A new method for embedding sparse high-order interactions.
problem Learning embeddings from sparse high-order interaction events.
method Hybridizing sparse hypergraph and matrix Gaussian processes.
result Strong asymptotic bounds on sparsity ratio.
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48 results for “high-order relationships”
New tests detect high-order interactions without permutations.
problem Scalability issues in kernel-based tests for high-order interactions.
method Permutation-free high-order tests using V-statistics and cross-centring.
result Tests yield standard normal distribution under null hypothesis.
Proposes a novel SAM operator for separate item and relational memories.
problem Limited memory interactions in neural networks.
method Introduces a Self-attentive Associative Memory (SAM) operator to separate item and relational memories.
result Achieves competitive results in various tasks, including geometry, graph, reinforcement learning, and question answering.
New measures and tests for high-order interactions in complex data.
problem Challenges in capturing high-order interactions in multivariate data.
method Hierarchy of -order interaction measures and kernel-based tests.
result Established statistical significance of high-order interactions.
Genomics has revolutionized biology, enabling the interrogation of whole transcriptomes, genome-wide binding sites for proteins, and many other molecular processes. However, individual genomic assays measure elements that interact in vivo as components of larger molecular machines. Understanding how these high-order in…
Paper learns hypergraph structures from signals with smoothness priors.
problem Learning hypergraph structures from signals with high-order relationships.
method Proposes HGSL framework with dual smoothness prior to map signals to hypergraph structure.
result HGSL efficiently infers meaningful hypergraph topologies from signals.
Efficient video captioning model captures cross-modal interactions.
problem Capturing frame-level cross-modal interactions in video captioning.
method Proposes High-Order Cross-Modal Attention (HOCA) and Low-Rank HOCA.
result Low-Rank HOCA achieves state-of-the-art performance.
A new method learns node embeddings for signed directed networks by capturing both first-order and high-order topologies.
problem Learning representative node embeddings for signed directed networks considering both first-order and high-order topologies.
method Proposes a decoupled variational embedding (DVE) method that leverages a specially designed auto-encoder structure to capture both first-order and high-order topologies.
result Extensive experiments on real-world datasets show the effectiveness of DVE in link sign prediction and node recommendation tasks.
Maximum Likelihood Training for Score-Based Diffusion ODEs by High-Order Denoising Score Matchingstat.ML
This work improves likelihood of score-based diffusion ODEs using high-order denoising score matching.
problem The gap between maximum likelihood and score matching objectives for score-based diffusion ODEs.
method High-order denoising score matching to maximize likelihood.
result Score-based diffusion ODEs achieve better likelihood on synthetic and CIFAR-10 data.
Improved fourth-order compact scheme for option valuation with Robin boundary condition.
problem Lower convergence rates in numerical methods for American options.
method High-order compact scheme, Robin boundary condition, coupled nonlinear PDEs.
result Fourth-order convergence rate achieved without mesh refinement.
High-order Klein geometries constructed using Lie algebras.
problem Constructing high-order Klein geometries.
method Irreducible representations of semi-simple Lie algebras.
result High-order Klein geometries constructed successfully.
Paper tackles high-order inference in structured prediction tasks.
problem Maximizing a score function on the space of labels in high-order Markov random fields.
method Generative model approach with two-stage convex optimization algorithm.
result Success in general high-order inference problems driven by hyperedge expansion properties.
Recently, graph neural networks have attracted great attention and achieved prominent performance in various research fields. Most of those algorithms have assumed pairwise relationships of objects of interest. However, in many real applications, the relationships between objects are in higher-order, beyond a pairwise …
Exact partitioning of high-order planted models achieved through convex optimization.
problem Efficiently partitioning hypergraphs generated by high-order planted models.
method Solving a computationally efficient convex optimization problem with a tensor nuclear norm constraint.
result Exact recovery of true underlying cluster structures with high probability.
A high-order recombination algorithm for weak approximation of stochastic differential equationsmath.PR
Paper develops a high-order recombination algorithm for financial modeling.
problem Creating accurate approximations of stochastic differential equations in finance.
method High-order recombination method applied to practical financial problems.
result Algorithm effectively avoids explosive growth in support cardinality for high-order approximations.
