Paper proposes data quality measures for large-scale high-dimensional data.
problem Lack of practical data quality measures for large-scale high-dimensional data.
method Proposes two data quality measures: class separability and in-class variability. Efficient algorithms based on random projections and bootstrapping are provided.
result Efficient algorithms for computing data quality measures on large-scale high-dimensional data.
Develops high-dimensional measurement error models for non-linear loss functions.
problem Measurement errors in ultrahigh-dimensional biomedical data.
method Lipschitz loss functions, L1 norm minimization, Lasso analog.
result Improved accuracy in classification and quantile regression problems.
This paper addresses measurement errors in high-dimensional compositional data using a log-contrast model calibration approach.
problem Measurement errors in high-dimensional regression models involving compositional covariates.
method Calibration approach for the linear log-contrast model under lenient sparsity conditions.
result Established asymptotic normality of the estimator for inference.
MASF improves score-based filters for high-dimensional nonlinear systems with spatially sparse measurements.
problem Challenges in data assimilation for nonlinear, high-dimensional systems with spatially sparse measurements.
method Developed a forward process tailored for filtering that transforms the system state toward the measurement space, enabling a theoretically sound formulation of the likelihood score.
result MASF shows improved performance over existing score-based filters and ensemble-type Kalman filters, achieving up to a 28.2× wall-clock speedup.
rags2ridges simplifies graphical modeling of high-dimensional data.
problem Graphical modeling of high-dimensional precision matrices.
method Modular framework for extraction, visualization, and analysis of Gaussian graphical models.
result Provides a one-stop-shop for graphical modeling of high-dimensional precision matrices.
Scalable approach for high-dimensional dynamical systems with noise filtering and parameter estimation.
problem Noise filtering and parameter estimation for high-dimensional dynamical systems.
method Flexible latent factor model with orthogonal factor loading matrix and closed-form parameter estimation.
result Substantial acceleration and higher accuracy compared to alternatives.
Skeleton clustering detects clusters in high-dimensional data without needing prototypes.
problem Detecting clusters in high-dimensional data with irregular shapes.
method Skeleton clustering combines prototype methods, density-based clustering, and hierarchical clustering using surrogate density measures.
result Skeleton clustering reliably detects clusters in multivariate and high-dimensional data.
Method learns low-dim. state vars from noisy high-dim. data.
problem Discovering dynamical models from noisy high-dimensional data.
method Stochastic Variational Deep Kernel Learning with encoder and latent model.
result Effective denoising, compact state representation, and uncertainty quantification.
A good measure of similarity between data points is crucial to many tasks in machine learning. Similarity and metric learning methods learn such measures automatically from data, but they do not scale well respect to the dimensionality of the data. In this paper, we propose a method that can learn efficiently similarit…
Robust variable selection for high-dimensional data with missing and measurement errors.
problem Missing data and measurement errors confound data distribution.
method Exponential loss function with inverse probability weighting and additive error models.
result The Atan punishment method improves robust variable selection.
Study proposes an active subsampling method for estimating individualized thresholds in high-dimensional data.
problem Estimating optimal individualized thresholds in high-dimensional data with limited labeled samples.
method Developed a K-step active subsampling algorithm to iteratively select and label the most informative data points.
result Revealed a phase transition phenomenon in the estimation of θ with respect to the smoothness of the conditional density. High-dimensional statistics advances in complex data domains.
problem Complex, rich datasets challenge traditional methods.
method Evolved to address sophisticated estimation and inference problems.
result Deepened connections with optimization, concentration, and information theory.
AdapDISCOM tackles high-dimensional multimodal data with missingness and errors, improving prediction and biomarker selection.
problem High-dimensional multimodal data with block-wise missingness and measurement errors.
method AdapDISCOM introduces modality-specific weighting schemes to address heterogeneity and error magnitudes.
result AdapDISCOM consistently outperforms existing methods under heterogeneous contamination and heavy-tailed distributions.
High-dimensional random geometry shows phase transitions in various problems.
problem Phase transitions in high-dimensional random geometry.
method Analysis of various financial, optimization, and ecological problems.
result Links between seemingly distant fields and further ramifications.
A new method optimizes slicing directions for SW distances to improve high-dimensional probability measure comparison.
problem Challenging identification of informative slicing directions for SW distances.
method Constrained learning approach to optimize slicing directions, using continuous relaxations and gradient-based primal-dual approach.
result Demonstrated efficacy in learning more informative slicing directions on various high-dimensional data.
