Neural networks can approximate high-dimensional classifiers with ReLU networks under margin conditions.
problem Approximating high-dimensional discontinuous classifiers with neural networks.
method Using ReLU neural networks with three hidden layers, approximating a classifier with a Barron-regular decision boundary.
result High-dimensional discontinuous classifiers can be approximated with a rate of n−1 under strong margin conditions. Quantum algorithms improve high-frequency trading efficiency.
problem Reducing calculation time in high-frequency statistical arbitrage trading.
method Variable time condition number estimation and quantum linear regression.
result Quantum advantage in trading algorithm complexity reduction.
Unified framework for estimating high-dimensional conditional factor models.
problem Estimating high-dimensional conditional latent factor models with practical limitations.
method Constrained nuclear norm regularization and cross-validation for parameter selection.
result Imposing homogeneity improves model predictability, with new method outperforming alternatives.
Conditions for integer signatures of high-dimensional knots.
problem Determining signatures of high-dimensional knots with specific Alexander polynomials.
method Necessary and sufficient conditions based on square-free Alexander polynomials.
result Identifies conditions for an integer to be the signature of a knot.
Study LASSO for high-dimensional VAR models with weakly dependent innovations.
problem Understanding sparse regularization in high-dimensional VAR models with weakly dependent innovations.
method LASSO estimation for weakly sparse VAR models with heavy tailed innovations, under L1 mixingale condition. result Oracle properties of LASSO estimation in high-dimensional VAR models with weakly dependent innovations.
We formulate and analyze a graphical model selection method for inferring the conditional independence graph of a high-dimensional nonstationary Gaussian random process (time series) from a finite-length observation. The observed process samples are assumed uncorrelated over time and having a time-varying marginal dist…
Study high-dimensional Bayesian linear regression using variational inference.
problem High-dimensional Bayesian linear regression with product priors.
method Non-linear large deviations theory and variational inference.
result Unique optimizer in variational problem governs posterior distribution under separation condition.
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…
A new framework generates high-dimensional event sequences efficiently.
problem Challenges in modeling high-dimensional marked temporal point processes.
method Conditional generator that learns from event history.
result Superior performance compared to existing methods.
There is a growing demand for nonparametric conditional density estimators (CDEs) in fields such as astronomy and economics. In astronomy, for example, one can dramatically improve estimates of the parameters that dictate the evolution of the Universe by working with full conditional densities instead of regression (i.…
trVAE improves conditional out-of-sample generation for unpaired data.
problem Challenges in generating high-dimensional samples conditional on low-dimensional descriptors out-of-sample.
method trVAE uses maximum mean discrepancy (MMD) to match distributions across conditions in the decoder layer.
result Improved robustness and accuracy in predicting cellular perturbation responses and disease.
High signal to noise ratio (SNR) consistency of model selection criteria in linear regression models has attracted a lot of attention recently. However, most of the existing literature on high SNR consistency deals with model order selection. Further, the limited literature available on the high SNR consistency of subs…
We are interested in attribute-guided face generation: given a low-res face input image, an attribute vector that can be extracted from a high-res image (attribute image), our new method generates a high-res face image for the low-res input that satisfies the given attributes. To address this problem, we condition the …
Study uses multi-kernel Hawkes models to analyze high-frequency price dynamics.
problem Understanding responsive speeds of market participants in high-frequency trading.
method Multi-kernel Hawkes models with conditional Hessian analysis for optimization.
result Existence of multi-kernels (UHF, VHF, HF) in high-frequency price dynamics.
New method improves SACOBRA's performance on high-conditioning optimization problems.
problem High-conditioning optimization problems with expensive objective functions.
method Online whitening applied to SACOBRA in the black-box optimization paradigm.
result Online whitening reduces optimization error by a factor of 10 to 1e12 compared to plain SACOBRA.
We propose Progressive Structure-conditional Generative Adversarial Networks (PSGAN), a new framework that can generate full-body and high-resolution character images based on structural information. Recent progress in generative adversarial networks with progressive training has made it possible to generate high-resol…
Unified CI test for categorical and ordinal data maintains power in high dimensions.
problem Rapid degradation of statistical power in existing CI tests for high-dimensional conditioning variables.
method Unified CI test for categorical and ordinal data, maintaining reasonable calibration and power in high dimensions.
result Our test outperforms existing baselines in model testing and structure learning for dense directed graphical models.