Paper proposes efficient methods for high-order clustering in tensor block models.
problem High-order clustering of multiway datasets in neuroimaging, genomics, etc.
method Tensor block model and computationally efficient algorithms (HLloyd, HSC)
result Achieves high-order exact clustering with statistical optimality and computational efficiency.
High order universal portfoliosq-fin.PM
New high-order universal portfolios outperform standard ones.
problem Improving upon the Cover universal portfolio.
method Constructing higher order universal portfolios by recurrence and analyzing their properties.
result Second high-order UP outperforms standard UP under perturbation.
Tensor decomposition is an important technique for capturing the high-order interactions among multiway data. Multi-linear tensor composition methods, such as the Tucker decomposition and the CANDECOMP/PARAFAC (CP), assume that the complex interactions among objects are multi-linear, and are thus insufficient to repres…
Paper proposes an algorithm to learn DAGs with indirect dependencies.
problem Learning DAGs misses indirect dependencies in local variables.
method Two-phase algorithm using high-order HSIC for local optimization.
result OT algorithm outperforms existing methods in structure estimation.
New method for pricing options in stochastic volatility models.
problem Pricing options in models with stochastic volatility.
method Time-adaptive, high-order compact finite difference scheme.
result Extends fourth-order multistep methods to stochastic volatility models.
New method finds significant high-order interactions efficiently.
problem Finding statistically significant high-order interactions in high-dimensional data.
method Extends selective inference to high-order interaction models with pruning strategy.
result Demonstrated efficient and powerful method for high-order interactions.
We propose a new high-order alternating direction implicit (ADI) finite difference scheme for the solution of initial-boundary value problems of convection-diffusion type with mixed derivatives and non-constant coefficients, as they arise from stochastic volatility models in option pricing. Our approach combines differ…
Algorithm for exact partitioning of high-order models using convex tensor relaxation.
problem Exact partitioning of high-order models.
method Defining a general class of -degree Homogeneous Polynomial Models, relaxing the high-order combinatorial problem to a convex conic form problem, defining the Carathéodory symmetric tensor cone, and constructing a primal-dual certificate.
result The solution of the convex relaxation is correct and provides a statistical upper bound for exact partitioning.
New method infers causal relationships from nonstationary time series data.
problem Challenges in inferring causal relationships from nonstationary time series data.
method Proposes a new class of restricted SCM with time-varying filters and stationary noise, leveraging asymmetry from nonstationarity.
result Demonstrates effectiveness of the proposed methodology on various synthetic and real datasets.
Explicit high-order feature interactions efficiently capture essential structural knowledge about the data of interest and have been used for constructing generative models. We present a supervised discriminative High-Order Parametric Embedding (HOPE) approach to data visualization and compression. Compared to deep emb…
Taking into account high-order interactions among covariates is valuable in many practical regression problems. This is, however, computationally challenging task because the number of high-order interaction features to be considered would be extremely large unless the number of covariates is sufficiently small. In thi…
Finding statistically significant high-order interaction features in predictive modeling is important but challenging task. The difficulty lies in the fact that, for a recent applications with high-dimensional covariates, the number of possible high-order interaction features would be extremely large. Identifying stati…
EPINE enhances network embedding by improving adjacency matrix-based high-order proximity.
problem Inaccurate and poorly designed calculation of high-order proximity in network embedding.
method EPINE redefines high-order proximity intuitively and proposes a scalable algorithm for accurate calculation.
result EPINE outperforms existing methods in network reconstruction, link prediction, and node classification.
New deep learning architecture learns martingales efficiently.
problem Efficiently learning martingales in financial derivatives pricing.
method High-order weak approximation algorithms of Runge-Kutta type.
result Deep neural networks based on this architecture learn martingales effectively.
SLTR model preserves tensor structure and reduces prediction time costs.
problem Efficiently predicting tensor data relationships with structural preservation.
method SLTR model enforces sparsity and low-rankness via proximal gradient method.
result SLTR achieves better solutions with significantly reduced time costs.
Graph-based methods are known to be successful in many machine learning and pattern classification tasks. These methods consider semi-structured data as graphs where nodes correspond to primitives (parts, interest points, segments, etc.) and edges characterize the relationships between these primitives. However, these …
THS-GAN uses tensorizing and high-order pooling for AD diagnosis.
problem Early diagnosis of Alzheimer's Disease (AD) using MRI images.
method Tensorizing a three-player cooperative game framework with high-order pooling for MRI images.
result THS-GAN achieves superior performance in AD diagnosis compared to existing methods.
