synthesizeTabularData

Synthesize tabular data

Since R2024b

Syntax

syntheticX = synthesizeTabularData(X,n)

syntheticX = synthesizeTabularData(X,n,Name=Value)

Description

syntheticX = synthesizeTabularData(X,n) generates n observations of synthetic data using the existing data X. The function returns the synthetic data syntheticX.

syntheticX = synthesizeTabularData(X,n,Name=Value) specifies additional options using one or more name-value arguments. For example, you can specify the bin method, the variables to use, and the options for computing in parallel.

Examples

Generate Synthetic Tabular Data

Generate synthetic data using an existing data set in a table. Visually compare the distributions of the existing and synthetic data sets.

Load the sample file fisheriris.csv, which contains iris data including sepal length, sepal width, petal width, and species type. Read the file into a table, and then convert the Species variable into a categorical variable. Display the first eight observations in the table.

fisheriris = readtable("fisheriris.csv");
fisheriris.Species = categorical(fisheriris.Species);
head(fisheriris)

    SepalLength    SepalWidth    PetalLength    PetalWidth    Species
    ___________    __________    ___________    __________    _______

        5.1           3.5            1.4           0.2        setosa 
        4.9             3            1.4           0.2        setosa 
        4.7           3.2            1.3           0.2        setosa 
        4.6           3.1            1.5           0.2        setosa 
          5           3.6            1.4           0.2        setosa 
        5.4           3.9            1.7           0.4        setosa 
        4.6           3.4            1.4           0.3        setosa 
          5           3.4            1.5           0.2        setosa 

Create 1000 new observations from the data in fisheriris by using the synthesizeTabularData function. The function uses a binning technique to learn the distribution of the variables in fisheriris before synthesizing data.

rng("default")
syntheticData = synthesizeTabularData(fisheriris,1000);

For each numeric variable, use box plots to visually compare the distribution of the values in fisheriris to the distribution of the values in syntheticData.

numericVariables = ["SepalLength","SepalWidth", ...
    "PetalLength","PetalWidth"];

boxchart(fisheriris{:,numericVariables})
hold on
boxchart(syntheticData{:,numericVariables})
hold off
legend(["Real Data","Synthetic Data"])
xticklabels(numericVariables)

Blue box plots show the distributions of real data, and red box plots show the distributions of synthetic data. For each of the four numeric variables, the real and synthetic data values have similar distributions.

Use histograms to compare the distribution of flower species in fisheriris and syntheticData.

histogram(fisheriris.Species, ...
    Normalization="probability")
hold on
histogram(syntheticData.Species, ...
    Normalization="probability")
hold off
legend(["Real Data","Synthetic Data"])

Overall, the distribution of flower species is similar across the two data sets. For example, 32% of the flowers in the synthetic data set are setosa irises, compared to 33% in the real data set.

Synthesize Data for Model Training

Synthesize data using existing training data. Train a model using the existing training data, and then train the same type of model using the synthetic data. Compare the performance of the two models using test data.

Load the carbig data set, which contains measurements of cars made in the 1970s and early 1980s. Create a table containing the predictor variables Acceleration, Displacement, and so on, as well as the response variable MPG.

load carbig
tbl = table(Acceleration,Cylinders,Displacement,Horsepower, ...
    Model_Year,Origin,MPG,Weight);

Remove rows of tbl where the table has missing values.

tbl = rmmissing(tbl);

Partition the data into training and test sets. Use approximately 60% of the observations for model training and synthesizing new data, and 40% of the observations for model testing. Use cvpartition to partition the data.

rng("default")
cv = cvpartition(size(tbl,1),"Holdout",0.4);
trainTbl = tbl(training(cv),:);
testTbl = tbl(test(cv),:);

Synthesize new data by using the trainTbl data set. Specify to generate 1000 observations using 20 equal-width bins for each variable. Specify the Cylinders and Model_Year variables as discrete numeric variables.

syntheticTbl = synthesizeTabularData(trainTbl,1000, ...
    BinMethod="equal-width",NumBins=20, ...
    DiscreteNumericVariables=["Cylinders","Model_Year"]);

To visualize the difference between the existing data and synthetic data, you can use the detectdrift function. The function uses permutation testing to detect drift between trainTbl and syntheticTbl.

dd = detectdrift(trainTbl,syntheticTbl);

dd is a DriftDiagnostics object with plotEmpiricalCDF and plotHistogram object functions for visualization.

For continuous variables, use the plotEmpiricalCDF function to see the difference between the empirical cumulative distribution function (ecdf) of the values in trainTbl and the ecdf of the values in syntheticTbl.

continuousVariable = "Acceleration";
plotEmpiricalCDF(dd,Variable=continuousVariable)
legend(["Real Data","Synthetic Data"])

For the Acceleration predictor, the ecdf plot for the existing values (in blue) matches the ecdf plot for the synthetic values (in red) fairly well.

