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Support Vector Regression Support vector regression (SVR) is a method for regression analogous to the support vector classifier. Let $(x_i, y_i) in mathbb{R}^d imes mathbb{R}$, $i = 1, dots, n$ be training data for a regression problem. In the case of linear regression, SVR solves egin{align} min_{mathbf{w}, b, xi^+, xi^-} & frac{1}{2} ||mathbf{w}||^2 + frac{C}{n} sum_{i=1}^n (xi_i^+ + xi_i^-) \ ext{s.t.} & y_i - mathbf{w}^T mathbf{x}_i - b le epsilon + xi_i^+ quad forall i \ & mathbf{w}^T mathbf{x}_i + b - y_i le epsilon + xi_i^- quad forall i \ & xi_i^+ ge 0 quad forall i \ & xi_i^- ge 0 quad forall i end{align} where $mathbf{w} in mathbb{R}^d$, $b in mathbb{R}$, $xi^+ = (xi_1^+, dots, xi_n^+)^T$, and $xi^- = (xi_1^-, dots, xi_n^-)^T$. Here $epsilon$ is fixed.

          Support Vector Regression Support vector regression (SVR) is a method for regression analogous to the support vector classifier. Let $(x_i, y_i) in mathbb{R}^d 	imes mathbb{R}$, $i = 1, dots, n$ be training data for a regression problem. In the case of linear regression, SVR solves
egin{align*} min_{mathbf{w}, b, xi^+, xi^-} & frac{1}{2} ||mathbf{w}||^2 + frac{C}{n} sum_{i=1}^n (xi_i^+ + xi_i^-) \ 	ext{s.t.} & y_i - mathbf{w}^T mathbf{x}_i - b le epsilon + xi_i^+ quad forall i \ & mathbf{w}^T mathbf{x}_i + b - y_i le epsilon + xi_i^- quad forall i \ & xi_i^+ ge 0 quad forall i \ & xi_i^- ge 0 quad forall i end{align*} where $mathbf{w} in mathbb{R}^d$, $b in mathbb{R}$, $xi^+ = (xi_1^+, dots, xi_n^+)^T$, and $xi^- = (xi_1^-, dots, xi_n^-)^T$. Here $epsilon$ is fixed.

$Support Vector Regression Support vector regression (SVR) is a method for regression analogous to the support vector classifier. Let (xi, yi) in mathbbR^d imes mathbbR, i = 1, dots, n be training data for a regression problem. In the case of linear regression, SVR solves eginalign* minmathbfw, b, xi^+, xi^- frac12 ||mathbfw||^2 + fracCn sumi=1^n (xii^+ + xii^-) exts.t. yi - mathbfw^T mathbfxi - b le epsilon + xii^+ quad forall i mathbfw^T mathbfxi + b - yi le epsilon + xii^- quad forall i xii^+ ge 0 quad forall i xii^- ge 0 quad forall i endalign* where mathbfw in mathbbR^d, b in mathbbR, xi^+ = (xi1^+, dots, xin^+)^T, and xi^- = (xi1^-, dots, xin^-)^T. Here epsilon is fixed.$

Added by Hunter J.

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