AF improves sampling from high-dimensional, multi-modal distributions.
problem Sampling from high-dimensional, multi-modal distributions is challenging.
method Annealing Flow (AF) using Continuous Normalizing Flow (CNF) with dynamic Optimal Transport (OT) objective and annealing procedures.
result AF significantly improves training efficiency and stability, outperforming state-of-the-art methods.
Improved sampling for high-dimensional posteriors with underdamped Langevin.
problem Scalability issues in high-dimensional problems with approximate Thompson sampling.
method Underdamped Langevin Monte Carlo for accelerated posterior concentration.
result Logarithmic regret improvement from i l d e O ( d ) \mathcal{ ilde O}(d) i l d e O ( d ) to i l d e O ( d ) \mathcal{ ilde O}(\sqrt{d}) i l d e O ( d ) . The paper studies how more data affects prediction risk in high-dimensional models.
problem The impact of increasing data on prediction risk in high-dimensional models.
method Derives central limit theorem and provides finite-sample distribution and confidence interval for prediction risk.
result Demonstrates 'more data hurt' phenomenon in high-dimensional least squares estimation.
Improved Thompson Sampling for high-dimensional sparse bandits.
problem Stochastic linear contextual bandits with high-dimensional features.
method Thompson Sampling with spike-and-slab priors and variational inference.
result Nearly optimal upper bound on expected cumulative regret.
Proofs high-dimensional spectrum convergence of weighted sample covariance.
problem High-dimensional spectrum convergence of weighted sample covariance.
method Proposes a new, concise proof with stronger assumptions.
result Spectrum convergence proven for different weight distributions.
Improved CEM for fast real-time planning in high-dimensional control tasks.
problem Sampling inefficiency of CEM in real-time planning.
method Novel additions to CEM including temporally-correlated actions and memory.
result 2.7-22x less samples and 1.2-10x performance increase.
Unified framework for sampling and approximating high-dimensional energy landscapes.
problem Sampling and approximating complex energy landscapes in physical systems with constraints and energy barriers.
method Formulates a minimax optimization problem that jointly adapts surrogate approximation and adaptive sampling.
result Demonstrates effectiveness in biomolecular systems with up to 30 collective variables.
High-dimensional models become unstable when sample size falls below a critical level, leading to a phase transition.
problem Instability in high-dimensional learning models when sample size is insufficient.
method Proved the necessity of a Fisher eigenvalue threshold for stability, introduced Fisher floor for verification.
result A sharp phase transition between reliable concentration and inevitable failure in high-dimensional learning.
Study improves understanding of non-differentiable penalties in high-dimensional settings.
problem Theoretical understanding of non-differentiable penalties like generalized LASSO and nuclear norm in high-dimensional settings.
method Proportional high-dimensional regime analysis with finite sample upper bounds on expected squared error.
result LO provides accurate estimation of out-of-sample risk in high-dimensional settings.
Paper analyzes high-dimensional portfolio risks and finds empirical out-of-sample relative loss is more reliable.
problem Analyzing risks in high-dimensional portfolios using empirical variance.
method Derives asymptotic behavior of out-of-sample variance and relative loss in high-dimensional settings.
result Empirical out-of-sample relative loss is more reliable than variance in high-dimensional portfolios.
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.
New algorithm uniformly samples high-dimensional convex bodies efficiently.
problem Uniform sampling of high-dimensional convex bodies.
method Stochastic diffusion perspective to show contraction to the target distribution.
result Achieves state-of-the-art runtime complexity with strong guarantees on output.
Method identifies change points in high-dimensional models using sample weights.
problem Identifying change points in high-dimensional generalized linear models.
method Sample-weighted empirical risk minimization (Weighted ERM).
result Weighted ERM yields precise asymptotic performance characterization for Gaussian designs.
SLMC improves sampling efficiency for high-dimensional distributions.
problem Sampling from high-dimensional distributions is computationally challenging.
method SLMC projects Langevin updates onto subsampled eigenblocks of a time-varying preconditioner.
result SLMC offers superior adaptability and computational efficiency compared to traditional methods.
Enhances Bayesian model selection for high-dimensional problems.
problem Bayesian model selection for high-dimensional problems.
method Proximal nested sampling with data-driven priors.
result Improves model selection for log-convex likelihood models.
