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Related Concept Videos

Correlation and Regression00:53

Correlation and Regression

In statistics, correlation describes the degree of association between two variables. In the subfield of linear regression, correlation is mathematically expressed by the correlation coefficient, which describes the strength and direction of the relationship between two variables. The coefficient is symbolically represented by 'r' and ranges from -1 to +1. A positive value indicates a positive correlation where the two variables move in the same direction. A negative value suggests a negative...
Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
Multiple Regression01:25

Multiple Regression

Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables. It has many practical applications.
Farmers can use multiple regression to determine the crop yield based on more than one factor, such as water availability, fertilizer, soil properties, etc. Here, the crop yield is the response or dependent variable as it depends on the other independent variables. The analysis requires the construction of a scatter plot...
Coefficient of Correlation01:12

Coefficient of Correlation

The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y.
If you suspect a linear relationship between x and y, then r can measure how strong the linear relationship is.
What the VALUE of r tells us:
The value of r is always between –1 and +1: –1 ≤ r ≤ 1.
The size of the correlation r indicates the strength of the linear...

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CorrelationCalculator and Filigree: Tools for Data-Driven Network Analysis of Metabolomics Data
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CorrelationCalculator and Filigree: Tools for Data-Driven Network Analysis of Metabolomics Data

Published on: November 10, 2023

Partial Correlation Estimation by Joint Sparse Regression Models.

Jie Peng1, Pei Wang, Nengfeng Zhou

  • 1Department of Statistics, University of California, Davis, CA 95616.

Journal of the American Statistical Association
|November 3, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces Sparse Partial Correlation Estimation (space), an efficient method for identifying gene networks in high-dimensional data. The approach accurately selects partial correlations and identifies key genes, outperforming existing methods.

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Area of Science:

  • Computational Biology
  • Statistical Genetics
  • Bioinformatics

Background:

  • High-dimensional data, common in genomics, presents challenges for statistical analysis.
  • Identifying gene regulatory networks is crucial for understanding biological processes.

Purpose of the Study:

  • To develop a computationally efficient method for selecting non-zero partial correlations.
  • To identify hub genes in gene regulatory networks using a sparse approach.

Main Methods:

  • Proposed Sparse Partial Correlation Estimation (space) method.
  • Utilized sparse regression techniques for model fitting.
  • Assumed overall sparsity of the partial correlation matrix.

Main Results:

  • space demonstrated strong performance in selecting non-zero partial correlations.
  • The method successfully identified hub variables and outperformed two existing methods.
  • Application to microarray breast cancer data identified significant hub genes.

Conclusions:

  • space is an effective and computationally efficient tool for network inference in high-dimensional settings.
  • The identified hub genes offer potential insights into breast cancer genetic regulatory networks.
  • The proposed method is asymptotically consistent for model selection and parameter estimation.