[jira] [Updated] (SPARK-26173) Prior regularization for Logistic Regression

["Dongjoon Hyun (JIRA)" <ji...@apache.org>]

     [ https://issues.apache.org/jira/browse/SPARK-26173?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel ]

Dongjoon Hyun updated SPARK-26173:
----------------------------------
    Affects Version/s:     (was: 2.4.0)
                       3.0.0

> Prior regularization for Logistic Regression
> --------------------------------------------
>
>                 Key: SPARK-26173
>                 URL: https://issues.apache.org/jira/browse/SPARK-26173
>             Project: Spark
>          Issue Type: New Feature
>          Components: MLlib
>    Affects Versions: 3.0.0
>            Reporter: Facundo Bellosi
>            Priority: Minor
>         Attachments: Prior regularization.png
>
>
> This feature enables Maximum A Posteriori (MAP) optimization for Logistic Regression based on a Gaussian prior. In practice, this is just implementing a more general form of L2 regularization parameterized by a (multivariate) mean and precisions (inverse of variance) vectors.
> Prior regularization is calculated through the following formula:
> !Prior regularization.png!
> where:
>  * λ: regularization parameter ({{regParam}})
>  * K: number of coefficients (weights vector length)
>  * w~i~ with prior Normal(μ~i~, β~i~^2^)
> _Reference: Bishop, Christopher M. (2006). Pattern Recognition and Machine Learning (section 4.5). Berlin, Heidelberg: Springer-Verlag._
> h3. Existing implementations
> * Python: [bayes_logistic|https://pypi.org/project/bayes_logistic/]
> h2.  Implementation
>  * 2 new parameters added to {{LogisticRegression}}: {{priorMean}} and {{priorPrecisions}}.
>  * 1 new class ({{PriorRegularization}}) implements the calculations of the value and gradient of the prior regularization term.
>  * Prior regularization is enabled when both vectors are provided and {{regParam}} > 0 and {{elasticNetParam}} < 1.
> h2. Tests
>  * {{DifferentiableRegularizationSuite}}
>  ** {{Prior regularization}}
>  * {{LogisticRegressionSuite}}
>  ** {{prior precisions should be required when prior mean is set}}
>  ** {{prior mean should be required when prior precisions is set}}
>  ** {{`regParam` should be positive when using prior regularization}}
>  ** {{`elasticNetParam` should be less than 1.0 when using prior regularization}}
>  ** {{prior mean and precisions should have equal length}}
>  ** {{priors' length should match number of features}}
>  ** {{binary logistic regression with prior regularization equivalent to L2}}
>  ** {{binary logistic regression with prior regularization equivalent to L2 (bis)}}
>  ** {{binary logistic regression with prior regularization}}



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