Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Problem Solving: Dimensional Analysis

Problem Solving: Dimensional Analysis

Every mathematical equation that connects separate distinct physical quantities must be dimensionally consistent, which implies it must abide by two rules. For this reason, the concept of dimension is crucial. The first rule is that an equation's expressions on either side of an equality must have the exact same dimension, i.e., quantities of the same dimension can be added or removed. The second rule stipulates that all popular mathematical functions, such as exponential, logarithmic, and...

Dimensional Analysis

Dimensional Analysis

Dimensional analysis, also known as the factor label method, is a versatile approach for mathematical operations. The main principle behind this approach is: the units of quantities must be subjected to the same mathematical operations as their associated numbers. This method can be applied to computations ranging from simple unit conversions to more complex and multi-step calculations involving several different quantities and their units.
Conversion Factors and Dimensional Analysis
The unit...

Extraction: Partition and Distribution Coefficients

Extraction: Partition and Distribution Coefficients

The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
For extracting a solute from an aqueous phase into an...

Linear Approximation in Frequency Domain

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....

Downsampling

Downsampling

When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...

Reducing Line Loss

Reducing Line Loss

In a three-phase circuit, line loss is an indicator of energy dissipated as heat due to the resistance of transmission lines. To address this, incorporating transformers into the system—a step-up transformer at the source and a step-down transformer at the load—is a strategic solution. Two three-phase transformers are introduced to improve this.
With a step-up transformer at the source, the voltage is increased, thereby reducing the current in the transmission lines since power loss...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

A Non-Canonical Core Transcriptional Regulatory Circuit Orchestrates Chromatin Reprogramming to Drive Osimertinib Resistance in Non-Small Cell Lung Cancer.

Advanced science (Weinheim, Baden-Wurttemberg, Germany)·2026

Same author

Super-enhancer-driven TCF4 orchestrates neuroblastoma metastasis by sphingolipid-dependent membrane remodeling and ITGB1-FAK activation.

Neuro-oncology·2026

Same author

Chemoenzymatic Synthesis of Glycopeptide Library Decodes Sialylation-Dependent Immunodominance to Enable a Potent Multicomponent Antitumor Vaccine.

Angewandte Chemie (International ed. in English)·2026

Same author

Theoretical Guarantees for Sparse Principal Component Analysis based on the Elastic Net.

IEEE transactions on information theory·2025

Same author

A LATENT VARIABLE MIXTURE MODEL FOR COMPOSITION-ON-COMPOSITION REGRESSION WITH APPLICATION TO CHEMICAL RECYCLING.

The annals of applied statistics·2025

Same author

NONLINEAR GLOBAL FRÉCHET REGRESSION FOR RANDOM OBJECTS VIA WEAK CONDITIONAL EXPECTATION.

Annals of statistics·2025

Same journal

A KL-divergence-based test for elliptical distribution.

Journal of nonparametric statistics·2026

Same journal

Soft Bayesian Additive Regression Trees (SBART) for correlated survey response with non-Gaussian error.

Journal of nonparametric statistics·2026

Same journal

A comparison of causal inference methods for evaluating multiple treatment groups.

Journal of nonparametric statistics·2025

Same journal

Regression analysis of multiplicative hazards model with time-dependent coefficient for sparse longitudinal covariates.

Journal of nonparametric statistics·2025

Same journal

TSSS: A Novel Triangulated Spherical Spline Smoothing for Surface-Based Data.

Journal of nonparametric statistics·2025

Same journal

Nonparametric Density Estimation for Data Scattered on Irregular Spatial Domains: A Likelihood-Based Approach Using Bivariate Penalized Spline Smoothing.

Journal of nonparametric statistics·2025

See all related articles

Search research articles

Related Experiment Video

Updated: Sep 11, 2025

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

Sparse kernel sufficient dimension reduction.

Bingyuan Liu¹, Lingzhou Xue¹

¹Department of Statistics, The Pennsylvania State University, University Park, PA, USA.

Journal of Nonparametric Statistics

|August 18, 2025

Summary

This summary is machine-generated.

We introduce sparse kernel sufficient dimension reduction (KSDR) for high-dimensional data analysis. Our method achieves statistical consistency and efficient estimation, with novel algorithms offering computational guarantees.

Keywords:

Sufficient dimension reduction alternating direction method of multipliers kernel dimension reduction nonconvex optimization

More Related Videos

Assisted Selection of Biomarkers by Linear Discriminant Analysis Effect Size LEfSe in Microbiome Data

Assisted Selection of Biomarkers by Linear Discriminant Analysis Effect Size LEfSe in Microbiome Data

Published on: May 16, 2022

Analysis of SEC-SAXS data via EFA deconvolution and Scatter

Analysis of SEC-SAXS data via EFA deconvolution and Scatter

Published on: January 28, 2021

Related Experiment Videos

Last Updated: Sep 11, 2025

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

Assisted Selection of Biomarkers by Linear Discriminant Analysis Effect Size LEfSe in Microbiome Data

Assisted Selection of Biomarkers by Linear Discriminant Analysis Effect Size LEfSe in Microbiome Data

Published on: May 16, 2022

Analysis of SEC-SAXS data via EFA deconvolution and Scatter

Analysis of SEC-SAXS data via EFA deconvolution and Scatter

Published on: January 28, 2021

Area of Science:

Statistics
Machine Learning
Data Science

Background:

High-dimensional data analysis presents challenges for traditional methods.
Sufficient Dimension Reduction (SDR) aims to find a low-dimensional subspace capturing essential information.
Incorporating sparsity enhances interpretability in SDR.

Purpose of the Study:

To develop a nonparametric sparse kernel sufficient dimension reduction (KSDR) method.
To extend existing sparse SDR techniques using reproducing kernel Hilbert spaces.
To establish theoretical guarantees for KSDR in high-dimensional settings.

Main Methods:

Utilizing reproducing kernel Hilbert spaces for nonparametric SDR.
Extending inverse moment-based sparse SDR methodology.
Developing novel nonconvex alternating directional method of multipliers (ADMM) algorithms for sparse SDR and KSDR.
Analyzing computational guarantees and iteration complexity of ADMMs.

Main Results:

Statistical consistency and efficient estimation of sparse KSDR are established under diverging high-dimensional settings.
New nonconvex ADMM algorithms are proposed for solving sparse SDR and KSDR.
Explicit iteration complexity bounds are derived for the proposed ADMMs.
Finite-sample properties are demonstrated through simulations and a real-world application.

Conclusions:

Sparse KSDR provides a powerful framework for high-dimensional data analysis.
The proposed ADMM algorithms offer efficient and theoretically guaranteed solutions.
The method shows promise for both theoretical and practical applications in data analysis.