Two novel methods estimate multiple FDR directions for binary categorical responses.
problem Estimating multiple FDR directions for categorical responses.
method Information maximization and square loss mutual information.
result Statistical consistency of the proposed methods established.
Paper introduces a nonparametric functional graphical model for random functions.
problem Estimating probabilistic conditional independence in functional graphical models.
method Functional sufficient dimension reduction to relax Gaussian or copula Gaussian assumptions.
result Enhances estimation accuracy and retains probabilistic conditional independence.
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.
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.
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.
Sufficient dimension reduction (SDR) using distance covariance (DCOV) was recently proposed as an approach to dimension-reduction problems. Compared with other SDR methods, it is model-free without estimating link function and does not require any particular distributions on predictors (see Sheng and Yin, 2013, 2016). …
We consider forecasting a single time series using a large number of predictors in the presence of a possible nonlinear forecast function. Assuming that the predictors affect the response through the latent factors, we propose to first conduct factor analysis and then apply sufficient dimension reduction on the estimat…
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.
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.
R package psvmSDR simplifies SDR computation for machine learning.
problem Sufficient dimension reduction in machine learning.
method Principal machine (PM) generalized from PSVM.
result Efficient computation of SDR estimators in various scenarios.
Paper improves SDR estimation speed and conditions.
problem Improving sufficient dimension reduction for multi-index models.
method Estimating expected smoothed gradient outer product.
result Achieves fast parametric convergence rate of Cd⋅n−1/2. 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.
Proposes a deep learning method for effective data representation.
problem Constructing effective data representations for prediction.
method A deep dimension reduction approach to learning representations with sufficiency, low dimensionality, and disentanglement.
result The proposed deep nonparametric representation is consistent and performs better than existing methods.
This paper reviews SDR methods for multivariate response regression.
problem Handling sufficient dimension reduction for multivariate response regression.
method Characterizes SDR estimators as inverse or forward regression methods.
result Pooled marginal, projective resampling, distance-based, ordinary least squares, partial least squares, and semiparametric SDR estimators are discussed.
Improves MARS for nonparametric multivariate regression with dimension reduction.
problem High number of basis functions in MARS for high-order interactions.
method Linear combinations of covariates for dimension reduction, facilitating gradient calculation and eigen-analysis for estimation.
result Asymptotic theory and numerical studies show improved performance over MARS.
The purpose of sufficient dimension reduction (SDR) is to find the low-dimensional subspace of input features that is sufficient for predicting output values. In this paper, we propose a novel distribution-free SDR method called sufficient component analysis (SCA), which is computationally more efficient than existing …
The principal support vector machines method (Li et al., 2011) is a powerful tool for sufficient dimension reduction that replaces original predictors with their low-dimensional linear combinations without loss of information. However, the computational burden of the principal support vector machines method constrains …
GenSDR tackles SDR by leveraging generative models to fully recover lower-dimensional structures.
problem Challenges in identifying low-dimensional sufficient structures in nonlinear SDR.
method Proposes GenSDR, a method that uses modern generative models to fully recover information in the central σ-field.
result Establishes consistency of GenSDR estimator for sample-level data and extends its applicability to non-Euclidean responses.
New method for reducing dimensions of distributional data.
problem Nonlinear sufficient dimension reduction for distribution-on-distribution regression.
method Building universal kernels on metric spaces to characterize conditional independence.
result Method outperforms competing methods in synthetic and real data applications.
MSRL learns a representation maximizing mutual info with response variables.
problem Learning sufficient representations for complex, multi-dimensional data.
method Variational mutual information, deep neural networks, generalized Dudley's inequality.
result MSRL achieves consistent and accurate representation learning.
FlowSDR learns a low-dimensional projection preserving the response's conditional distribution.
problem Learning a low-dimensional projection that captures the response's conditional distribution.
method FlowSDR uses conditional log-likelihood maximization with monotone rational-quadratic spline flows to learn the projection and conditional density.
result FlowSDR outperforms existing SDR methods in various simulation settings and a face-age prediction task.
Modified relative universality for unbiasedness and consistency in dimension reduction.
problem Gap in proof of unbiasedness and Fisher consistency in relative universality.
method Modified definition of relative universality using ǫ-measurability.
result Established unbiasedness and Fisher consistency rigorously.
A new dimension reduction method based on Gaussian finite mixtures is proposed as an extension to sliced inverse regression (SIR). The model-based SIR (MSIR) approach allows the main limitation of SIR to be overcome, i.e., failure in the presence of regression symmetric relationships, without the need to impose further…
Reduces IB problem to a simpler, lower-dimensional problem.
problem Information bottleneck problem in high-dimensional spaces.
method Identifies sufficient statistic that factors conditional distribution, reducing IB to a lower-dimensional problem.
result Preserves full IB curve and optimal representations, making IB tractable.
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.