For discrete variables, use the plotHistogram function to see the difference between the histogram of the values in trainTbl and the histogram of the values in syntheticTbl.

discreteVariable = "Cylinders";
plotHistogram(dd,Variable=discreteVariable)
legend(["Real Data","Synthetic Data"])

For the Cylinders predictor, the histogram for the existing values (in blue) matches the histogram for the synthetic values (in red) fairly well.

Train a bagged ensemble of trees using the original training data trainTbl. Specify MPG as the response variable. Then, train the same kind of regression model using the synthetic data syntheticTbl.

originalMdl = fitrensemble(trainTbl,"MPG",Method="Bag");
newMdl = fitrensemble(syntheticTbl,"MPG",Method="Bag");

Evaluate the performance of the two models on the test set by computing the test mean squared error (MSE). Smaller MSE values indicate better performance.

originalMSE = loss(originalMdl,testTbl)

originalMSE = 
7.0784

newMSE = loss(newMdl,testTbl)

newMSE = 
6.1031

The model trained on the synthetic data performs slightly better on the test data.

Evaluate Synthetic Tabular Data

Evaluate data synthesized from an existing data set. Compare the existing and synthetic data sets to determine distribution similarity.

Load the carsmall data set. The file contains measurements of cars from 1970, 1976, and 1982. Create a table containing the data and display the first eight observations.

load carsmall
carData = table(Acceleration,Cylinders,Displacement,Horsepower, ...
    Mfg,Model,Model_Year,MPG,Origin,Weight);
head(carData)

    Acceleration    Cylinders    Displacement    Horsepower         Mfg                       Model                  Model_Year    MPG    Origin     Weight
    ____________    _________    ____________    __________    _____________    _________________________________    __________    ___    _______    ______

          12            8            307            130        chevrolet        chevrolet chevelle malibu                70        18     USA         3504 
        11.5            8            350            165        buick            buick skylark 320                        70        15     USA         3693 
          11            8            318            150        plymouth         plymouth satellite                       70        18     USA         3436 
          12            8            304            150        amc              amc rebel sst                            70        16     USA         3433 
        10.5            8            302            140        ford             ford torino                              70        17     USA         3449 
          10            8            429            198        ford             ford galaxie 500                         70        15     USA         4341 
           9            8            454            220        chevrolet        chevrolet impala                         70        14     USA         4354 
         8.5            8            440            215        plymouth         plymouth fury iii                        70        14     USA         4312 

Generate 100 new observations using the synthesizeTabularData function. Specify the Cylinders and Model_Year variables as discrete numeric variables. Display the first eight observations.

rng("default")
syntheticData = synthesizeTabularData(carData,100, ...
    DiscreteNumericVariables=["Cylinders","Model_Year"]);
head(syntheticData)

    Acceleration    Cylinders    Displacement    Horsepower         Mfg                       Model                  Model_Year     MPG      Origin     Weight
    ____________    _________    ____________    __________    _____________    _________________________________    __________    ______    _______    ______

       11.215           8           309.73         137.28      dodge            dodge coronet brougham                   76          17.3    USA          4038
       10.198           8           416.68         215.51      plymouth         plymouth fury iii                        70        9.5497    USA        4507.2
       17.161           6           258.38         77.099      amc              amc pacer d/l                            76        18.325    USA        3199.8
       9.4623           8           426.19          197.3      plymouth         plymouth fury iii                        70        11.747    USA        4372.1
       13.992           4           106.63         91.396      datsun           datsun pl510                             70         30.56    Japan      1950.7
       17.965           6           266.24         78.719      oldsmobile       oldsmobile cutlass ciera (diesel)        82        36.416    USA        2832.4
       17.028           4           139.02         100.24      chevrolet        chevrolet cavalier 2-door                82        36.058    USA        2744.5
       15.343           4           118.93         100.22      toyota           toyota celica gt                         82        26.696    Japan      2600.5

Visualize the synthetic and existing data sets. Create a DriftDiagnostics object using the detectdrift function. The object has the plotEmpiricalCDF and plotHistogram object functions you can use to visualize continuous and discrete variables.

dd = detectdrift(carData,syntheticData);

Use plotEmpiricalCDF to visualize the empirical cumulative distribution function (ECDF) of the values in carData and syntheticData.

continuousVariable = "Acceleration";
plotEmpiricalCDF(dd,Variable=continuousVariable)
legend(["Real Data","Synthetic Data"])

For the variable Acceleration, the ECDF of the existing data (in blue) and the ECDF of the synthetic data (in red) appear to be similar.

