A review of contrastive dimension reduction methods for treatment vs control studies.
problem Traditional dimension reduction techniques fail to isolate treatment-specific signals.
method Systematic overview and taxonomy of CDR methods.
result Unified framework for CDR methods and applications.
CIR method preserves relation for case-control studies.
problem Learning low-dimensional structure in case-control studies.
method Contrastive inverse regression (CIR) on Stiefel manifold.
result CIR outperforms other methods for high-dimensional data.
This paper examines how labeling error affects contrastive learning and proposes data dimensionality reduction methods to mitigate its impact.
problem The impact of labeling error on the performance of contrastive learning.
method Data dimensionality reduction methods (e.g., SVD) are applied to reduce false positive samples and improve downstream classification accuracy.
result Data dimensionality reduction methods can mitigate the negative impacts of labeling error on downstream classification performance.
New algorithms for clustering and dimension reduction using relative von Neumann entropy.
problem Clustering and dimension reduction for complex data sets.
method Construct graphs from data points, select graph maximizing relative von Neumann entropy, use eigenvectors for dimension reduction.
result Outperforms existing methods on non-trivial data sets.
Optimal persuasion involves projecting state vectors onto lower-dimensional 'optimal information manifolds'.
problem Optimal persuasion of another agent observing multi-dimensional data.
method Performing non-linear dimension reduction by projecting state vectors onto the 'optimal information manifold'.
result Optimal information design splits information into 'good' and 'bad' components, revealing only the direction of good information.
We consider the problem of high-dimensional classification between the two groups with unequal covariance matrices. Rather than estimating the full quadratic discriminant rule, we propose to perform simultaneous variable selection and linear dimension reduction on original data, with the subsequent application of quadr…
Proposes a tool to contrast global vs personalized models in clinical prediction.
problem Balancing global vs personalized models in clinical prediction.
method Localized regression approach using autoencoder for dimension reduction.
result Identification of patient subgroups where global models fall short.
Data balancing reduces variance in machine learning models.
problem Reduction of variance in machine learning models.
method Non-asymptotic statistical bound and eigenvalue decay of Markov operators.
result Data balancing across modalities and sources reduces variance.
New method corrects missing data bias in dimension reduction.
problem Missing data complicates high-dimensional data analysis.
method Developed a bias-corrected Gram matrix for heterogeneous missingness.
result Proposed method improves dimension reduction techniques significantly.
Proposes a method to estimate personalized treatments from high-dimensional data.
problem Estimating individualized treatment regimes (ITRs) from high-dimensional covariates.
method Directly targets the contrast between potential outcomes, using dimension-reduced outcome-weighted learning.
result Achieves universal consistency, converging to the Bayes risk under mild conditions.
Contrastive learning adapts to data intrinsic dimensions, learning low-dimensional representations.
problem Learning high-dimensional representations from multi-modal data.
method Multi-modal contrastive learning with temperature optimization.
result Contrastive learning adapts to intrinsic dimensions of data, not specified dimensions.
Consensus dimension reduction combines multiple visualizations to identify shared patterns.
problem Conflicting visualizations from different dimension reduction methods.
method Multi-view learning to identify stable patterns across multiple views.
result Consensus visualization effectively identifies shared low-dimensional data structure.
Unified neural network for linear and nonlinear dimension reduction.
problem Efficiently perform linear and nonlinear sufficient dimension reduction.
method Belted and Ensembled Neural Network (BENN) framework.
result Unified framework for both linear and nonlinear dimension reduction.
RC flow learns molecular kinetics in low dimensions.
problem Discovering interpretable low-dimensional models of molecular kinetics.
method Normalizing flow for coordinate transformation and Brownian dynamics for kinetics approximation.
result Tractable and trainable model of reduced kinetics in continuous time and space.
This paper classifies instantons with closed reductions and provides examples of non-closed reductions.
problem Understanding the geometry of toric Kähler instantons with and without closed reductions.
method Sharp geometric criteria and examples of instantons with different reduction types.
result Established geometric criteria for closed reductions and classified asymptotic geometries.
The study connects Hilbert entropy to non-differentiability points of limit sets in flag spaces.
problem Understanding non-differentiability points in limit sets of convex projective structures.
method Introduces hyperplane conicality for θ-Anosov representations and uses it to prove properties of boundary maps. result Hilbert entropy is linked to the Hausdorff dimension of non-differentiability points in flag spaces.
