APG_EN2

Applies accelerated proximal gradient algorithm to the l1-regularized quadratic program
$$f(\mathbf{x}) + g(\mathbf{x}) = \frac{1}{2}\mathbf{x}^TA\mathbf{x} - d^T\mathbf{x} + \lambda |\mathbf{x}|_1$$

internal

Implementation of sparse linear discriminant analysis, which is a supervised
classification method for multiple classes. Various novel optimization approaches to
this problem are implemented including alternating direction method of multipliers ('ADMM'),
proximal gradient (PG) and accelerated proximal gradient ('APG') (See Atkins 'et al'. <arXiv:1705.07194>).
Functions for performing cross validation are also supplied along with basic prediction
and plotting functions.
Sparse zero variance discriminant analysis ('SZVD') is also included in the package
(See Ames and Hong, <arXiv:1401.5492>). See the 'github' wiki for a more extended description.

Gudmundur Einarsson

accSDA

Accelerated Sparse Discriminant Analysis

Line Clemmensen

Brendan Ames

Summer Atkins

APG_EN2 function

<dl><dt>A</dt>
<dd>p by p positive definite coefficient matrix
$$A = (\gamma Om + X^T X/n)$$.</dd>
<dt>d</dt>
<dd>nx1 dimensional column vector.</dd>
<dt>lam</dt>
<dd>Regularization parameter for l1 penalty, must be greater than zero.</dd>
<dt>alpha</dt>
<dd>Step length.</dd>
<dt>maxits</dt>
<dd>Number of iterations to run</dd>
<dt>tol</dt>
<dd>Stopping tolerance for proximal gradient algorithm.</dd>
<dt>selector</dt>
<dd>Vector to choose which parameters in the discriminant vector will be used to calculate the
regularization terms. The size of the vector must be *p* the number of predictors. The
default value is a vector of all ones. This is currently only used for ordinal classification.</dd></dl>

Arguments

Accelerated Proximal Gradient on l1 regularized quadratic program — APG_EN2

<dl>

<dt>A</dt>
<dd>p by p positive definite coefficient matrix
$$A = (\gamma Om + X^T X/n)$$.</dd>


<dt>d</dt>
<dd>nx1 dimensional column vector.</dd>


<dt>lam</dt>
<dd>Regularization parameter for l1 penalty, must be greater than zero.</dd>


<dt>alpha</dt>
<dd>Step length.</dd>


<dt>maxits</dt>
<dd>Number of iterations to run</dd>


<dt>tol</dt>
<dd>Stopping tolerance for proximal gradient algorithm.</dd>


<dt>selector</dt>
<dd>Vector to choose which parameters in the discriminant vector will be used to calculate the
regularization terms. The size of the vector must be *p* the number of predictors. The
default value is a vector of all ones. This is currently only used for ordinal classification.</dd>

</dl>

APG_EN2: Accelerated Proximal Gradient on l1 regularized quadratic program

Description

Usage

Value

Arguments

Details

See Also