# IntervalRegressionInternal: IntervalRegressionInternal In penaltyLearning: Penalty Learning

## Description

Solve the squared hinge loss interval regression problem for one `regularization` parameter: w* = argmin_w L(w) + `regularization` * ||w||_1 where L(w) is the average squared hinge loss with respect to the `targets`, and ||w||_1 is the L1-norm of the weight vector (excluding the first element, which is the un-regularized intercept or bias term). This function performs no scaling of input `features`, and is meant for internal use only! To learn a regression model, try `IntervalRegressionCV` or `IntervalRegressionUnregularized`.

## Usage

 ```1 2 3 4 5 6 7 8``` ```IntervalRegressionInternal(features, targets, initial.param.vec, regularization, threshold = 0.001, max.iterations = 1000, weight.vec = NULL, Lipschitz = NULL, verbose = 2, margin = 1, biggest.crit = 100) ```

## Arguments

 `features` Scaled numeric feature matrix (problems x `features`). The first column/feature should be all ones and will not be regularized. `targets` Numeric target matrix (problems x 2). `initial.param.vec` initial guess for weight vector (`features`). `regularization` Degree of L1-regularization. `threshold` When the stopping criterion gets below this `threshold`, the algorithm stops and declares the solution as optimal. `max.iterations` If the algorithm has not found an optimal solution after this many iterations, increase `Lipschitz` constant and `max.iterations`. `weight.vec` A numeric vector of weights for each training example. `Lipschitz` A numeric scalar or NULL, which means to compute `Lipschitz` as the mean of the squared L2-norms of the rows of the feature matrix. `verbose` Cat messages: for restarts and at the end if >= 1, and for every iteration if >= 2. `margin` Margin size hyper-parameter, default 1. `biggest.crit` Restart FISTA with a bigger `Lipschitz` (smaller step size) if crit gets larger than this.

## Value

Numeric vector of scaled weights w of the affine function f_w(X) = X %*% w for a scaled feature matrix X with the first row entirely ones.

## Author(s)

Toby Dylan Hocking

penaltyLearning documentation built on July 1, 2020, 10:26 p.m.