Linear Regression¶
Linear regression is a method to model the connection between a dependent variable, which can be a vector, and one or more explanatory variables. This is done by fitting the linear equations to the observed data.
Operation |
Computational methods |
Programming Interface |
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Mathematical Formulation¶
Training¶
Given a \((x_{11}, \ldots, x_{1p}, y_1, \ldots, x_{n1}, \ldots, x_{np}, y_n)\) set of training data, \(n \gg p\). The \(X\) matrix of the \(n \times p\) size contains \(x_{ij}\), \(i=1, \ldots, n\), \(j = 1, \ldots, p\) observations of independent variables.
To estimate the coefficients \((\beta_{0j}, \ldots, \beta_{pj})\), you can use the Normal Equation method.
Partial Training¶
Given a \((x_{11}, \ldots, x_{1p}, y_1, \ldots, x_{n1}, \ldots, x_{np}, y_n)\) block of training data, \(n \gg p\). The \(X\) matrix of \(n \times p\) size contains \(x_{ij}\), \(i=1, \ldots, n\), \(j = 1, \ldots, p\) observations of independent variables.
To compute a cross product of Linear Regression, you can use the Normal Equation method.
Finalize Training¶
Given a partial result with partial products.
To compute a cross product of Linear Regression, you can use the Normal Equation method.
Inference¶
The linear regression-based prediction is made for the input vector using the \(y_j = \beta_{0j} + \beta_{1j}x_1 + \ldots + \beta_{pj}x_p\) equation for each \(j=1, \ldots, k\).
Computation Method: norm_eq¶
The method computes means, variance-covariance, or correlation matrix for the dense data. This is the default and the only supported method.
Programming Interface¶
Refer to API Reference: Linear Regression.
Online mode¶
The algorithm supports online mode.
Distributed mode¶
The algorithm supports distributed execution in SPMD mode (only on GPU).