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Related Concept Videos

Random Sampling Method01:09

Random Sampling Method

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Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. Data are the result of sampling from a population. The sampling method ensures that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest. Among the various sampling methods used by...
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The randomization process involves assigning study participants randomly to experimental or control groups based on their probability of being equally assigned. Randomization is meant to eliminate selection bias and balance known and unknown confounding factors so that the control group is similar to the treatment group as much as possible. A computer program and a random number generator can be used to assign participants to groups in a way that minimizes bias.
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Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
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A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.
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Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data
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Randomized sketches for kernel CCA.

Heng Lian1, Fode Zhang2, Wenqi Lu3

  • 1Department of Mathematics, City University of Hong Kong, Hong Kong; City University of Hong Kong Shenzhen Research Institute, Shenzhen, China.

Neural Networks : the Official Journal of the International Neural Network Society
|April 21, 2020
PubMed
Summary
This summary is machine-generated.

Kernel canonical correlation analysis (KCCA) is computationally expensive. This study introduces a randomized sketches method to significantly reduce KCCA

Keywords:
Canonical correlation analysisCovariance/cross-covariance operatorKernel methodRandom projection

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Area of Science:

  • Machine Learning
  • Statistical Analysis
  • Dimensionality Reduction

Background:

  • Kernel canonical correlation analysis (KCCA) is a powerful nonlinear extension of canonical correlation analysis.
  • Existing KCCA methods face computational challenges due to O(n^3) time complexity, limiting scalability for large datasets.

Purpose of the Study:

  • To develop a computationally efficient approach for KCCA.
  • To address the scalability issues of KCCA for large-scale data analysis.

Main Methods:

  • A novel m-dimensional randomized sketches approach is proposed for KCCA, where m << n.
  • The method leverages recent advancements in randomized sketches for kernel ridge regression (KRR).
  • A "duality tracking" technique is employed, connecting KCCA and KRR through operator-theory and kernel-matrix views.

Main Results:

  • The proposed randomized sketches method significantly reduces the time complexity of KCCA.
  • Theoretical guarantees for consistency and optimal convergence rates are established for the new approach.

Conclusions:

  • The randomized sketches approach offers a scalable and efficient alternative to traditional KCCA.
  • This work bridges KCCA and KRR, providing new theoretical insights and practical computational advantages.