In many fields of science, high-dimensional integration is required. Numerical methods have been developed to evaluate these complex integrals. We introduce the code i-flow, a python package that performs high-dimensional numerical integration utilizing normalizing flows. Normalizing flows are machine-learned, bijectiv…
Proposes a new signal model for high-dimensional, small-sample-size data.
problem Signal detection in high-dimensional, small-sample-size datasets.
method Intrinsic signal model based on dynamical system assumption.
result Taguchi method effectively detects signals in the proposed model.
The paper improves high-dimensional linear regression prediction and estimation using auxiliary samples.
problem Estimating and predicting high-dimensional linear regression models with auxiliary samples.
method Proposes Trans-Lasso for data-driven transfer learning, establishing optimality for prediction and estimation.
result Knowledge from auxiliary samples can improve learning performance in target problems.
A new method speeds up sampling of Boltzmann distribution in high-dimensional systems.
problem High computational cost of obtaining Jacobian of flow-based models in high dimensions.
method Flow perturbation method that incorporates stochastic perturbations and reweighting.
result Achieves unbiased sampling of Boltzmann distribution with orders of magnitude speedup.
New method improves sampling from complex, multi-peaked distributions.
problem Sampling from high-dimensional, multimodal distributions using HMC.
method Combines tempered HMC with automatic tuning strategies.
result Demonstrates more effective scaling with dimension than adaptive methods.
Characterizes uncertainty in high-dimensional linear classification models.
problem Assessing uncertainty in high-dimensional linear classification models.
method Approximate message passing algorithm for posterior marginals, closed-form formula for joint statistics.
result Closed-form formula for joint statistics between logistic classifier, Bayesian uncertainty, and ground-truth probit uncertainty.
The paper provides guarantees for high-dimensional DML estimators in observational studies.
problem Estimating treatment effects in observational settings with many covariates.
method Debiased machine learning (DML) with finite-sample guarantees.
result Bounding the deviation of finite-sample distribution from asymptotic Gaussian approximation.
New method for cross-validation in high-dimensional data with dependent or heavy-tailed covariates.
problem Inconsistent cross-validation in high-dimensional settings with dependent or heavy-tailed covariates.
method ROTI-GCV framework for cross-validation under proportional asymptotics regime.
result Demonstrated accuracy of ROTI-GCV in synthetic and semi-synthetic settings.
New method improves high-dimensional Bayesian optimization efficiency using MCMC.
problem High-dimensional optimization challenges and computational complexity.
method Markov Chain Monte Carlo (MCMC) to efficiently sample from approximated posterior.
result Metropolis-Hastings and Langevin Dynamics versions outperform state-of-the-art methods.
Generative algorithms learn high-dimensional data efficiently and generate new samples.
problem Learning from scarce high-dimensional data.
method Lipschitz-regularized gradient flows and particle-based algorithms.
result Correctly transports gene expression data points with high dimensionality.
E-C2ST uses E-values for high-dimensional data two-sample tests.
problem Statistical testing for high-dimensional data.
method Combines split likelihood ratio tests and predictive independence tests, using E-values for anytime-valid sequential tests.
result E-C2ST achieves enhanced statistical power by partitioning datasets into multiple batches.
New partition designs reduce star discrepancy in high-dimensional sampling.
problem Improving the expected star discrepancy in high-dimensional sampling.
method Developed non-equal volume partitions to achieve lower expected star discrepancy.
result Explicit upper bounds for expected star discrepancy under non-equal volume partitions.
Nested Slice Sampling accelerates Nested Sampling for GPU acceleration.
problem Challenging inference for complex, multimodal targets.
method Vectorized Nested Slice Sampling using Hit-and-Run Slice Sampling.
result NSS maintains accurate evidence estimates and high-quality posterior samples, robust on multimodal problems.
A new algorithm detects changes in high-dimensional data efficiently under sampling constraints.
problem Real-time monitoring of high-dimensional streaming data with limited sampling.
method Incorporates multi-armed bandit approaches into sequential change-point detection.
result Proposes TSSRP algorithm for efficient detection of changes.
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…
The paper analyzes LOCV for high-dimensional risk estimation, proving error bounds.
problem Estimating out-of-sample prediction error in high-dimensional settings.
method Theoretical analysis of leave-one-out cross validation (LOCV) in penalized regression.
result Finite sample upper bounds on LOCV error, showing it converges to zero as n,p → ∞.
This paper presents a new approach, called perturb-max, for high-dimensional statistical inference that is based on applying random perturbations followed by optimization. This framework injects randomness to maximum a-posteriori (MAP) predictors by randomly perturbing the potential function for the input. A classic re…
Bayesian method for high-dimensional VECM analysis of cointegration.
problem Efficiently determining cointegration rank in high-dimensional time series.
method Bayesian approach to analyze cointegration matrix.
result Promising results in high-dimensional settings with low sample size.