FMCIT accelerates CI tests for causal discovery, maintaining power and efficiency.
problem High computational complexity in CI tests limits practical applicability of causal discovery methods.
method Flow Matching-based Conditional Independence Test (FMCIT) that leverages flow matching for fast CI tests.
result FMCIT effectively controls type-I error and maintains high testing power under the alternative hypothesis.
Paper extends quantile factor analysis with probabilistic methods for better economic policy and financial condition prediction.
problem Improving accuracy in economic and financial condition prediction.
method Probabilistic quantile factor analysis with regularization and variational approximations.
result The probabilistic estimator outperforms a recent loss-based estimator in many cases.
We study high codimension mean curvature flow of a submanifold Mn of dimension n in Euclidean space Rn+k subject to the quadratic curvature condition ∣A∣2≤cn∣H∣2,cn=min{3n4,n−21}. This condition extends the notion of two-convexity for hypersurface…
New curvature condition helps organize high-curvature regions in geometric flows.
problem Organizing high-curvature regions in geometric flows.
method Introducing quasi-parallel mean curvature (QPMC) and proving canonical foliation.
result Bubblesheets can be placed in a suitable normal form.
Paper introduces a novel method for dynamic covariance estimation with random forests.
problem Estimating high-dimensional dynamic covariance matrices with multiple covariates.
method Nonparametric approach using random forests.
result Uniform consistency theory and error rates established for high-dimensional scenarios.
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.
Generative adversarial networks sample unknown high-dimensional conditional distributions.
problem Sampling from unknown high-dimensional conditional distributions with limited data.
method Generative adversarial networks (GAN) for both sampling and distribution inference.
result GAN effectively samples target conditional distribution with minimal impact on sample quality.
AP-CDE uses NF to estimate high-dimensional conditional densities, improving interpretability.
problem Estimating conditional densities for high-dimensional responses like images.
method Extends NF neural networks to handle high-dimensional y with a latent z. result Improves interpretation of latent components, especially zP. New algorithms improve sampling from complex distributions.
problem Sampling from high-dimensional target distributions with super-linearly growing potentials.
method Proposed aHOLA and aHOLLA algorithms with non-asymptotic convergence bounds.
result Achieved state-of-the-art rates of convergence in non-convex settings.
MAPS algorithm creates reliable prediction intervals for high-dimensional data.
problem Computing reliable conditional prediction intervals in high-dimensional settings.
method Lifted predictive model (LPM) and MAPS algorithm for distribution-free intervals.
result MAPS algorithm produces valid prediction intervals for any trained model.
Efficiently computes optimal transport maps and Wasserstein barycenters using conditional normalizing flows.
problem Computing optimal transport maps and Wasserstein barycenters in high-dimensional spaces.
method Uses conditional normalizing flows to approximate distributions and solve the primal problem.
result Shows computational feasibility for hundreds of input distributions and yields accurate results.
New test detects conditional dependence using GAN approximations.
problem Detecting conditional dependence in high-dimensional feature spaces.
method Generative adversarial networks (GANs) for approximating conditional distributions.
result Significant gains in power over competing methods.
PROD method improves high-dimensional regression by handling strong correlations.
problem Violation of Irrepresentable Condition in LASSO for high-dimensional data.
method PROD procedure based on orthogonal decomposition of design matrix.
result PROD enhances performance of high-dimensional penalized regression.
New method improves simulation efficiency in high dimensions.
problem Efficiency in estimating functionals of conditional expectations in high dimensions.
method Kernel ridge regression exploiting smoothness of conditional expectation.
result Effective reduction of the curse of dimensionality, bridging convergence rates.
High-dimensional PDEs have been a longstanding computational challenge. We propose to solve high-dimensional PDEs by approximating the solution with a deep neural network which is trained to satisfy the differential operator, initial condition, and boundary conditions. Our algorithm is meshfree, which is key since mesh…
Neural framework for conditional OT maps learns from categorical and continuous variables.
problem Learning conditional optimal transport maps between complex distributions.
method Hypernetwork generates adaptive transport layer parameters based on conditioning variables.
result Our method outperforms simpler conditioning methods in comprehensive ablation studies.