Neural networks simplify SDR in regression tasks.
problem Sufficient dimension reduction in regression problems.
method Applying neural networks with rank regularization to estimate the central mean subspace.
result Neural networks effectively perform SDR, consistent with theoretical estimations.
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.
SMAVE optimizes SDR by projecting onto a low-dimensional subspace on a Riemannian manifold.
problem High-dimensional regression challenges due to the curse of dimensionality.
method SMAVE combines nearest-neighbor localization and Riemannian stochastic gradient ascent.
result SMAVE achieves almost-sure convergence and matches RMAVE's synthetic subspace recovery rate.
A method for reducing dimensions in Fréchet regression models.
problem Complex data objects in metric space-valued responses.
method Mapping metric-space valued random objects to real-valued variables and applying classical SDR.
result Consistent and asymptotically convergent method for Fréchet SDR.
Motivated by the idea of turbomachinery active subspace performance maps, this paper studies dimension reduction in turbomachinery 3D CFD simulations. First, we show that these subspaces exist across different blades---under the same parametrization---largely independent of their Mach number or Reynolds number. This is…
Unified framework for fair representation learning in machine learning.
problem Ensuring fairness in machine learning models, especially when biased data representations lead to unfair predictions.
method Integrates nonlinear sufficient dimension reduction with deep learning to construct fair and informative representations, introducing a penalty term to enforce conditional independence between sensitive attributes and learned representations.
result Achieves a superior balance between fairness and utility, significantly outperforming state-of-the-art baselines on various data structures.
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…
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.
A novel approach combines interpretability and performance in machine learning models.
problem Lack of transparency in black box machine learning models.
method Semiparametric approach using ideas from sufficient dimension reduction and influence function based estimators.
result Optimized model combining interpretability and performance, demonstrated through simulations and a real-world ICU patient data application.
The application of standard sufficient dimension reduction methods for reducing the dimension space of predictors without losing regression information requires inverting the covariance matrix of the predictors. This has posed a number of challenges especially when analyzing high-dimensional data sets in which the numb…
A new geometry-preserving method for interpreting compositional data.
problem Statistical challenges in high-dimensional compositional data.
method Geometry-preserving framework for dimension reduction of compositional data.
result Identification of a central compositional subspace for compositional predictors.
We reformulate unsupervised dimension reduction problem (UDR) in the language of tempered distributions, i.e. as a problem of approximating an empirical probability density function by another tempered distribution, supported in a k-dimensional subspace. We show that this task is connected with another classical prob…
A theory of sufficient dimension reduction (SDR) is developed from an optimizational perspective. In our formulation of the problem, instead of dealing with raw data, we assume that our ground truth includes a mapping f:Rn→Rm and a probability distribution function p over…
The abstract discusses conditions for hyperkähler manifolds and Kähler reduction.
problem Conditions for hyperkähler manifolds and Kähler reduction methods.
method Explicit proof and two-stage Kähler reduction process.
result Explicit proof of necessary and sufficient condition for hyperkähler manifolds.
The paper simplifies conditions for optimal paths on manifolds avoiding obstacles.
problem Finding optimal paths on manifolds avoiding obstacles.
method Study of sufficient conditions for optimality on Riemannian manifolds and Lie groups.
result New conditions for optimality are provided in terms of matrix invertibility.
FSIR extends SIR for federated learning with privacy and efficiency.
problem Privacy-preserving dimension reduction in federated learning.
method FSIR employs sliced inverse regression with differential privacy and collaborative variable screening.
result FSIR achieves effective dimension reduction and privacy protection in federated learning.
New method estimates Gaussian vector functions more efficiently.
problem Estimating functions of Gaussian vectors with high dimensions.
method Combines randomized dimension reduction and PCA.
result Algorithm outperforms Monte Carlo method by a factor of d.
The paper proposes differentially private sliced inverse regression algorithms for high-dimensional data.
problem Privacy concerns in high-dimensional data analysis.
method Differentially private sliced inverse regression algorithms designed for privacy preservation.
result Achieves minimax lower bounds up to logarithmic factors.
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.
A new deep neural network tackles nonlinear functional regression with improved dimensionality reduction.
problem Nonlinear functional regression in infinite-dimensional functional data analysis.
method Functional deep neural network with adaptive kernel embedding and projection steps.
result Explicit rates of approximating nonlinear smooth functionals are derived, and the network is shown to be effective in both simulated and real datasets.
New algorithm reduces dimensionality in federated learning.
problem Estimating central dimension reduction subspace and variable selection in federated learning.
method Federated sparse sliced inverse regression, convex optimization, linearized alternating direction method of multipliers.
result Upper bound of statistical error rate established under heterogeneous setting.
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…
New methods for functional data analysis improve manifold methods for continuous data.
problem Challenges in evaluating embeddings for functional data.
method Transfer manifold methods from tabular and image data to functional data, define a theoretical framework, and propose nuanced evaluation strategies.
result Manifold methods can be successfully applied to functional data, but careful evaluation is needed.