This paper treats the problem of screening for variables with high correlations in high dimensional data in which there can be many fewer samples than variables. We focus on threshold-based correlation screening methods for three related applications: screening for variables with large correlations within a single trea…
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48 results for “correlated variables”
Study examines challenges in variable importance ranking due to feature correlation.
problem Challenges in variable importance ranking under correlation.
method Simulation study and theoretical analysis of feature knockoffs and conditional predictive impact (CPI).
result Highly correlated features increase the correlation of knockoff variables, posing a limitation for CPI.
The study uses DCC for financial market analysis, revealing hidden correlations.
problem Identifying hidden nonlinear correlations in financial markets.
method Agglomerative hierarchical clustering with distance correlation coefficient.
result DCC reveals more information than Pearson correlation for financial data.
Distance Correlation Methods for Discovering Associations in Large Astrophysical Databasesastro-ph.CO
High-dimensional, large-sample astrophysical databases of galaxy clusters, such as the Chandra Deep Field South COMBO-17 database, provide measurements on many variables for thousands of galaxies and a range of redshifts. Current understanding of galaxy formation and evolution rests sensitively on relationships between…
The paper develops a test for independence of selected Gaussian variables after thresholding correlations.
problem Testing independence of selected Gaussian variables after thresholding correlations.
method The approach involves conditioning on the selection event and using a new characterization of the conditioning event in terms of canonical correlation.
result The proposed test has higher power than a naive approach that ignores selection effects.
Predictive Correlation Screening: Application to Two-stage Predictor Design in High Dimensionstat.ML
We introduce a new approach to variable selection, called Predictive Correlation Screening, for predictor design. Predictive Correlation Screening (PCS) implements false positive control on the selected variables, is well suited to small sample sizes, and is scalable to high dimensions. We establish asymptotic bounds f…
Proposes -CCA for sparse CCA with improved representation learning.
problem CCA models break with too many variables, and sparsity is beneficial.
method Sparse CCA with stochastic gates and -regularization.
result Improves representation learning by gating nuisance variables.
Enhances sensitivity analysis for correlated inputs.
problem Estimating sensitivity indices in models with correlated inputs.
method Proposes an extension of Sobol' estimator using a linear correlation model.
result Improves accuracy in variance-based sensitivity analysis.
Neurons in the visual cortex are correlated in their variability. The presence of correlation impacts cortical processing because noise cannot be averaged out over many neurons. In an effort to understand the functional purpose of correlated variability, we implement and evaluate correlated noise models in deep convolu…
Study uses VC correlation to uncover directional financial relationships.
problem Understanding causal relationships between financial variables.
method Volatility constrained correlation (VC correlation) method.
result Operating income is most influential, while market capitalization and revenue are most susceptible.
The paper extends Pearson correlation to multi-variables, useful for noise measurement and feature selection.
problem The standard Pearson correlation coefficient is limited to two variables and doesn't meet the needs for multi-variable analysis.
method The authors use random matrix theory to extend Pearson's correlation coefficient to an arbitrary number of variables.
result The extended correlation coefficient is useful for gauging noise and selecting features, particularly in classification.
Causal Explainability of Machine Learning in Heart Failure Prediction from Electronic Health Recordsstat.ML
The paper investigates causal relationships in heart failure prediction using machine learning.
problem Understanding the causal relationships between clinical variables and heart failure.
method Proposes a new computational framework for causal structure discovery (CSD) of mixed-type clinical variables for binary disease outcomes.
result Feature importance from nonlinear classifiers strongly correlates with causal strength of variables, but not differentiating cause and effect.
This work explores variably scaled kernels to improve non-stationary Gaussian processes.
problem Limited ability of stationary kernels to represent heterogeneous correlation structures.
method Introduces variably scaled kernels to modify correlation structures explicitly.
result Improved reconstruction accuracy and better uncertainty estimates for non-stationary data.
We consider a binary sequence generated by thresholding a hidden continuous sequence. The hidden variables are assumed to have a compound symmetry covariance structure with a single parameter characterizing the common correlation. We study the parameter estimation problem under such one-parameter models. We demonstrate…
Statistical inference can be computationally prohibitive in ultrahigh-dimensional linear models. Correlation-based variable screening, in which one leverages marginal correlations for removal of irrelevant variables from the model prior to statistical inference, can be used to overcome this challenge. Prior works on co…
Mean representations of VAEs are correlated but still useful for tasks.
problem Correlation between mean and sampled representations of VAEs.
method Selective posterior collapse to identify active and passive variables.
result Passive variables in mean representations are correlated but uncorrelated in sampled ones.