Wiener-Granger causality is a widely used framework of causal analysis for temporally resolved events. We introduce a new measure of Wiener-Granger causality based on kernelization of partial canonical correlation analysis with specific advantages in the context of large high-dimensional data. The introduced measure is…
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 …
High dimensional data analysis is known to be as a challenging problem. In this article, we give a theoretical analysis of high dimensional classification of Gaussian data which relies on a geometrical analysis of the error measure. It links a problem of classification with a problem of nonparametric regression. We giv…
New scalable algorithm estimates barycenters of measures in high dimensions.
problem Estimating barycenters of measures in high-dimensional settings.
method Optimizes generative models to estimate barycenters, scaling by introducing inductive biases.
result First scalable method to estimate barycenters in thousands of dimensions.
The paper proposes a new method for product recommendation that considers revenue contributions and user similarity.
problem High dimensionality and sparsity in user-item data, especially in terms of revenue contributions.
method The approach encodes revenue contributions in the user-item matrix and computes customer similarity using suitable distance measures.
result The method segments users based on revenue-based similarity and supports recommendations aligned with profitability objectives.
We consider the high-dimensional sparse linear regression problem of accurately estimating a sparse vector using a small number of linear measurements that are contaminated by noise. It is well known that the standard cadre of computationally tractable sparse regression algorithms---such as the Lasso, Orthogonal Matchi…
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.
Develops a measure-theoretic framework for complex co-occurrence data.
problem Modeling and interpreting complex co-occurrences in high-dimensional data.
method Introduces measure-theoretic probability and conditional probability, investigates E-integrals.
result Establishes a rigorous measure-theoretic foundation for co-occurrence modeling.
To model modern large-scale datasets, we need efficient algorithms to infer a set of P unknown model parameters from N noisy measurements. What are fundamental limits on the accuracy of parameter inference, given finite signal-to-noise ratios, limited measurements, prior information, and computational tractability …
Method identifies low-dimensional structure in high-dimensional probability measures.
problem Identifying low-dimensional structure in high-dimensional probability measures.
method Extends prior work on minimizing majorizations of the Kullback-Leibler divergence to identify optimal approximations within a specific class of measures.
result Connection between dimensional logarithmic Sobolev inequality and approximations with the ansatz.
A new perceptual adjustment query for metric learning reduces complexity in high-dimensional data.
problem Metric learning in high-dimensional data with limited human feedback.
method Inverted measurement scheme and two-stage estimator for PAQs.
result Sample complexity guarantees for the two-stage estimator of metric learning from PAQs.
This paper tackles deep clustering evaluation challenges in high-dimensional data.
problem Evaluation of deep clustering methods is problematic due to the curse of dimensionality and variations in embedding spaces.
method Develops a theoretical framework to highlight the ineffectiveness of internal validation measures and proposes a systematic approach to applying clustering validity indices in deep learning.
result The proposed framework reduces misguidance from improper use of clustering validity indices in deep learning.
HI-SIGMA improves sensitivity in high-dimensional statistical inference with data-driven background models.
problem Performing high-dimensional statistical inference with complex backgrounds in high-energy physics.
method HI-SIGMA uses generative ML models to learn signal and background distributions, incorporating systematic uncertainties.
result HI-SIGMA provides improved sensitivity compared to classifier-based methods.
New method estimates shape distance in neural representations with limited data.
problem Measuring geometric similarity between high-dimensional network representations.
method Method-of-moments estimator with tunable bias-variance tradeoff.
result New estimator achieves lower bias than standard methods in high-dimensional settings.
When recovering an unknown signal from noisy measurements, the computational difficulty of performing optimal Bayesian MMSE (minimum mean squared error) inference often necessitates the use of maximum a posteriori (MAP) inference, a special case of regularized M-estimation, as a surrogate. However, MAP is suboptimal in…
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 tackles sampling from Gibbs measures with constrained support, providing a sampling guarantee.
problem Sampling from Gibbs measures with constrained support, especially in the pre-asymptotic regime.
method Analyzing the spectral gap of Langevin dynamics to provide a non-asymptotic sampling guarantee.
result The low-temperature Gibbs distribution concentrates on a neighborhood of its mode in the pre-asymptotic regime.