Use plotHistogram to visualize the distribution of values for discrete variables in carData and syntheticData.

discreteVariable = "Cylinders";
plotHistogram(dd,Variable=discreteVariable)
legend(["Real Data","Synthetic Data"])

For the variable Cylinders, the distribution of data between the bins for the existing data (in blue) and the synthetic data (in red) appear similar.

Compare the synthetic and existing data sets using the mmdtest function. The function performs a two-sample hypothesis test for the null hypothesis that the samples come from the same distribution.

[mmd,p,h] = mmdtest(carData,syntheticData)

mmd = 
0.0078

p = 
0.8860

h = 
0

The returned value of h = 0 indicates that mmdtest fails to reject the null hypothesis that the samples come from different distributions at the 5% significance level. As with other hypothesis tests, this result does not guarantee that the null hypothesis is true. That is, the samples do not necessarily come from the same distribution, but the low MMD value and high p-value indicate that the distributions of the real and synthetic data sets are similar.

Input Arguments

X — Existing data set

numeric matrix | table

Existing data set, specified as a numeric matrix or a table. Rows of X correspond to observations, and columns of X correspond to variables. Multicolumn variables and cell arrays other than cell arrays of character vectors are not allowed in X.

Data Types: single | double | table

n — Number of synthetic data observations to generate

positive integer scalar

Number of synthetic data observations to generate, specified as a positive integer scalar.

Example: 100

Data Types: single | double

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: synthesizeTabularData(X,100,BinMethod="equiprobable",NumBins=10) specifies to use 10 equiprobable bins for each variable in X to generate 100 synthetic observations.

BinMethod — Binning algorithm

"auto" (default) | "equal-width" | "equiprobable" | "dagostino-stephens" | "freedman-diaconis" | "scott" | ...

Binning algorithm, specified as one of the values in this table.

Value	Description
"auto"	"auto" corresponds to: "dagostino-stephens" when the existing data X contains nonfinite values and you do not specify the NumBins name-value argument "equiprobable" when the existing data X contains nonfinite values and you specify the NumBins name-value argument "equal-width" when the existing data X contains finite values only and you specify the NumBins name-value argument "terrell-scott" otherwise
"equal-width"	Equal-width binning, where you must specify the number of bins using the NumBins name-value argument
"equiprobable"	Equiprobable binning, where you must specify the number of bins using the NumBins name-value argument
"dagostino-stephens" or "ds"	Equiprobable binning with ceil(2*m^(2/5)) bins, where m is the number of observations in the existing data
"freedman-diaconis" or "fd"	Equal-width binning, where each bin for variable k has a width of ceil(2*iqr(X(:,k))*m^(-1/3)) X is the existing data set. m is the number of observations in variable k (that is, in X(:,k)).
"scott"	Equal-width binning, where each bin for variable k has a width of ceil(3.5*std(X(:,k))*m^(-1/3)) X is the existing data set. m is the number of observations in variable k (that is, in X(:,k)).
"scott-multivariate"	Equal-width binning, where each bin for variable k has a width of 3.5*std(X(:,k))*m^(-1/(2+d)) X is the existing data set. m is the number of observations in variable k (that is, in X(:,k)). d is the number of variables in X.
"terrell-iqr"	Equal-width binning, where each bin for variable k has a width of 2.603*iqr(X(:,k))*m^(-1/3) X is the existing data set. m is the number of observations in variable k (that is, in X(:,k)).
"terrell-scott" or "ts"	Equal-width binning with ceil((2*m)^(1/3)) bins, where m is the number of observations in the existing data
"terrell-std"	Equal-width binning, where each bin for variable k has a width of 3.729*std(X(:,k))*m^(-1/3) X is the existing data set. m is the number of observations in variable k (that is, in X(:,k)).

Example: BinMethod="scott"

Data Types: char | string

NumBins — Number of bins to use for continuous variables

[] (default) | positive integer scalar | positive integer vector

Number of bins to use for continuous variables, specified as a positive integer scalar or vector.

• If NumBins is a scalar, then the function uses the same number of bins for each continuous variable.

• If NumBins is a vector, then the function uses NumBins(k) number of bins for continuous variable k.

Specify this value only when BinMethod is "equal-width" or "equiprobable".

Example: NumBins=[10 25 10 15]

Data Types: single | double

VariableNames — Variable names

string array | cell array of character vectors

Variable names, specified as a string array or a cell array of character vectors. You can specify VariableNames to choose which variables to use in table X. That is, synthesizeTabularData uses only the variables in VariableNames to generate synthetic data.

• X must be a table, and VariableNames must be a subset of X.Properties.VariableNames.

• By default, VariableNames contains the names of all variables.

Example: VariableNames=["SepalLength","SepalWidth","PetalLength","PetalWidth"]

Data Types: string | cell

CategoricalVariables — List of categorical variables

positive integer vector | logical vector | string array | cell array of character vectors | "all"

List of the categorical variables, specified as one of the values in this table.

