loss3

regression

classification

Algorithms compute robust estimators for loss functions in the concave convex (CC) family by the iteratively reweighted convex optimization (IRCO), an extension of the iteratively reweighted least squares (IRLS). The IRCO reduces the weight of the observation that leads to a large loss; it also provides weights to help identify outliers. Applications include robust (penalized) generalized linear models and robust support vector machines. The package also contains penalized Poisson, negative binomial, zero-inflated Poisson, zero-inflated negative binomial regression models and robust models with non-convex loss functions. Wang et al. (2014) <doi:10.1002/sim.6314>,
Wang et al. (2015) <doi:10.1002/bimj.201400143>,
Wang et al. (2016) <doi:10.1177/0962280214530608>,
Wang (2021) <doi:10.1007/s11749-021-00770-2>,
Wang (2024) <doi:10.1111/anzs.12409>.

Zhu Wang

mpath

Regularized Linear Models

loss3 function

<dl> <dt>y</dt>
<dd>response variable values, 0/1 if <code>family=2</code>, or binomial</dd> <dt>mu</dt>
<dd>response prediction of <code>y</code>. If <code>mu</code> is linear predictor, use function <code>loss2</code> instead</dd> <dt>theta</dt>
<dd>scale parameter for <code>family=4</code>, negative binomial</dd> <dt>weights</dt>
<dd>observation weights, same length as <code>y</code></dd> <dt>cfun</dt>
<dd>integer from 1-8, concave function as in <code>irglm_fit</code></dd> <dt>family</dt>
<dd>integer 2, 3 or 4, convex function binomial, Poisson or negative binomial, respectively</dd><dt>s</dt>
<dd>tuning parameter of <code>cfun</code>. <code>s &gt; 0</code> and can be equal to 0 for <code>cfun="tcave"</code>.</dd>
 
 <dt>delta</dt>
<dd>a small positive number provided by user only if <code>cfun="gcave"</code> and <code>0 &lt; s &lt;1</code></dd></dl>

Arguments

Zhu Wang &lt;zwang145@uthsc.edu&gt;

Author

Composite Loss Value for GLM — loss3

<dl>

 <dt>y</dt>
<dd>response variable values, 0/1 if <code>family=2</code>, or binomial</dd>

 <dt>mu</dt>
<dd>response prediction of <code>y</code>. If <code>mu</code> is linear predictor, use function <code>loss2</code> instead</dd>

 <dt>theta</dt>
<dd>scale parameter for <code>family=4</code>, negative binomial</dd>

 <dt>weights</dt>
<dd>observation weights, same length as <code>y</code></dd>

 <dt>cfun</dt>
<dd>integer from 1-8, concave function as in <code>irglm_fit</code></dd>

 <dt>family</dt>
<dd>integer 2, 3 or 4, convex function binomial, Poisson or negative binomial, respectively</dd>

<dt>s</dt>
<dd>tuning parameter of <code>cfun</code>. <code>s &gt; 0</code> and can be equal to 0 for <code>cfun="tcave"</code>.</dd>
 
 <dt>delta</dt>
<dd>a small positive number provided by user only if <code>cfun="gcave"</code> and <code>0 &lt; s &lt;1</code></dd>

</dl>

loss3: Composite Loss Value for GLM

Description

Usage

Value

Arguments

Author

Details

References

See Also