Sparse Estimation with Strongly Correlated Variables using Ordered Weighted L1 Regularizationstat.ML
This paper studies ordered weighted L1 (OWL) norm regularization for sparse estimation problems with strongly correlated variables. We prove sufficient conditions for clustering based on the correlation/colinearity of variables using the OWL norm, of which the so-called OSCAR is a particular case. Our results extend pr…
Graph Structured Prediction Energy Networks model correlations for joint inference.
problem Joint inference over multiple variables with high-order correlations.
method Energy Networks for modeling explicit local and implicit higher-order correlations.
result Tractable inference with explicit modeling of correlations.
LMMVAE improves VAE for correlated data by separating latent variables into fixed and random parts.
problem Correlated data in tabular and image datasets.
method Integrates random effects into VAE architecture, separating latent variables into fixed and random parts.
result Significant improvement in reconstruction error and likelihood loss on unseen data.
Proposes a new method to estimate variable importance in black box models, mitigating correlation effects.
problem Correlation between covariates affects the interpretation of variable importance parameters.
method Develops a modified LOCO (Leave Out COvariates) method and uses semiparametric models for estimation.
result Shows how to estimate a modified LOCO method that mitigates correlation effects.
SPPCSO addresses multicollinearity in high-dimensional data, improving model stability and predictive accuracy.
problem Multicollinearity in high-dimensional data leads to unstable estimation and reduced predictive accuracy.
method SPPCSO integrates principal component regression and L1 regularization to adaptively adjust shrinkage factors.
result SPPCSO achieves stable and reliable estimation in high-noise settings, distinguishing signal variables from noise.
In this paper, we introduce Adaptive Cluster Lasso(ACL) method for variable selection in high dimensional sparse regression models with strongly correlated variables. To handle correlated variables, the concept of clustering or grouping variables and then pursuing model fitting is widely accepted. When the dimension is…
New method for accurate permutation inference in CCA.
problem Inaccurate permutation inference in CCA.
method Proposed solutions for permutation inference in CCA, including transforming residuals and stepwise estimation.
result Valid permutation tests for CCA with and without nuisance variables.
In this paper, a class of statistics named ART (the alternant recursive topology statistics) is proposed to measure the properties of correlation between two variables. A wide range of bi-variable correlations both linear and nonlinear can be evaluated by ART efficiently and equitably even if nothing is known about the…
Better Together: Cross and Joint Covariances Enhance Signal Detectability in Undersampled Datacond-mat.dis-nn
Better signal detection in undersampled data using joint and cross covariances.
problem Detecting shared signals in high-dimensional data with limited samples.
method Analysis of three covariance matrices: individual, cross, and joint.
result Joint and cross covariance matrices detect signals earlier than individual covariances.
TimeCNN improves forecasting by refining cross-variable interactions over time.
problem Multivariate time series forecasting struggles with dynamic and multifaceted cross-variable correlations.
method TimeCNN uses timepoint-independent convolution kernels to capture evolving relationships among variables.
result TimeCNN outperforms state-of-the-art models in real-world datasets with significant computational and speed advantages.
tvGP-VAE models tensor-valued latent variables with Gaussian processes for better data structure representation.
problem Agnostic latent variables in VAEs ignore data structure correlations.
method Proposes tensor-variate Gaussian process prior for variational autoencoder.
result Explicitly modeling correlation structures improves model performance in reconstruction.
Discovering a correlation from one variable to another variable is of fundamental scientific and practical interest. While existing correlation measures are suitable for discovering average correlation, they fail to discover hidden or potential correlations. To bridge this gap, (i) we postulate a set of natural axioms …
A new screening method for high-dimensional data reduces computational cost.
problem Challenges in variable selection for ultrahigh-dimensional linear regression.
method Ordering absolute sample ridge partial correlations to screen variables.
result The method provides sure screening property without strong assumptions.
Proposes a two-stage method for selecting correlated predictors in high-dimensional data.
problem Selecting correlated predictors in high-dimensional data with unknown group structures.
method Two-stage approach: variable clustering followed by group selection.
result The two-stage method improves prediction accuracy and active predictor selection.
Proposes a method to improve Lasso stability via variable decorrelation.
problem Stability of Lasso in high-dimensional settings with correlated variables.
method Variable decorrelation before applying the Lasso.
result Improves stability of variable selection regardless of predictor correlation.
LMLFM tackles predictive modeling from longitudinal data with mixed correlations.
problem Learning predictive models from longitudinal data with complex correlations and non-linear interactions.
method Longitudinal Multi-Level Factorization Machine (LMLFM) that selects predictive fixed and random effects.
result LMLFM outperforms state-of-the-art methods in predictive accuracy, variable selection, and scalability.
