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Showing content from https://spark.apache.org/docs/latest/api/java/org/apache/spark/ml/regression/FMRegressor.html below:

FMRegressor (Spark 4.0.0 JavaDoc)

All Implemented Interfaces:
Serializable, org.apache.spark.internal.Logging, Params, HasFeaturesCol, HasFitIntercept, HasLabelCol, HasMaxIter, HasPredictionCol, HasRegParam, HasSeed, HasSolver, HasStepSize, HasTol, HasWeightCol, PredictorParams, FactorizationMachines, FactorizationMachinesParams, FMRegressorParams, DefaultParamsWritable, Identifiable, MLWritable

Factorization Machines learning algorithm for regression. It supports normal gradient descent and AdamW solver.

The implementation is based on: S. Rendle. "Factorization machines" 2010.

FM is able to estimate interactions even in problems with huge sparsity (like advertising and recommendation system). FM formula is:

$$ \begin{align} y = w_0 + \sum\limits^n_{i-1} w_i x_i + \sum\limits^n_{i=1} \sum\limits^n_{j=i+1} \langle v_i, v_j \rangle x_i x_j \end{align} $$

First two terms denote global bias and linear term (as same as linear regression), and last term denotes pairwise interactions term. v_i describes the i-th variable with k factors.

FM regression model uses MSE loss which can be solved by gradient descent method, and regularization terms like L2 are usually added to the loss function to prevent overfitting.

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