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…
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48 results for “High-order data”
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.
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.
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.
Bayesian tensor train method recovers streaming data with high accuracy.
problem Recovering high-order, incomplete, and noisy streaming data.
method Bayesian tensor train decomposition using streaming variational Bayes method.
result The proposed SPTT algorithm excels in recovering streaming data compared to state-of-the-art methods.
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.
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.
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.
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.
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.
Generative Adversarial Networks (GANs) have become the gold standard when it comes to learning generative models for high-dimensional distributions. Since their advent, numerous variations of GANs have been introduced in the literature, primarily focusing on utilization of novel loss functions, optimization/regularizat…
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.
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.
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.
New method identifies nonstationary causal structures in time series data.
problem Identifying causal relationships in time series data that change over time.
method High-order Markov Switching Models for regime-dependent causal discovery.
result Scalable approach for estimating high-order regime-dependent causal structures.
We study non-variational degenerate elliptic equations with high order singular structures. No boundary data are imposed and singularities occur along an {\it a priori} unknown interior region. We prove that positive solutions have a universal modulus of continuity that does not depend on their infimum value. We furthe…
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.
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.
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.
DTCCA learns nonlinear transformations of multi-view data for high-order correlation.
problem Learning complex nonlinear transformations of multiple data views.
method Maximizes high-order canonical correlation by jointly learning transformations of each view using a reformulated tensor decomposition.
result DTCCA efficiently handles high-dimensional and large number of views, overcoming scalability issues.
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…
JigSaw discovers high-order interactions from random forests.
problem Identifying complex interactions in biological data.
method Random forest structure analysis to find high-order interactions.
result JigSaw can explain outcomes in heart disease and breast cancer.
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.
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 method quantifies feature interactions in machine learning models.
problem Capturing high-order interactions and feature contributions in predictive models.
method Information-theoretic approach using Conditional Mutual Information (CMI) via k-NN.
result Accurately recovers feature interactions in synthetic and real-world datasets.
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.
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.
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.
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…
A method to estimate high order derivatives of data distributions from samples.
problem Estimating high order derivatives of data distributions efficiently and accurately.
method Generalizing denoising score matching via Tweedie's formula to estimate higher order derivatives.
result Models trained with the proposed method can approximate second order derivatives more efficiently and accurately than via automatic differentiation.
Study how neural networks learn from non-Gaussian data models.
problem Understanding neural network learning dynamics with non-Gaussian data.
method Developed a two-layer neural network with Hermite polynomial activations to control high-order cumulants.
result Neural networks progressively learn high-order cumulants after capturing low-order statistics.
Hutchinson Trace Estimation for High-Dimensional and High-Order Physics-Informed Neural Networkscs.LG
HTE improves PINNs for high-dimensional, high-order PDEs by reducing computational cost and memory usage.
problem Challenges in solving high-dimensional, high-order PDEs with PINNs due to computational cost and memory constraints.
method Introduces Hutchinson Trace Estimation (HTE) to transform Hessian matrix calculations into Hessian vector products (HVP), reducing computational cost and memory usage.
result HTE significantly reduces memory consumption and computational cost, enabling faster and more efficient solution of high-dimensional and high-order PDEs.
This paper addresses the challenging task of video captioning which aims to generate descriptions for video data. Recently, the attention-based encoder-decoder structures have been widely used in video captioning. In existing literature, the attention weights are often built from the information of an individual modali…
Learning rate needs to decrease with higher data moments for effective ICA in high dimensions.
problem Slower convergence of ICA in high-dimensional data with high-order moments.
method High-dimensional ODE analysis of ICA algorithm under controlled moment structure.
result Critical learning rate threshold for effective ICA when moments are high.
New framework discovers PDEs from sparse, noisy data.
problem Discovering PDEs with high-order derivatives and heterogeneous parameters.
method Combines deep-learning and integral form to handle sparse and noisy data.
result More robust and accurate compared to existing methods.
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…
A new method for predicting with confidence for complex models.
problem Lack of reliable confidence in high-stake decision-making models.
method Developed a full-CP for sparse high-order interaction model using homotopy mining.
result SHIM achieves comparable accuracy to complex models and superior statistical power.
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.
Paper accelerates diffusion models without retraining, reducing evaluations.
problem Approximating target data distributions efficiently.
method Training-free sampling algorithm using high-order Lagrange interpolation.
result Requires fewer score function evaluations than previous methods.
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.
Currently, Markov-Gibbs random field (MGRF) image models which include high-order interactions are almost always built by modelling responses of a stack of local linear filters. Actual interaction structure is specified implicitly by the filter coefficients. In contrast, we learn an explicit high-order MGRF structure b…