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.
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.
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.
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.
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.
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…
We consider a general class of high order weak approximation schemes for stochastic differential equations driven by Lévy processes with infinite activity. These schemes combine a compound Poisson approximation for the jump part of the Lévy process with a high order scheme for the Brownian driven component, applied bet…
Second-order estimator improves continuous-time policy evaluation.
problem Estimating value surfaces from discrete data with time-inhomogeneous dynamics.
method Moment-matching coefficients for high-order generator regression.
result Second-order estimator consistently outperforms Bellman baseline.
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.
In this paper, we propose a general framework for sparse and low-rank tensor estimation from cubic sketchings. A two-stage non-convex implementation is developed based on sparse tensor decomposition and thresholded gradient descent, which ensures exact recovery in the noiseless case and stable recovery in the noisy cas…
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.
In this paper we propose a new kind of high order numerical scheme for backward stochastic differential equations(BSDEs). Unlike the traditional θ-scheme, we reduce truncation errors by taking θ carefully for every subinterval according to the characteristics of integrands. We give error estimates of this nonlinear…
This paper shows how many samples are needed for smooth functions in high dimensions.
problem The challenge of obtaining meaningful estimates of high-order derivatives in machine learning with limited data.
method Deriving new lower bounds on the generalization error.
result Formalizes the intuition that smoothness requires enough samples close to each other.
New algorithms optimize convex functions with high-order derivatives.
problem Optimizing convex functions with high-order derivatives under various norms.
method Developed a non-Euclidean inexact accelerated proximal point method using an inexact uniformly convex regularizer.
result Showed nearly optimal algorithms for high dimensions in the black-box oracle model for ℓp-settings and all q≥1. In this paper we present a new approach for tightening upper bounds on the partition function. Our upper bounds are based on fractional covering bounds on the entropy function, and result in a concave program to compute these bounds and a convex program to tighten them. To solve these programs effectively for general r…
Paper analyzes normal approximation for two-timescale stochastic algorithms, revealing interaction between fast and slow timescales.
problem Non-asymptotic bounds for accuracy of normal approximation in linear two-timescale stochastic approximation algorithms.
method Established bounds for normal approximation in terms of convex distance, focusing on last iterate and Polyak-Ruppert averaging.
result Normal approximation rate for the last iterate improves with increased timescale separation, while it decreases in the averaged setting.
In this paper we propose an algorithm for exact partitioning of high-order models. We define a general class of m-degree Homogeneous Polynomial Models, which subsumes several examples motivated from prior literature. Exact partitioning can be formulated as a tensor optimization problem. We relax this high-order combi…
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 establishes tight lower bounds for minimizing certain smooth and convex functions.
problem Minimizing high-order Hölder smooth and uniformly convex functions.
method Analyzes two asymmetric cases of q>p+ν and q<p+ν using worst-case oracle complexities. result Establishes worst-case oracle complexities for reaching an ε-approximate solution.
Paper proves higher-order flow matching preserves optimality in generative modeling.
problem Theoretical guarantees for higher-order flow matching in generative modeling.
method Neural network approximations with controlled depth, width, and sparsity.
result Proves worst case optimality for second-order flow matching.
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.
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.
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.
Sharp bounds for curve isoperimetric deficit derived.
problem Finding sharp bounds for the isoperimetric deficit of curves.
method Fourier analysis applied to derive Wirtinger-type inequalities.
result Sharp lower and upper bounds for the isoperimetric deficit proved.
Novel tensor perturbation bounds for orthogonal iteration methods.
problem Developing robust bounds for tensor reconstruction and subspace estimation.
method Blockwise tensor perturbation bounds for high-order orthogonal iteration (HOOI).
result Upper bounds for singular subspace estimation converge linearly and tensor reconstruction error bound is characterized by a simple quantity.
Vanishing long-term gradients are a major issue in training standard recurrent neural networks (RNNs), which can be alleviated by long short-term memory (LSTM) models with memory cells. However, the extra parameters associated with the memory cells mean an LSTM layer has four times as many parameters as an RNN with the…
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 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 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.
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.
This paper addresses the problem of blind demixing of instantaneous mixtures in a multiple-input multiple-output communication system. The main objective is to present efficient blind source separation (BSS) algorithms dedicated to moderate or high-order QAM constellations. Four new iterative batch BSS algorithms are p…
New method improves inference for discrete diffusion models, achieving better quality and efficiency.
problem High dimensionality of discrete diffusion models causes inference challenges.
method Developed high-order numerical inference schemes for discrete diffusion models.
result Second-order accuracy of the θ-Trapezoidal method in KL divergence. 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…
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.
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.
Deep networks can efficiently approximate functions on curved manifolds.
problem Approximating functions and their derivatives on complex, curved domains.
method Proved constant-depth ReLU networks can approximate functions in Sobolev spaces on manifolds.
result Deep networks with bounded weights can approximate functions in Wpk(Md) to an error of ε using O(ε−d/(k−s)) parameters. Unified approach to discrete and smooth isoperimetric inequalities of arbitrary order.
problem Finding higher order isoperimetric inequalities for both discrete and smooth curves.
method Unified approach via Fourier analysis of linear operators.
result Unified upper and lower bounds for isoperimetric deficit in smooth curves.
Artificial neural network training with stochastic gradient descent can be destabilized by "bad batches" with high losses. This is often problematic for training with small batch sizes, high order loss functions or unstably high learning rates. To stabilize learning, we have developed adaptive learning rate clipping (A…
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…