# 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 for each response variable.

**Data Types: **`single`

| `double`

`LayerWeights`

— Learned layer weights

cell array

This property is read-only.

Learned layer weights for the fully connected layers, returned as a cell array. Entry
*i* in the cell array corresponds to the layer weights for the
fully connected layer *i*. 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 the fully connected layers, returned as a cell array. Entry
*i* in the cell array corresponds to the layer biases for the fully
connected layer *i*. 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`

— Names of response variables

character vector | cell array of character vectors

This property is read-only.

Names of the response variables, returned as a character vector or cell array of character vectors.

**Data Types: **`char`

| `cell`

`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 the original response values
and returns an output 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

### Create `dlnetwork`

`dlnetwork` (Deep Learning Toolbox) | Deep learning neural network |

### 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 |

### Assess Predictive Performance on New Observations

### Gather Properties of Compact Regression Neural Network Model

`gather` | Gather properties of Statistics and Machine Learning Toolbox object from GPU |

## 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 52253 RegressionNeuralNetwork compactMdl 1x1 6768 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.

### GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™. (since R2024b)

Usage notes and limitations:

The following object functions fully support GPU arrays:

The object functions execute on a GPU if at least one of the following applies:

The model was fitted with GPU arrays.

The predictor data that you pass to the object function is a GPU array.

The response data that you pass to the object function is a GPU array.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

## Version History

**Introduced in R2021a**

### R2024b: Specify GPU arrays (requires Parallel Computing Toolbox)

You can fit a `CompactRegressionNeuralNetwork`

object with GPU arrays by using `fitrnet`

to fit a
`RegressionNeuralNetwork`

object to `gpuArray`

data, and then
passing the object to `compact`

. Most
`CompactRegressionNeuralNetwork`

object functions now support GPU array input arguments so
that the functions can execute on a GPU. The object functions that do not support GPU array
inputs are `lime`

and
`shapley`

.

### R2024b: Convert to `dlnetwork`

Convert a `CompactRegressionNeuralNetwork`

object to a `dlnetwork`

(Deep Learning Toolbox) object using the `dlnetwork`

function. Use
`dlnetwork`

objects to make further edits and customize the underlying
neural network of a `CompactRegressionNeuralNetwork`

object and retrain it using the `trainnet`

(Deep Learning Toolbox)
function or a custom training loop.

### 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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