Spaces with similar long paths have similar shapes.
problem Comparing shapes of Gromov hyperbolic spaces.
method Examining asymptotic marked length spectra.
result Spaces with identical spectra are roughly isometric.
A new algorithm for high-dimensional hedging problems.
problem High-dimensional, path-dependent hedging problems.
method Signature-based algorithm using operator-valued kernels and geometric rough paths.
result Theoretical guarantees on existence and uniqueness of a global minimum.
Single-Path NAS reduces NAS search cost to 3 hours, achieving state-of-the-art mobile image classification.
problem Efficiently automate ConvNet design under mobile latency constraints.
method Single-Path NAS, using one single-path ConvNet with shared parameters.
result Achieves state-of-the-art top-1 ImageNet accuracy (75.62%) in 8 epochs (24 TPU-hours).
Develops geometric integration for rough differential forms.
problem Integrating rough differential forms with low regularity.
method Uses rough path theory to construct geometric integration.
result Constructs geometric integration for rough differential forms.
Geometrically represents the Jacobian for a mechanical system with symmetry.
problem Path integral reduction for a mechanical system with symmetry.
method Geometric representation using scalar curvature and adapted coordinates.
result Obtained geometric representation of the Jacobian.
This paper uses probability tensors for efficient path planning in complex scenarios.
problem Efficient path planning in complex environments with obstacles and multiple goals.
method Probability tensors are used to model agent motion and decision-making, incorporating past and future information.
result The model finds solutions in complex scenarios, demonstrating realistic emergent behaviors.
We present the symmetric thermal optimal path (TOPS) method to determine the time-dependent lead-lag relationship between two stochastic time series. This novel version of the previously introduced TOP method alleviates some inconsistencies by imposing that the lead-lag relationship should be invariant with respect to …
We show that shortfall risks of American options in a sequence of multinomial approximations of the multidimensional Black--Scholes (BS) market converge to the corresponding quantities for similar American options in the multidimensional BS market with path dependent payoffs. In comparison to previous papers we conside…
We compute a sharp small-time estimate for the price of a basket call under a bi-variate SABR model with both β parameters equal to 1 and three correlation parameters, which extends the work of Bayer,Friz&Laurence [BFL14] for the multivariate Black-Scholes flat vol model. The result follows from the heat kernel on …
We provide an explicit aggregation in the neoclassical growth model with aggregate shocks and uninsurable employment risk. We show there are two restrictions on the unemployment shock for approximate aggregation to occur. First the probability of unemployment must be positive for each agent in each time period. That en…
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.
Study the landscape of Lipschitz functions between manifolds using persistent homology.
problem Understanding the structure of homotopy paths between maps with high Lipschitz constants.
method Using persistent homology to analyze the landscape of Lipschitz functions between manifolds.
result First results on the persistence of higher-dimensional cycles in function spaces.
Motivated by the unceasing interest in hidden Markov models (HMMs), this paper re-examines hidden path inference in these models, using primarily a risk-based framework. While the most common maximum a posteriori (MAP), or Viterbi, path estimator and the minimum error, or Posterior Decoder (PD), have long been around, …
The paper proposes a method to infer differentiation trees from RNA velocity data.
problem Reconstructing dynamic cellular processes from sequencing data.
method Defining varifold distances between RNA velocity curves to approximate shortest-path distances in a tree.
result The varifold distance method approximates the shortest-path distance in a tree isomorphic to the target differentiation tree.