# CompactRegressionNeuralNetwork

## Description

`CompactRegressionNeuralNetwork`

is a compact version of a `RegressionNeuralNetwork`

model object. The compact model does not include the data
used for training the regression model. Therefore, you cannot perform some tasks, such as
cross-validation, using the compact model. Use a compact model for tasks such as predicting
the response values of new data.

## Creation

Create a `CompactRegressionNeuralNetwork`

object from a full `RegressionNeuralNetwork`

model object by using `compact`

.

## Properties

### Neural Network Properties

`LayerSizes`

— Sizes of fully connected layers

positive integer vector

This property is read-only.

Sizes of the fully connected layers in the neural network model, returned as a
positive integer vector. The *i*th element of
`LayerSizes`

is the number of outputs in the
*i*th fully connected layer of the neural network model.

`LayerSizes`

does not include the size of the final fully
connected layer. This layer always has one output.

**Data Types: **`single`

| `double`

`LayerWeights`

— Learned layer weights

cell array

This property is read-only.

Learned layer weights for fully connected layers, returned as a cell array. The
*i*th entry in the cell array corresponds to the layer weights for
the *i*th fully connected layer. For example,
`Mdl.LayerWeights{1}`

returns the weights for the first fully
connected layer of the model `Mdl`

.

`LayerWeights`

includes the weights for the final fully
connected layer.

**Data Types: **`cell`

`LayerBiases`

— Learned layer biases

cell array

This property is read-only.

Learned layer biases for fully connected layers, returned as a cell array. The
*i*th entry in the cell array corresponds to the layer biases for
the *i*th fully connected layer. For example,
`Mdl.LayerBiases{1}`

returns the biases for the first fully
connected layer of the model `Mdl`

.

`LayerBiases`

includes the biases for the final fully connected
layer.

**Data Types: **`cell`

`Activations`

— Activation functions for fully connected layers

`'relu'`

| `'tanh'`

| `'sigmoid'`

| `'none'`

| cell array of character vectors

This property is read-only.

Activation functions for the fully connected layers of the neural network model, returned as a character vector or cell array of character vectors with values from this table.

Value | Description |
---|---|

`'relu'` | Rectified linear unit (ReLU) function — Performs a threshold operation on each element of the input, where any value less than zero is set to zero, that is, $$f\left(x\right)=\{\begin{array}{cc}x,& x\ge 0\\ 0,& x<0\end{array}$$ |

`'tanh'` | Hyperbolic tangent (tanh) function — Applies the |

`'sigmoid'` | Sigmoid function — Performs the following operation on each input element: $$f(x)=\frac{1}{1+{e}^{-x}}$$ |

`'none'` | Identity function — Returns each input element without performing any transformation, that is, |

If

`Activations`

contains only one activation function, then it is the activation function for every fully connected layer of the neural network model, excluding the final fully connected layer, which does not have an activation function (`OutputLayerActivation`

).If

`Activations`

is an array of activation functions, then the*i*th element is the activation function for the*i*th layer of the neural network model.

**Data Types: **`char`

| `cell`

`OutputLayerActivation`

— Activation function for final fully connected layer

`'none'`

This property is read-only.

Activation function for final fully connected layer, returned as
`'none'`

.

### Data Properties

`PredictorNames`

— Predictor variable names

cell array of character vectors

This property is read-only.

Predictor variable names, returned as a cell array of character vectors. The order
of the elements of `PredictorNames`

corresponds to the order in which
the predictor names appear in the training data.

**Data Types: **`cell`

`CategoricalPredictors`

— Categorical predictor indices

vector of positive integers | `[]`

This property is read-only.

Categorical predictor indices, returned as a
vector of positive integers. Assuming that the predictor data contains observations in
rows, `CategoricalPredictors`

contains index values corresponding to
the columns of the predictor data that contain categorical predictors. If none of the
predictors are categorical, then this property is empty
(`[]`

).

**Data Types: **`double`

`ExpandedPredictorNames`

— Expanded predictor names

cell array of character vectors

This property is read-only.

Expanded predictor names, returned as a cell array of character vectors. If the
model uses encoding for categorical variables, then
`ExpandedPredictorNames`

includes the names that describe the
expanded variables. Otherwise, `ExpandedPredictorNames`

is the same
as `PredictorNames`

.

**Data Types: **`cell`

`Mu`

— Predictor means

numeric vector | `[]`

*Since R2023b*

This property is read-only.

