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Related Concept Videos

Regression Analysis01:11

Regression Analysis

Regression analysis is a statistical tool that describes a mathematical relationship between a dependent variable and one or more independent variables.
In regression analysis, a regression equation is determined based on the line of best fit– a line that best fits the data points plotted in a graph. This line is also called the regression line. The algebraic equation for the regression line is called the regression equation. It is represented as:
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...
Survival Tree01:19

Survival Tree

Survival trees are a non-parametric method used in survival analysis to model the relationship between a set of covariates and the time until an event of interest occurs, often referred to as the "time-to-event" or "survival time." This method is particularly useful when dealing with censored data, where the event has not occurred for some individuals by the end of the study period, or when the exact time of the event is unknown.
 Building a Survival Tree
Constructing a survival tree begins...
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...
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...
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...

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Related Experiment Videos

Efficient Decision Trees for Tensor Regressions.

Hengrui Luo1,2, Akira Horiguchi3, Li Ma4

  • 1Department of Statistics, Rice University.

Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
|May 11, 2026
PubMed
Summary
This summary is machine-generated.

We introduce the tensor-input tree (TT) method for regression with tensor data. This novel approach efficiently handles scalar-on-tensor and tensor-on-tensor problems, offering a competitive alternative to existing models.

Keywords:
Decision tree regressionsensemble methodsscalar-on-tensor regressionstensor-on-tensor regressions

Related Experiment Videos

Area of Science:

  • Statistics
  • Machine Learning
  • Data Science

Background:

  • Tensor data, represented as multi-way arrays, presents unique challenges in statistical modeling.
  • Existing methods for regression with tensor inputs can be computationally intensive.
  • There is a need for efficient and robust methods to analyze scalar-on-tensor and tensor-on-tensor relationships.

Purpose of the Study:

  • To propose the tensor-input tree (TT) method for scalar-on-tensor regression.
  • To extend the TT method for tensor-on-tensor regression problems.
  • To provide efficient algorithms and demonstrate the performance of TT on various datasets.

Main Methods:

  • Development of scalar-output regression tree models with tensor inputs.
  • Implementation of fast randomized and deterministic algorithms for fitting scalar-on-tensor trees.
  • Extension to tensor-on-tensor regression using additive tree ensemble techniques.

Main Results:

  • The TT method demonstrates competitive performance against established tensor-input Gaussian process models.
  • The method shows robustness to entrywise input tensor noise.
  • Extensive experiments on synthetic and real datasets validate the efficacy of TT.

Conclusions:

  • The tensor-input tree (TT) method offers an efficient and effective approach for scalar-on-tensor and tensor-on-tensor regression.
  • TT provides a valuable tool for analyzing complex, multi-way array data.
  • The open-source implementation facilitates broader adoption and further research.