We show that the two-stage adaptive Lasso procedure (Zou, 2006) is consistent for high-dimensional model selection in linear and Gaussian graphical models. Our conditions for consistency cover more general situations than those accomplished in previous work: we prove that restricted eigenvalue conditions (Bickel et al.…
We present a novel procedure for scaling relatively high frequency tail probability and quantile estimates for the conditional distribution of returns.
Improved image generation with fewer labels.
problem Generating high-fidelity images with limited labeled data.
method Self- and semi-supervised learning techniques.
result Outperforms state-of-the-art models using 10-20% of labels.
Develops a nonparametric graphical model for conditional independence.
problem Evaluation of conditional independence without distributional assumptions.
method Nonlinear sufficient dimension reduction techniques applied to a nonparametric graphical model.
result Method outperforms existing methods in non-Gaussian settings and high-dimensional data.
A new method improves SVI for high-dimensional, poorly-conditioned distributions.
problem Challenges in existing SVI methods for high-dimensional, poorly-conditioned distributions.
method Trust-region optimization approach leveraging conditional independences and second-order information.
result Superior numerical performance and better scalability in high-dimensional distributions.
Measuring conditional dependence is an important topic in statistics with broad applications including graphical models. Under a factor model setting, a new conditional dependence measure based on projection is proposed. The corresponding conditional independence test is developed with the asymptotic null distribution …
New method tests CMI using deep neural networks for high-dimensional data.
problem Testing conditional mean independence in high-dimensional settings.
method Population CMI measure and bootstrap-based testing with deep generative neural networks.
result Strong empirical performance and versatility in various scenarios.
The paper analyzes ℓq optimization methods for high-dimensional linear regression.
problem Estimating sparse parameters from noisy observations in high-dimensional settings.
method Introduces and analyzes ℓq optimization methods for sparse estimation. result Shows stable recovery properties and bounds for ℓq minimization and regularization methods. Paper proves conditions for estimating precision matrices with Laplacian constraints.
problem Estimating high-dimensional precision matrices with Laplacian constraints.
method Minimizing Stein's loss with conditions on graph connectivity and Laplacian constraints.
result High-dimensional consistency achieved with Laplacian constraints, independent of graph structure.
Modeling implied volatility surface dynamics with Hawkes kernels.
problem Understanding and predicting high-frequency dynamics of the implied volatility surface.
method Hawkes modeling of the volatility surface, with coefficients governing skew and convexity.
result Simple conditions on Hawkes kernel coefficients ensure no-arbitrage and reduce parameter estimation.
New method samples from any causal effect given conditional generative models.
problem Sampling from un/conditional interventional distributions in high-dimensional data.
method Sequence of push-forward computations of conditional generative models.
result Algorithm enables sampling from any identifiable interventional distribution.
We introduce a new framework for training deep generative models for high-dimensional conditional density estimation. The Bottleneck Conditional Density Estimator (BCDE) is a variant of the conditional variational autoencoder (CVAE) that employs layer(s) of stochastic variables as the bottleneck between the input x a…
Develops a tensor mixture model for high-dimensional data clustering.
problem Jointly modeling and clustering tensors in high dimensions.
method High-dimensional tensor mixture model with plausible dimension reduction assumptions. EHCMA algorithm for efficient estimation.
result The HECM algorithm converges geometrically to a neighborhood within statistical precision of the true parameter.
Given n i.i.d. observations of a random vector (X,Z), where X is a high-dimensional vector and Z is a low-dimensional index variable, we study the problem of estimating the conditional inverse covariance matrix Ω(z)=(E[(X−E[X∣Z])(X−E[X∣Z])T∣Z=z])−1 under the assumption that the set of non…
Deep learning model predicts material microstructures from processing methods.
problem Linking processing conditions to material properties for material design.
method Conditional image synthesis using Wasserstein GAN with gradient penalty.
result Deep learning model synthesizes high-quality microstructures for given cooling methods.