New method uses neural networks to solve complex PDEs from optimal control theory.
problem Solving high-dimensional Hamilton-Jacobi-Bellman PDEs.
method Iterative diffusion optimization techniques, focusing on path measures and divergences.
result Favourable properties of log-variance divergence for Monte Carlo estimators.
New coherence parameter for GNNs with Fourier measurements improves signal recovery.
problem Characterizing generative compressed sensing with Fourier measurements.
method Subspace counting arguments and high-dimensional probability theory.
result First known restricted isometry guarantee for generative compressed sensing with subsampled isometries.
Algorithm recovers factors of rank-1 matrices from noisy measurements.
problem Estimating factors of a rank-1 matrix from nonlinearly transformed and noisy measurements.
method Alternating minimization with random initialization and analysis of empirical error recursion.
result Algorithm converges geometrically fast from random initialization, with sharp guarantees.
Generalizes causal inference to high-dimensional outcomes.
problem Limited causal inference methods for multivariate outcomes.
method Formulates causal discrepancy tests for nominal variables, uses conditional independence tests.
result Causal CDcorr method improves finite sample validity and power.
High-dimensional spectroscopy data makes ML models achieve near-perfect accuracy, even when chemical distinctions are absent.
problem Why machine learning models achieve near-perfect accuracy in spectroscopic classification tasks without chemically meaningful features.
method Theoretical analysis grounded in the Feldman-Hajek theorem and concentration of measure, combined with specific experiments on synthetic and real fluorescence spectra.
result Infinitesimal distributional differences in high-dimensional spaces can lead to perfect separability, making models achieve near-perfect accuracy in spectroscopy.
We analyze the dynamics of an online algorithm for independent component analysis in the high-dimensional scaling limit. As the ambient dimension tends to infinity, and with proper time scaling, we show that the time-varying joint empirical measure of the target feature vector and the estimates provided by the algorith…
Brain decoding involves the determination of a subject's cognitive state or an associated stimulus from functional neuroimaging data measuring brain activity. In this setting the cognitive state is typically characterized by an element of a finite set, and the neuroimaging data comprise voluminous amounts of spatiotemp…
We proposed a new statistical dependency measure called Copula Dependency Coefficient(CDC) for two sets of variables based on copula. It is robust to outliers, easy to implement, powerful and appropriate to high-dimensional variables. These properties are important in many applications. Experimental results show that C…
High-dimensional unimodal distributions can cause MCMC methods to fail.
problem Failure of MCMC methods in high-dimensional unimodal distributions.
method Examples and theoretical analysis of MCMC methods, including Metropolis-Hastings adjusted methods.
result MCMC methods can take an exponential run-time for high-dimensional unimodal distributions.
We study high-dimensional asymptotic performance limits of binary supervised classification problems where the class conditional densities are Gaussian with unknown means and covariances and the number of signal dimensions scales faster than the number of labeled training samples. We show that the Bayes error, namely t…
Modeling dynamical systems is important in many disciplines, e.g., control, robotics, or neurotechnology. Commonly the state of these systems is not directly observed, but only available through noisy and potentially high-dimensional observations. In these cases, system identification, i.e., finding the measurement map…
Adaptive algorithm improves nonlinear data assimilation for non-Gaussian systems.
problem Challenges of non-Gaussian statistics in data assimilation.
method Triangular measure transport with P-spline basis functions and an information criterion.
result Automatic selection of parsimonious parametrization for efficient adaptation.
Study shows simple vector quantization measures correlate with deep learning generalization.
problem Understanding and predicting generalization in deep learning models.
method Applying complexity measures from approximation and information theory to deep learning features.
result Simple vector quantization measures correlate well with generalization performance in deep learning.
Cross-sectional "Information Coefficient" (IC) is a widely and deeply accepted measure in portfolio management. The paper gives an insight into IC in view of high-dimensional directional statistics: IC is a linear operator on the components of a centralizing-unitizing standardized random vector of next-period cross-sec…
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.
Quantum machine learning tackles large datasets with randomized measurements.
problem Efficiently process large, high-dimensional datasets on quantum computers.
method Randomized measurements to scale linearly with dataset size and quadratic for post-processing.
result Substantial speed-up for noisy quantum computers, enabling image classification.