Predictor means, returned as a numeric vector. If you set `Standardize`

to
`1`

or `true`

when
you train the neural network model, then the length of the
`Mu`

vector is equal to the
number of expanded predictors (see
`ExpandedPredictorNames`

). The
vector contains `0`

values for dummy variables
corresponding to expanded categorical predictors.

If you set `Standardize`

to `0`

or `false`

when you train the neural network model, then the `Mu`

value is an empty vector (`[]`

).

**Data Types: **`double`

`ResponseName`

— Response variable name

character vector

This property is read-only.

Response variable name, returned as a character vector.

**Data Types: **`char`

`ResponseTransform`

— Response transformation function

`'none'`

| function handle

Response transformation function, specified as `'none'`

or a function handle.
`ResponseTransform`

describes how the software transforms raw
response values.

For a MATLAB^{®} function or a function that you define, enter its function handle. For
example, you can enter ```
Mdl.ResponseTransform =
@
```

, where
*function*

accepts a numeric vector of the
original responses and returns a numeric vector of the same size containing the
transformed responses.*function*

**Data Types: **`char`

| `function_handle`

`Sigma`

— Predictor standard deviations

numeric vector | `[]`

*Since R2023b*

This property is read-only.

Predictor standard deviations, returned as a numeric vector. If you set
`Standardize`

to `1`

or `true`

when you train the neural network model, then the length of the
`Sigma`

vector is equal to the number of expanded predictors (see
`ExpandedPredictorNames`

). The vector contains
`1`

values for dummy variables corresponding to expanded
categorical predictors.

If you set `Standardize`

to `0`

or `false`

when you train the neural network model, then the `Sigma`

value is an empty vector (`[]`

).

**Data Types: **`double`

## Object Functions

### Interpret Prediction

`lime` | Local interpretable model-agnostic explanations (LIME) |

`partialDependence` | Compute partial dependence |

`plotPartialDependence` | Create partial dependence plot (PDP) and individual conditional expectation (ICE) plots |

`shapley` | Shapley values |

## Examples

### Reduce Size of Regression Neural Network Model

Reduce the size of a full regression neural network model by removing the training data from the model. You can use a compact model to improve memory efficiency.

Load the `patients`

data set. Create a table from the data set. Each row corresponds to one patient, and each column corresponds to a diagnostic variable. Use the `Systolic`

variable as the response variable, and the rest of the variables as predictors.

```
load patients
tbl = table(Age,Diastolic,Gender,Height,Smoker,Weight,Systolic);
```

Train a regression neural network model using the data. Specify the `Systolic`

column of `tblTrain`

as the response variable. Specify to standardize the numeric predictors.

Mdl = fitrnet(tbl,"Systolic","Standardize",true)

Mdl = RegressionNeuralNetwork PredictorNames: {'Age' 'Diastolic' 'Gender' 'Height' 'Smoker' 'Weight'} ResponseName: 'Systolic' CategoricalPredictors: [3 5] ResponseTransform: 'none' NumObservations: 100 LayerSizes: 10 Activations: 'relu' OutputLayerActivation: 'none' Solver: 'LBFGS' ConvergenceInfo: [1x1 struct] TrainingHistory: [619x7 table]

`Mdl`

is a full `RegressionNeuralNetwork`

model object.

Reduce the size of the model by using `compact`

.

compactMdl = compact(Mdl)

compactMdl = CompactRegressionNeuralNetwork LayerSizes: 10 Activations: 'relu' OutputLayerActivation: 'none'

`compactMdl`

is a `CompactRegressionNeuralNetwork`

model object. `compactMdl`

contains fewer properties than the full model `Mdl`

.

Display the amount of memory used by each neural network model.

whos("Mdl","compactMdl")

Name Size Bytes Class Attributes Mdl 1x1 52007 RegressionNeuralNetwork compactMdl 1x1 6512 classreg.learning.regr.CompactRegressionNeuralNetwork

The full model is larger than the compact model.

## Extended Capabilities

### C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

The

`predict`

object function supports code generation.

For more information, see Introduction to Code Generation.

## Version History

**Introduced in R2021a**

### R2023b: Neural network models include standardization properties

Neural network models include `Mu`

and `Sigma`

properties that contain the means and standard deviations, respectively, used to standardize the predictors before training. The properties are empty when the fitting function does not perform any standardization.

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