# LbfgsMaximumEntropyMulticlassTrainer Class

## Definition

The IEstimator<TTransformer> to predict a target using a maximum entropy multiclass classifier trained with L-BFGS method.

public sealed class LbfgsMaximumEntropyMulticlassTrainer : Microsoft.ML.Trainers.LbfgsTrainerBase<Microsoft.ML.Trainers.LbfgsMaximumEntropyMulticlassTrainer.Options,Microsoft.ML.Data.MulticlassPredictionTransformer<Microsoft.ML.Trainers.MaximumEntropyModelParameters>,Microsoft.ML.Trainers.MaximumEntropyModelParameters>
type LbfgsMaximumEntropyMulticlassTrainer = class
inherit LbfgsTrainerBase<LbfgsMaximumEntropyMulticlassTrainer.Options, MulticlassPredictionTransformer<MaximumEntropyModelParameters>, MaximumEntropyModelParameters>
Public NotInheritable Class LbfgsMaximumEntropyMulticlassTrainer
Inherits LbfgsTrainerBase(Of LbfgsMaximumEntropyMulticlassTrainer.Options, MulticlassPredictionTransformer(Of MaximumEntropyModelParameters), MaximumEntropyModelParameters)
Inheritance
LbfgsMaximumEntropyMulticlassTrainer

## Remarks

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

### Input and Output Columns

The input label column data must be key type and the feature column must be a known-sized vector of Single.

This trainer outputs the following columns:

Output Column Name Column Type Description
Score Vector of Single The scores of all classes. Higher value means higher probability to fall into the associated class. If the i-th element has the largest value, the predicted label index would be i. Note that i is zero-based index.
PredictedLabel key type The predicted label's index. If its value is i, the actual label would be the i-th category in the key-valued input label type.

### Trainer Characteristics

Machine learning task Multiclass classification
Is normalization required? Yes
Is caching required? No
Required NuGet in addition to Microsoft.ML None
Exportable to ONNX Yes

### Scoring Function

Maximum entropy model is a generalization of linear logistic regression. The major difference between maximum entropy model and logistic regression is the number of classes supported in the considered classification problem. Logistic regression is only for binary classification while maximum entropy model handles multiple classes. See Section 1 in this paper for a detailed introduction.

Assume that the number of classes is $m$ and number of features is $n$. Maximum entropy model assigns the $c$-th class a coefficient vector $\textbf{w}_c \in {\mathbb R}^n$ and a bias $b_c \in {\mathbb R}$, for $c=1,\dots,m$. Given a feature vector $\textbf{x} \in {\mathbb R}^n$, the $c$-th class's score is $\hat{y}^c = \textbf{w}_c^T \textbf{x} + b_c$. The probability of $\textbf{x}$ belonging to class $c$ is defined by $\tilde{P}(c | \textbf{x}) = \frac{ e^{\hat{y}^c} }{ \sum_{c' = 1}^m e^{\hat{y}^{c'}} }$. Let $P(c, \textbf{ x})$ denote the joint probability of seeing $c$ and $\textbf{x}$. The loss function minimized by this trainer is $-\sum_{c = 1}^m P(c, \textbf{ x}) \log \tilde{P}(c | \textbf{x})$, which is the negative log-likelihood function.

### Training Algorithm Details

The optimization technique implemented is based on the limited memory Broyden-Fletcher-Goldfarb-Shanno method (L-BFGS). L-BFGS is a quasi-Newtonian method, which replaces the expensive computation of the Hessian matrix with an approximation but still enjoys a fast convergence rate like Newton's method where the full Hessian matrix is computed. Since L-BFGS approximation uses only a limited amount of historical states to compute the next step direction, it is especially suited for problems with a high-dimensional feature vector. The number of historical states is a user-specified parameter, using a larger number may lead to a better approximation of the Hessian matrix but also a higher computation cost per step.

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.

Check the See Also section for links to usage examples.

## 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 LbfgsTrainerBase)

## Methods

 Trains and returns a ITransformer. (Inherited from TrainerEstimatorBase) Continues the training of a LbfgsMaximumEntropyMulticlassTrainer using an already trained modelParameters and returns a MulticlassPredictionTransformer. (Inherited from TrainerEstimatorBase)

## Extension Methods

 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.