# SdcaRegressionTrainer Class

## Definition

The IEstimator<TTransformer> for training a regression model using the stochastic dual coordinate ascent method.

public sealed class SdcaRegressionTrainer : Microsoft.ML.Trainers.SdcaTrainerBase<Microsoft.ML.Trainers.SdcaRegressionTrainer.Options,Microsoft.ML.Data.RegressionPredictionTransformer<Microsoft.ML.Trainers.LinearRegressionModelParameters>,Microsoft.ML.Trainers.LinearRegressionModelParameters>
type SdcaRegressionTrainer = class
inherit SdcaTrainerBase<SdcaRegressionTrainer.Options, RegressionPredictionTransformer<LinearRegressionModelParameters>, LinearRegressionModelParameters>
Public NotInheritable Class SdcaRegressionTrainer
Inherits SdcaTrainerBase(Of SdcaRegressionTrainer.Options, RegressionPredictionTransformer(Of LinearRegressionModelParameters), LinearRegressionModelParameters)
Inheritance

## Remarks

To create this trainer, use Sdca or Sdca(Options).

### Input and Output Columns

The input label column data must be Single. The input features column data must be a known-sized vector of Single.

This trainer outputs the following columns:

Output Column Name Column Type Description
Score Single The unbounded score that was predicted by the model.

### Trainer Characteristics

Is normalization required? Yes
Is caching required? No
Required NuGet in addition to Microsoft.ML None
Exportable to ONNX Yes

### Training Algorithm Details

This trainer is based on the Stochastic Dual Coordinate Ascent (SDCA) method, a state-of-the-art optimization technique for convex objective functions. The algorithm can be scaled because it's a streaming training algorithm as described in a KDD best paper.

Convergence is underwritten by periodically enforcing synchronization between primal and dual variables in a separate thread. Several choices of loss functions are also provided such as hinge-loss and logistic loss. Depending on the loss used, the trained model can be, for example, support vector machine or logistic regression. The SDCA method combines several of the best properties such the ability to do streaming learning (without fitting the entire data set into your memory), reaching a reasonable result with a few scans of the whole data set (for example, see experiments in this paper), and spending no computation on zeros in sparse data sets.

Note that SDCA is a stochastic and streaming optimization algorithm. The result depends on the order of training data because the stopping tolerance is not tight enough. In strongly-convex optimization, the optimal solution is unique and therefore everyone eventually reaches the same place. Even in non-strongly-convex cases, you will get equally-good solutions from run to run. For reproducible results, it is recommended that one sets 'Shuffle' to False and 'NumThreads' to 1.

This class uses empirical risk minimization (i.e., ERM) to formulate the optimization problem built upon collected data. Note that empirical risk is usually measured by applying a loss function on the model's predictions on collected data points. If the training data does not contain enough data points (for example, to train a linear model in $n$-dimensional space, we need at least $n$ data points), overfitting may happen so that the model produced by ERM is good at describing training data but may fail to predict correct results in unseen events. Regularization is a common technique to alleviate such a phenomenon by penalizing the magnitude (usually measured by the norm function) of model parameters. This trainer supports elastic net regularization, which penalizes a linear combination of L1-norm (LASSO), $|| \textbf{w}_c ||_1$, and L2-norm (ridge), $|| \textbf{w}_c ||_2^2$ regularizations for $c=1,\dots,m$. L1-norm and L2-norm regularizations have different effects and uses that are complementary in certain respects.

Together with the implemented optimization algorithm, L1-norm regularization can increase the sparsity of the model weights, $\textbf{w}_1,\dots,\textbf{w}_m$. For high-dimensional and sparse data sets, if users carefully select the coefficient of L1-norm, it is possible to achieve a good prediction quality with a model that has only a few non-zero weights (e.g., 1% of total model weights) without affecting its prediction power. In contrast, L2-norm cannot increase the sparsity of the trained model but can still prevent overfitting by avoiding large parameter values. Sometimes, using L2-norm leads to a better prediction quality, so users may still want to try it and fine tune the coefficients of L1-norm and L2-norm. Note that conceptually, using L1-norm implies that the distribution of all model parameters is a Laplace distribution while L2-norm implies a Gaussian distribution for them.

An aggressive regularization (that is, assigning large coefficients to L1-norm or L2-norm regularization terms) can harm predictive capacity by excluding important variables from the model. For example, a very large L1-norm coefficient may force all parameters to be zeros and lead to a trivial model. Therefore, choosing the right regularization coefficients is important in practice.

## Fields

 The feature column that the trainer expects. (Inherited from TrainerEstimatorBase) The label column that the trainer expects. Can be null, which indicates that label is not used for training. (Inherited from TrainerEstimatorBase) The weight column that the trainer expects. Can be null, which indicates that weight is not used for training. (Inherited from TrainerEstimatorBase)

## Properties

 (Inherited from StochasticTrainerBase)

## Methods

 Trains and returns a ITransformer. (Inherited from TrainerEstimatorBase) (Inherited from TrainerEstimatorBase)

## Extension Methods

 Append a 'caching checkpoint' to the estimator chain. This will ensure that the downstream estimators will be trained against cached data. It is helpful to have a caching checkpoint before trainers that take multiple data passes. Given an estimator, return a wrapping object that will call a delegate once Fit(IDataView) is called. It is often important for an estimator to return information about what was fit, which is why the Fit(IDataView) method returns a specifically typed object, rather than just a general ITransformer. However, at the same time, IEstimator are often formed into pipelines with many objects, so we may need to build a chain of estimators via EstimatorChain where the estimator for which we want to get the transformer is buried somewhere in this chain. For that scenario, we can through this method attach a delegate that will be called once fit is called.