POTD estimates SDR subspace using optimal transport for binary response.
problem Insufficient performance of existing SDR methods for categorical responses.
method Principal optimal transport direction (POTD) using optimal transport coupling.
result POTD exclusively estimates SDR subspace for error-free class labels.
We consider dimension reduction for solutions of the Kähler-Ricci flow with nonegative bisectional curvature. When the complex dimension n=2, we prove an optimal dimension reduction theorem for complete translating Kähler-Ricci solitons with nonnegative bisectional curvature. We also prove a general dimension reducti…
With the development of multimedia era, multi-view data is generated in various fields. Contrast with those single-view data, multi-view data brings more useful information and should be carefully excavated. Therefore, it is essential to fully exploit the complementary information embedded in multiple views to enhance …
NCVis speeds up data visualization for large datasets.
problem Performance issues in t-SNE for large datasets.
method Noise contrastive estimation for scalable visualization.
result NCVis outperforms state-of-the-art techniques in speed and quality.
Enhances SDR via Hellinger correlation for better data dependency understanding.
problem Improving sufficient dimension reduction in single-index models.
method Developed a new method using Hellinger correlation for detecting the dimension reduction subspace.
result Significantly enhances and outperforms existing SDR methods through deeper data dependency understanding.
Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to the data. This dimension reduction procedure succeeds when it preserves certain …
Non-split almost complex supermanifolds and non-split Riemannian supermanifolds are studied. The first obstacle for a splitting is parametrized by group orbits on an infinite dimensional vector space. Further it is shown that non-split structures appear in the first case as deformations of a split reduction and in the …
PSMM method optimizes matrix sufficient dimension reduction.
problem Feature matrices with row- and column-wise interpretations require efficient dimension reduction.
method PSMM method converts matrix problem into classification problems using rank-1 normal matrix.
result PSMM outperforms existing methods and provides strong interpretability.
New methods improve feature extraction and representation quality in supervised and unsupervised DR.
problem Statistical dependence, data diversity, contrast, and interpretability in conventional DR methods.
method Combines linear and nonlinear formulations for three new independence criteria.
result Significant improvements in contrast, accuracy, and interpretability over baselines.
Scalability of statistical estimators is of increasing importance in modern applications and dimension reduction is often used to extract relevant information from data. A variety of popular dimension reduction approaches can be framed as symmetric generalized eigendecomposition problems. In this paper we outline how t…
A new method reduces speckles in high contrast imaging.
problem Over-subtraction from speckles and self-subtraction in data reduction.
method Data Imputation concept using Karhunen-Loève transform (DIKL).
result DIKL achieves high-quality results with significantly reduced computational cost.
Survey of SDR methods for high-dimensional regression and embedding.
problem Reducing dimensionality in high-dimensional data.
method Involves both statistical and machine learning approaches, covering inverse and forward regression methods.
result Supervised Kernel Dimension Reduction is equivalent to supervised PCA.
Gaussian Process Latent Variable Model (GPLVM) is a flexible framework to handle uncertain inputs in Gaussian Processes (GPs) and incorporate GPs as components of larger graphical models. Nonetheless, the standard GPLVM variational inference approach is tractable only for a narrow family of kernel functions. The most p…
New neural network method simplifies high-dimensional data.
problem Scalability issues in nonlinear sufficient dimension reduction.
method Stochastic neural network with adaptive gradient algorithm.
result Proposed method outperforms existing methods on large-scale data.
A method, due to Élie Cartan, is used to give an algebraic classification of the non-reductive homogeneous pseudo-Riemannian manifolds of dimension four. Only one case with Lorentz signature can be Einstein without having constant curvature, and two cases with (2,2) signature are Einstein of which one is Ricci-flat. If…
The study reveals how synaptic correlations promote dimension reduction in neural networks.
problem Understanding how synaptic correlations affect neural correlations and dimension reduction in deep neural networks.
method A simplified model of dimension reduction considering pairwise correlations among synapses, using mathematical self-consistency for both binary and continuous synapses.
result Weakly-correlated synapses encourage dimension reduction compared to orthogonal synapses, and they also slow down the decorrelation process.