Value	Description
Positive integer vector	Each entry in the vector is an index value indicating that the corresponding variable is categorical. The index values are between 1 and v, where v is the number of variables listed in VariableNames.
Logical vector	A true entry means that the corresponding variable is categorical. The length of the vector is v.
String array or cell array of character vectors	Each element in the array is the name of a categorical variable. The names must match the entries in VariableNames.
"all"	All variables are categorical.

By default, if the variables are in a numeric matrix, the software assumes all the variables are continuous. If the variables are in a table, the software assumes they are categorical if they are logical vectors, categorical vectors, character arrays, string arrays, or cell arrays of character vectors. To identify any other variables as categorical, specify them by using the CategoricalVariables name-value argument.

Do not specify discrete numeric variables as categorical variables. Use the DiscreteNumericVariables name-value argument instead.

Example: CategoricalVariables="all"

Data Types: single | double | logical | string | cell

DiscreteNumericVariables — List of discrete numeric variables

[] (default) | positive integer vector | logical vector | string array | cell array of character vectors | "all"

List of the discrete numeric variables, specified as one of the values in this table.

Value	Description
Positive integer vector	Each entry in the vector is an index value indicating that the corresponding variable is a discrete numeric variable. The index values are between 1 and v, where v is the number of variables listed in VariableNames.
Logical vector	A true entry means that the corresponding variable is a discrete numeric variable. The length of the vector is v.
String array or cell array of character vectors	Each element in the array is the name of a discrete numeric variable. The names must match the entries in VariableNames.
"all"	All variables are discrete numeric variables.

You cannot specify categorical variables as discrete numeric variables.

Example: DiscreteNumericVariables=[2 5]

Data Types: single | double | logical | string | cell

Options — Options for computing in parallel and setting random streams

structure

Options for computing in parallel and setting random streams, specified as a structure. Create the Options structure using statset. This table lists the option fields and their values.

Field Name	Value	Default
UseParallel	Set this value to true to run computations in parallel.	false
UseSubstreams	Set this value to true to run computations in a reproducible manner. To compute reproducibly, set Streams to a type that allows substreams: "mlfg6331_64" or "mrg32k3a".	false
Streams	Specify this value as a RandStream object or cell array of such objects. Use a single object except when the UseParallel value is true and the UseSubstreams value is false. In that case, use a cell array that has the same size as the parallel pool.	If you do not specify Streams, then synthesizeTabularData uses the default stream or streams.

Note

You need Parallel Computing Toolbox™ to run computations in parallel.

Example: Options=statset(UseParallel=true,UseSubstreams=true,Streams=RandStream("mlfg6331_64"))

Data Types: struct

Output Arguments

syntheticX — Synthetic data set

numeric matrix | table

Synthetic data set, returned as a numeric matrix or a table. syntheticX and X have the same data type.

Algorithms

Estimate Multivariate Data Distribution by Binning

The synthesizeTabularData function estimates the distribution of the multivariate data set X by performing these steps:

1. Bin each continuous variable using equiprobable or equal-width binning, as specified by the BinMethod and NumBins name-value arguments.

2. Encode the continuous variables using the bin indices.

3. One-hot encode all binned and discrete variables.

4. Compute the probability of each unique row in the encoded data set.

The synthesizeTabularData function uses the computed probabilities to generate synthetic data.

Generate Synthetic Data

The process for estimating the multivariate data distribution includes computing the probability of each unique row in the one-hot encoded data set (after binning continuous variables). The synthesizeTabularData function uses this estimated multivariate data distribution to generate synthetic observations. The function performs these steps:

1. Use the previously computed probabilities to sample with replacement n rows from the unique rows in the encoded data set.

2. Decode the sampled data to obtain the bin indices (for continuous variables) and categories (for discrete variables).

3. For the binned variables, uniformly sample from within the bin edges to obtain continuous values. If you use equiprobable binning (BinMethod) and the extreme bin widths are greater than 1.5 times the median of the nonextreme bin widths, then the function samples from the cumulative distribution function (cdf) in the extreme bins.

Alternative Functionality

Instead of calling the synthesizeTabularData function to generate synthetic data directly, you can first create a binningTabularSynthesizer object using an existing data set, and then call the synthesizeTabularData object function to synthesize data using the object. By creating an object, you can easily generate synthetic data multiple times without having to relearn characteristics of the existing data set.

Extended Capabilities

Automatic Parallel Support

Accelerate code by automatically running computation in parallel using Parallel Computing Toolbox™.

To run in parallel, specify the Options name-value argument in the call to this function and set the UseParallel field of the options structure to true using statset:

Options=statset(UseParallel=true)

For more information about parallel computing, see Run MATLAB Functions with Automatic Parallel Support (Parallel Computing Toolbox).

Version History

Introduced in R2024b