In this work, the possibility of clustering correlated random variables was examined, both because of their mutual similarity and because of their similarity to the principal components. The k-means algorithm and spectral algorithms were used for clustering. For spectral methods, the similarity matrix was both the matr…
Paper proposes ASCCA for sparse CCA with trace Lasso regularization.
problem Sparse CCA in high-dimensional settings with correlated variables.
method Trace Lasso regularization, reformulated to Riemannian manifolds, inexact augmented Lagrangian method.
result Improved stability and interpretation of sparse CCA.
Develops a method for stress testing correlations of financial portfolios.
problem Stress testing correlations in financial asset portfolios.
method Parametric representation of correlations, Bayesian variable selection, joint distribution of stress scenarios.
result Inference of worst-case correlation scenarios using stress tests.
Interpreting the Latent Space of GANs via Correlation Analysis for Controllable Concept Manipulationcs.CV
Method interprets GAN latent space via latent variable correlation analysis.
problem Understanding the inner workings of GANs.
method Analyzing correlation between latent variables and semantic contents in generated images.
result A method for controllable semantic content generation in GANs.
A new method estimates conditional canonical correlations using random forests.
problem Estimating relationships between two sets of variables given covariates.
method Random Forest with Canonical Correlation Analysis (RFCCA)
result RFCCA provides accurate canonical correlation estimations and well-controlled Type-1 error.
VC-PCR improves prediction by clustering correlated variables.
problem Decreased prediction accuracy due to cluster structure in predictor variables.
method Supervised variable selection and clustering to integrate cluster information into a sparse modeling process.
result VC-PCR achieves better prediction, variable selection, and clustering performance.
Dynamical analysis of financial stocks network: improving forecasting using network propertiesq-fin.ST
Network analysis improves stock return forecasting.
problem Improving stock return forecasting using network properties.
method Network analysis of stock return correlations, using individual and global properties of stocks.
result 50% improvement in R2 score for long-term stock returns forecasting, 3% for short-term.
In this paper we use wavelet concepts to show that correlation coefficient between two financial data's is not constant but varies with scale from high correlation value to strongly anti-correlation value This studies is important because correlation coefficient is used to quantify degree of independence between two va…
Many inference problems involving questions of optimality ask for the maximum or the minimum of a finite set of unknown quantities. This technical report derives the first two posterior moments of the maximum of two correlated Gaussian variables and the first two posterior moments of the two generating variables (corre…
Sliding down the stairs: how correlated latent variables accelerate learning with neural networksstat.ML
Neural networks learn faster with correlated latent variables.
problem Efficiently learning from higher-order correlations in neural networks.
method Analytical derivation and simulations of two-layer neural networks.
result Correlations between latent variables speed up learning from higher-order correlations.
New framework for inference with LAR, explaining variable contributions and providing stopping rules.
problem LAR's lack of well-understood termination point and basic behavioral properties.
method Developed a novel framework for inference with LAR, providing new mathematical properties and stopping rules.
result LAR estimates of non-zero population correlations have independent normal distributions for inference, and zero-valued correlations have a non-normal joint distribution.
Methods to find correlation among variables are of interest to many disciplines, including statistics, machine learning, (big) data mining and neurosciences. Parameters that measure correlation between two variables are of limited utility when used with multiple variables. In this work, I propose a simple criterion to …
We present an extension of sparse Canonical Correlation Analysis (CCA) designed for finding multiple-to-multiple linear correlations within a single set of variables. Unlike CCA, which finds correlations between two sets of data where the rows are matched exactly but the columns represent separate sets of variables, th…
This study shows how trade policy uncertainty affects stock-T bill correlations.
problem The impact of trade policy uncertainty on stock-T bill relationships.
method Extended Dynamic Conditional Correlation (DCC) framework incorporating exogenous variables.
result Trade policy uncertainty significantly alters stock-T bill correlations, especially under specific political conditions.
Enhances robustness of MOGP regression for multiple correlated outputs.
problem Model misspecification and outliers in MOGP regression.
method Extends RCGP framework to multi-output setting.
result Provable robust MOGP with joint correlation capture.
FREEtree: A Tree-based Approach for High Dimensional Longitudinal Data With Correlated Featuresstat.ML
FREEtree improves tree-based methods for correlated longitudinal data.
problem Poor performance of Random Forests in high dimensional longitudinal data with correlated features.
method FREEtree uses a piecewise random effects model and clustering with WGCNA to select features and maintain interpretability.
result FREEtree outperforms other tree-based methods in prediction and feature selection accuracy.