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