Typical graph embeddings may not capture type-specific bipartite graph features that arise in such areas as recommender systems, data visualization, and drug discovery. Machine learning methods utilized in these applications would be better served with specialized embedding techniques. We propose two embeddings for bip…
RotEqNet preserves rotation symmetry in fluid systems using high-order tensors.
problem Lack of rotational symmetry in machine learning models for fluid systems.
method Introduces RotEqNet, a network that guarantees rotation-equivariance for high-order tensors.
result RotEqNet reduces errors and maintains rotation-equivariance in fluid systems.
Pontryagin's Maximum Principle is an outstanding result for solving optimal control problems by means of optimizing a specific function on some particular variables, the so called controls. However, this is not always enough for solving all these problems. A high order maximum principle (Krener, 1977) must be used in o…
Deep model learns protein interfaces from high-order interactions.
problem Predicting protein interfaces from amino acid pairs.
method Graph neural networks and convolutional neural networks for 2D dense predictions.
result Our method consistently improves interface prediction performance.
The paper analyzes cryptocurrency trading networks using pairwise and high-order dependencies.
problem Understanding information flows and dependencies in cryptocurrency markets.
method Defined a cryptocurrency trading network using weekly log returns, analyzed using Granger causality and O-information.
result High-order dependencies reveal that stable coins play a major role in high-order effects.
Novel CG-EGNNs learn equivariant functions from Clifford algebras.
problem Lack of equivariance in high-order graph neural networks.
method Integrates high-order local structures with Clifford algebras for equivariant learning.
result CG-EGNNs outperform previous methods on various benchmarks.
AD-HOC simplifies high-order derivative calculations in C++.
problem Efficiently computing high-order derivatives in C++.
method A C++ package that calculates derivatives of arbitrary order without code generation.
result Derivatives of arbitrary order computed in a single pass.
The generalized correlation approach, which has been successfully used in statistical radio physics to describe non-Gaussian random processes, is proposed to describe stochastic financial processes. The generalized correlation approach has been used to describe a non-Gaussian random walk with independent, identically d…
Enhances clustering performance with a novel high-order Laplacian matrix.
problem Limited representation capability and insufficient information exploitation in multi-view spectral clustering.
method Proposes a multi-view spectral clustering algorithm that learns a high-order optimal neighborhood Laplacian matrix.
result Improves clustering performance through enhanced representation capacity of the learned optimal Laplacian matrix.
We extend the scheme developed in B. Düring, A. Pitkin, "High-order compact finite difference scheme for option pricing in stochastic volatility jump models", 2019, to the so-called stochastic volatility with contemporaneous jumps (SVCJ) model, derived by Duffie, Pan and Singleton. The performance of the scheme is asse…
We derive high-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids. The schemes are fourth-order accurate in space and second-order accurate in time for vanishing correlation. In our numerical study we obtain high-order numerical convergence also for non-zero …
Paper analyzes LSA algorithm bias and error bounds with RR extrapolation.
problem Analyzing bias and high-order error bounds of LSA with Markovian noise.
method Polyak-Ruppert averaging, linearization, Richardson-Romberg extrapolation.
result RR extrapolation effectively cancels the leading bias term.
We propose a novel method, Modality-based Redundancy Reduction Fusion (MRRF), for understanding and modulating the relative contribution of each modality in multimodal inference tasks. This is achieved by obtaining an -way tensor to consider the high-order relationships between modalities and the output laye…
Paper proposes an efficient algorithm to handle high-order portfolio moments.
problem Designing portfolios with high-order moments (skewness and kurtosis) is computationally challenging.
method Proposes a SCA algorithm framework for solving high-order portfolios efficiently.
result Demonstrates the efficiency of the proposed algorithm through numerical experiments.
New method disentangles high-order effects in feature importance.
problem Quantifying cooperative effects in feature importance.
method Adaptive Leave One Covariate Out (LOCO) method to decompose LOCO into two-body and higher-order components.
result Decomposes LOCO into two-body and higher-order components, highlighting synergistic and redundant effects.
Neural network learns from higher-order connections in molecules.
problem Graph neural networks fail to account for local and hidden structures in graphs.
method Developed a neural network that can pass messages and aggregate information across higher-order paths.
result The model improves molecular property prediction.