This paper reviews and compares supervised linear dimension-reduction techniques.
problem Lack of information in the response during unsupervised PCA reduces predictive performance.
method Review and comparison of supervised linear dimension-reduction techniques.
result PLS and LSPCA consistently outperform other techniques in simulations.
This paper addresses overfitting in dimension reduction methods by calibrating hyperparameters considering noise.
problem Overfitting in dimension reduction methods, especially t-SNE and UMAP, when data contains noise.
method Present a framework to calibrate hyperparameters in the presence of noise for t-SNE and UMAP.
result Recommended hyperparameter values for t-SNE and UMAP are too small and overfit the noise.
In statistical learning, high covariate dimensionality poses challenges for robust prediction and inference. To address this challenge, supervised dimension reduction is often performed, where dependence on the outcome is maximized for a selected covariate subspace with smaller dimensionality. Prevalent dimension reduc…
We consider an enlarged dimension reduction space in functional inverse regression. Our operator and functional analysis based approach facilitates a compact and rigorous formulation of the functional inverse regression problem. It also enables us to expand the possible space where the dimension reduction functions bel…
In the covariate shift learning scenario, the training and test covariate distributions differ, so that a predictor's average loss over the training and test distributions also differ. In this work, we explore the potential of extreme dimension reduction, i.e. to very low dimensions, in improving the performance of imp…
Theory of symplectic reduction in infinite dimensions developed.
problem Challenges in symplectic reduction in infinite dimensions.
method Normal form of momentum map for infinite-dimensional equivariant maps.
result Theory of singular symplectic reduction in infinite dimensions.
Paper uses non-linear dimension reduction for better economic forecasting.
problem Analyzing economic effects of shocks in large datasets.
method Non-linear dimension reduction in factor-augmented vector autoregressions.
result Non-linear dimension reduction techniques improve forecasting, especially in volatile data.
Study extends Kobayashi's method to non-reductive subgroups for homogeneous spaces.
problem Existence of compact Clifford-Klein forms in homogeneous spaces.
method Extend Kobayashi's method to non-reductive subgroups and compare Cartan projections and non-compact dimensions.
result Examples of homogeneous spaces without compact Clifford-Klein forms.
Paper tackles exposure bias in recommender systems using contrastive learning.
problem Exposure bias in large-scale recommender systems.
method Contrastive learning to reduce exposure bias via inverse propensity weighting.
result Contrastive learning effectively reduces exposure bias in recommender systems.
New algorithm balances spatial data approximation and prediction accuracy.
problem Lack of methods considering spatial correlation and downstream modeling in dimension reduction.
method Formalizes approximation and modeling utility as metrics, proposes a balanced algorithm.
result Optimal trade-off between approximation accuracy and downstream modeling utility.
In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential geometry tools such as moving frame and parallel transportation are successfully…
Paper compares dimension reduction methods using topological analysis on EEG data.
problem Comparing dimension reduction methods on EEG data.
method Topological data analysis, including persistent homology, Wasserstein distance, and hypothesis tests.
result Different dimension reduction methods show significant qualitative differences across topological homologies.
The study proves a rigidity theorem for compact manifolds with boundary.
problem Rigidity of compact manifolds with boundary in low dimensions.
method Dimension reduction argument for mean curvature, extending Schoen-Yau's for scalar curvature.
result Sharp spherical radius rigidity and best NNSC fill-in in terms of mean curvature.
Early stopping improves sample quality in latent diffusion models.
problem Latent diffusion models degrade sample quality with conventional early stopping.
method Analyzed the interaction between latent dimension and stopping time under Gaussian framework.
result Lower-dimensional representations benefit from earlier termination, higher-dimensional spaces require later stopping.
We discuss Poincaré duality complexes X and the question whether or not their Spivak normal fibration admits a reduction to a vector bundle in the case where the dimension of X is at most 4. We show that in dimensions less than 4 such a reduction always exists, and in dimension 4 such a reduction exists provided X is o…
Two methods preserve tensor structure for reduced dimensionality in tensor regression.
problem Reducing dimensionality of tensor predictors for improved interpretation and accuracy.
method Developed two tensor dimension reduction methods using Tucker and CP decompositions.
result Substantial improvement in accuracy over existing methods in simulations and applications.