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Related Concept Videos

Regression Toward the Mean01:52

Regression Toward the Mean

Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when researchers try to extrapolate results...
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...
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...
Calibration Curves: Linear Least Squares01:20

Calibration Curves: Linear Least Squares

A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
For data that follow a straight line, the standard method for fitting is the linear...
Linearization and Approximation01:26

Linearization and Approximation

Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
Application of Linearization and Approximation01:29

Application of Linearization and Approximation

A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...

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Related Experiment Videos

Transfer Learning for Moderate-Dimensional Ridge-Regularized Robust Linear Regression.

Lingfeng Lyu1, Xiao Guo1, Zongqi Liu1

  • 1Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei 230026, China.

Entropy (Basel, Switzerland)
|May 26, 2026
PubMed
Summary
This summary is machine-generated.

Transfer learning for robust linear regression improves accuracy by combining source and target data. An adaptive method prevents performance degradation when source data is uninformative, ensuring reliable results.

Keywords:
moderate dimensionnon-sparserobust regressiontransfer learning

Related Experiment Videos

Area of Science:

  • Statistics
  • Machine Learning
  • Data Science

Background:

  • Robust linear regression is essential for handling outliers in data.
  • Ridge regularization is commonly used in high-dimensional settings.
  • Transfer learning offers potential for improving model performance by leveraging external data.

Purpose of the Study:

  • To develop a transfer learning method for ridge-regularized robust linear regression.
  • To analyze the performance of the proposed method in the moderate-dimensional regime.
  • To investigate strategies for mitigating negative transfer.

Main Methods:

  • Proposed Trans-RR method combining source and target robust ridge estimators.
  • Asymptotic analysis of estimation error under mild assumptions.
  • Adaptive aggregation of Trans-RR with single-task estimator using cross-validation.

Main Results:

  • Transfer learning significantly improves estimation accuracy compared to single-study methods.
  • The proposed adaptive method effectively guards against negative transfer.
  • Demonstrated transition between positive and negative transfer based on data discrepancy.

Conclusions:

  • Trans-RR provides a robust and accurate approach for linear regression using transfer learning.
  • Adaptive aggregation ensures reliable performance even with dissimilar source data.
  • The findings have implications for various fields utilizing robust regression techniques.