AdaTrans adapts to feature and sample transfer in high-dimensional regression.
problem High-dimensional linear regression with more features than samples.
method F-AdaTrans and S-AdaTrans methods using fused-penalties and adaptive weights.
result AdaTrans achieves convergence rates close to oracle estimators and near-minimax optimal rates.
Regularized discriminant analysis (RDA), proposed by Friedman (1989), is a widely popular classifier that lacks interpretability and is impractical for high-dimensional data sets. Here, we present an interpretable and computationally efficient classifier called high-dimensional RDA (HDRDA), designed for the small-sampl…
MsIGN tackles high-dimensional Bayesian inference using multiscale structure.
problem High-dimensional Bayesian inference challenges due to the curse of dimensionality.
method MsIGN generates samples from coarse to fine scale, minimizing Jeffreys divergence.
result MsIGN outperforms previous approaches in posterior approximation and mode capture.
Derives a method to optimize high-dimensional functions on low-dimensional manifolds.
problem High-dimensional derivative-free optimization with high sample complexity.
method Online learning approach that learns the manifold while optimizing the function.
result Significantly reduces sample complexity compared to existing methods.
Study examines influence diagnostics in high-dimensional M-estimation.
problem Understanding influence diagnostics in high-dimensional settings.
method Characterized the distribution of leave-one-out influences in high-dimensional Gaussian M-estimation.
result The distribution of influences converges to a limiting measure in high-dimensional settings.
Paper proposes sparse classification method for high-dimensional data.
problem Sparse classification in high-dimensional data with positive-confidence samples.
method Developed a novel sparse-penalization framework using L1, SCAD, and MCP penalties for convex and non-convex shrinkage.
result Proved near minimax-optimal sparse recovery rates under Restricted Strong Convexity condition.
Paper finds sample complexity for learning high-dimensional simplices from noisy data.
problem Learning high-dimensional simplices from noisy samples.
method Combines sample compression, high-dimensional geometry, and Fourier analysis.
result Proves sample complexity bound for achieving a simplex within a certain distance from the true simplex.
New method distinguishes predictive distribution estimators in high-dimensional inputs.
problem Difficulty in evaluating predictive distributions for high-dimensional inputs.
method Introduces dyadic sampling to focus on predictive distributions associated with pairs of inputs.
result Demonstrates efficient distinction of predictive distribution estimators in high-dimensional examples.
New algorithms improve privacy in statistical estimation by making them robust.
problem Improving privacy in statistical estimation methods.
method Black-box reduction from privacy to robustness, using Sum-of-Squares method.
result Design of polynomial-time private estimators with optimal tradeoffs among sample complexity, accuracy, and privacy.
Biological data including gene expression data are generally high-dimensional and require efficient, generalizable, and scalable machine-learning methods to discover their complex nonlinear patterns. The recent advances in machine learning can be attributed to deep neural networks (DNNs), which excel in various tasks i…
PolytopeWalk library efficiently samples high-dimensional polytopes.
problem Sampling from high-dimensional polytopes efficiently.
method End-to-end solution including preprocessing and MCMC algorithms.
result Improved sampling efficiency and scalability to high dimensions.
Non-linear manifold learning enables high-dimensional data analysis, but requires out-of-sample-extension methods to process new data points. In this paper, we propose a manifold learning algorithm based on deep learning to create an encoder, which maps a high-dimensional dataset and its low-dimensional embedding, and …
New method detects changes in high-dimensional data from small samples.
problem Detecting changes in high-dimensional data with limited samples.
method Angular kernel scan framework for detecting marginal distributional shifts.
result Exact population mean factorization and asymptotically distribution-free test.
New method uses active importance sampling for rare event optimization in high-dimensional problems.
problem Optimizing complex, high-dimensional functions with rare events.
method Combines rare events sampling with neural network optimization.
result Importance sampling reduces asymptotic variance, improving generalization.
The paper uses machine learning to forecast macroeconomic outcomes with high-dimensional data.
problem Forecasting the full conditional distribution of macroeconomic outcomes.
method Systematically integrating three key principles: high-dimensional data with regularization, rigorous out-of-sample validation, and incorporating nonlinearities.
result Regularization via shrinkage is essential to control model complexity, while nonlinearities yield limited improvements in predictive accuracy.